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benchmarks:sum_trig_exp_root [2018/01/29 12:38]
pier4r
benchmarks:sum_trig_exp_root [2024/03/06 11:01] (current)
pier4r
Line 1: Line 1:
 +====== Calculator Benchmark: simple summation test that involves common trigonometric, exp/log and power/roots operations ======
  
 +Original: http://www.hpmuseum.org/forum/thread-9750.html . \\
 +The results are ported here to have versioning of the entries, without deleting them by mistake.
 +
 +**The idea** \\
 +The summation based test will be very similar to the [[benchmarks:savage|savage benchmark]] and I wonder how many similar tests were developed on various forum or groups regarding calculators.
 +
 +Anyway, inspired by the test done in the thread of [[http://www.hpmuseum.org/forum/thread-5047.html|Eddie linked in the 1st post]], I decided to pick randomly some scientific functions to assemble a summation that may give an idea of the performances of a calculator for common math functions.
 +
 +The idea is to have a loop working on an increment of the 'x' value that is somewhat independent from the step before (while the savage test uses the value picked from the step before) . Furthermore while the idea of using a function and its inverse is pretty neat (see savage benchmark), some calculators may be very carefully coded figuring this out and therefore simplifying the expression.
 +
 +I am not that interested in the accuracy, as it is well analyzed in many other posts using other examples (especially by Dieter, that for me will always be the ULPs man).
 +
 +Surely speed without accuracy is not that neat and so one could go on and build a metric that weights accuracy and speed, as done by a recent HHC (about egyptian fractions), anyway I will collect only timings.
 +
 +Timings will be collected here, and then moved on the wiki4hp if there are enough of them.
 +
 +People are encouraged to post timings and results.
 +
 +So to recap the idea of this test is there because:
 +
 +  * with a summation with increasing x (not dependent on the previous computed value) also some advanced scientific calculators can be tested. See casio fx991EX.
 +  * it is easier to type in and execute. It does not take much time (well unless one is forced to write a program to optimize some parts).
 +  * it may be used with a metric that combines speed and accuracy (a problem would be to get the right accuracy for the problem).
 +  * it avoids to use a function and its inverse to skip very careful optimizations done by the parser. (especially systems with CAS may use this)
 +
 +**The summation test** \\
 +\[ \sum_{x=1}^{1000} \sqrt[3]{e^{ sin \left (tan^{-1}(x)  \right ) }} \]
 +
 +**How to report the results** \\
 +reply here: http://www.hpmuseum.org/forum/thread-9750.html
 +
 +
 +===== Mobile devices with programming apps having math libraries =====
 +<file>
 +[i]max = 1'000'000[/i]
 +~ 5.22s - Nintendo New 2DS XL (2017) with SmileBasic A=1395612.15872538 post #159
 +
 +[i]max = 100'000[/i]
 +~ 0.52s  - Nintendo New 2DS XL (2017) with SmileBasic A=139560.97614105 post #159
 +</file>
 +
 +===== Mobile devices with calculator apps =====
 +<file>
 +[i]max = 1'000'000[/i]
 +~ 0.189s - ThetaCalc on iPhone 12 Sum=1395612.1587253837 p#227
 +~ 9s - iPhone 12 DB48X v0.7.1 32-bit IEEE-754 p#248
 +~ 9s - iPhone 12 DB48X v0.7.1 32-bit IEEE-754 p#248
 +
 +[i]max = 100'000[/i]
 +~ 7.9s  - Free42 iphone SE and 6s  http://www.hpmuseum.org/forum/thread-9750-post-94029.html#pid94029
 +~ 17.3s - Emu48 HP50 on Samsung S20 userRPL p#216
 +~ 32s   - Emu48 HP50 on Samsung S9+ userRPL p#213
 +
 +[i]max = 10'000[/i]
 +~ 3.2925s - Emu48 using flat HP50 on Samsung S9+ userRPL 13955.8578444 p#212
 +~ 3.29s   - Emu48 HP50 on Samsung S9+ userRPL p#213
 +
 +[i]max = 1000[/i]
 +~ 0.3s Emu48 HP50 on Samsung S9+ userRPL p#213
 +</file>
 +
 +===== Results physical calculators =====
 +<file>
 +[i]max = 10'000'000[/i]
 +~ 84.1s - HP Prime G2 V.14603 Python p#239
 +~ 103.724s - Prime using python p#238
 +
 +[i]max = 1'000'000[/i]
 +~ 8.4s - HP Prime G2 V.14603 Python p#239
 +~ 10.381s - Prime using python p#238
 +~ 14.046s - Prime G2 Beta 2.1.14549 using Python 1395612.158725383 p#221
 +~ 605s - DM42 DB48X v0.7.1 32-bit IEEE-754 p#248
 +~ 806s - DM42 DB48X v0.7.1 32-bit IEEE-754 p#248
 +~ 1748s - DM32 DB48X v0.7.1 32-bit IEEE-754 p#248
 +~ 2188s - DM32 DB48X v0.7.1 64-bit IEEE-754 p#248
 +
 +[i]max = 500'000[/i]
 +~ 3.5s  - Prime G2 summation built in post #178 (this seems suspicious though, maybe simplifications happening?)
 +~ 8s    - Prime A summation built in post #178 (this seems suspicious though, maybe simplifications happening?)
 +~ 1125s - TI-30X Pro MathPrint summation built-in  post #178
 +~ 6300s - TI 36X Pro summation built-in  post #178
 +
 +[i]max = 100'000[/i]
 +~ 0.84s - HP Prime G2 V.14603 Python p#239
 +~ 1.038s - Prime using python p#238
 +~ 1.425s - Prime G2 Beta 2.1.14549 using Python 139560.9761410521 p#221
 +~ 7.7s  - HG-Prime G2 , sum function http://www.hpmuseum.org/forum/thread-9750-post-102818.html#pid102818
 +~ 9s    - TI Nspire CX CAS, hardware version N-0118AB (2018), OS 4.5.0.1180 (2017): C with Ndless. Post #147
 +~ 9.5s  - TI Nspire CX II CAS 13955.8579044; Sum function; original f(x); HW Rev. M-0119AF; OS 5.1.0.177 p#185
 +~ 12s   - TI Nspire CX CAS, hardware version P-0411A (2011), OS 4.5.0.1180 (2017): 139560,97614105 . C with Ndless. Post #143
 +~ 17.7s - casio fx 9860GII power graphic 2 SHA4 overclock 236 +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 19.2s - HP-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 19.5s - TI nspire CX II CAS M-0720AK (2020), OS 5.2.0.771 (2020) micropython 139560.9761410522 p#205
 +~ 20.5s - casio fx cg50 SH4A 192MHz ptune C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.97614105
 +~ 23s   - HP 50g HPGCC 2.0 - 75 Mhz -  139560.8013952589
 +~ 29.9s - casio fx cg20 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 36s   - casio fx cg50 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 47s   - TI Nspire CX CAS, hardware version P-0411A (2011), OS 4.5.0.1180 (2017): Lua max= 100000: 47.1s - 139560,97614105 . Post #143
 +~ 51.5s - TI Nspire CX II CAS:  139560.976284; Sum function and CAS simplified f(x) - f(x) = e^(x/(3*sqrt(x^2+1))) p#185
 +~ 54.5s - TI Nspire CX II CAS 139560.976284; Sum function and ^1/3 power instead of cube root p#185
 +~ 52s   - casio fx 9860GII SH3 overclock 118MHz +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 53s   - casio fx-cg50 micropython 139560.9761410521 http://www.hpmuseum.org/forum/thread-9750-post-103457.html#pid103457
 +~ 57s   - casio fx-cg50 micropython 139560.9761410521 http://www.hpmuseum.org/forum/thread-9750-post-103448.html#pid103448
 +~ 65s   - numworks 139560.97614110521 micropython http://www.hpmuseum.org/forum/thread-9750-post-103445.html#pid103445
 +~ 84s   - numworks 2017.12 micropython
 +~ 94s   - TI Nspire CX II CAS 139560.976284; Sum function and cube root; HW Rev. M-0119AF; OS 5.1.0.177 p#185
 +~ 95s   - TI nspire CX II CAS M-0720AK (2020), OS 5.2.0.771 (2020) Sum function, approx. mode 139561 p#205
 +~ 117s - casio fx 9860GII power graphic 2 SHA4 normal 29Mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 147s - casio fx 9860GII SH3 normal 29 mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,100000) - 139560.976141052
 +~ 176s - HP 39gii Program with For loop p#188
 +~ 195s - Nspire CX sum function approx mode.
 +~ 222s - nspire CX CAS, sum function, approx mode.
 +~ 261s - DM42 on USB, RPN
 +~ 323s - 9750gII upgraded to 9860gII OS {sum:eqn,x,1, 100000} gives me 139560.9761 CPU frequency sitting at 235 MHz (F5 in FTune)
 +~ 653s - DM42 on batteries, RPN
 +~ 2009s - 9750gII upgraded to 9860gII OS {sum:eqn,x,1, 100000} gives me 139560.9761
 +~ 7080s - casio fx-570EX, 139560.9761 sum function p#206 p#207
 +
 +[i]max = 10'000[/i]
 +~ 0.101s - Prime using python p#238
 +~ 0.159s - Prime G2 Beta 2.1.14549 using Python 13955.857904429155 p#221
 +~ 0.74s - HP-Prime G2 , sum function http://www.hpmuseum.org/forum/thread-9750-post-103311.html#pid103311
 +~ 0.74s - Prime G2 HPPL p#209
 +~ 0.93s - Prime G2 HPPL p#209
 +~ 1.8s   - casio fx 9860GII power graphic 2 SHA4 overclock 236 +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 2.072s - HP-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 2s     - HP 50g HPGCC 2.0 - 75 Mhz - 13955.85790429154
 +~ 2.1s - casio fx cg50 SH4A 192MHz ptune C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 3.1s - casio fx cg20 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 3.8s - casio fx cg50 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 5.3s - casio fx 9860GII SH3 overclock 118MHz +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 8s - numworks 2017.12 python
 +~ 11.9s - casio fx 9860GII power graphic 2 SHA4 normal 29Mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 12.5s   - USB db48x for the dm42 https://www.hpmuseum.org/forum/thread-20157-post-174581.html#pid174581
 +~ 14.9s - casio fx 9860GII SH3 normal 29 mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^-1 X,X,1,10000) - 13955.8579042916
 +~ 16s - numworks 2017.12 sum function
 +~ 18s - HP 39gii Program with For loop p#188
 +~ 19s - nspire CX, sum function approx mode
 +~ 22.5s - nspire CX CAS, sum function, approx mode.
 +~ 20 sec - ti nspire handheld (2006). sum function. Degrees, float 12, approx. 13955.8579044 . OS 3.9.0.463
 +~ 23.9s - HP-Prime , Home, sum function. last os as 2017.12
 +~ 26s - DM42 on USB, RPN
 +~ 32s - 9750gII upgraded to 9860gII OS {sum:eqn,x,1,10000} gives me 13955.8579 CPU frequency sitting at 235 MHz (F5 in FTune)
 +~ 56,51s - Hp 50g newRPL 2017.12 FOR loop., 12 digits precision
 +~ 65.73s - DM42 on batteries, RPN
 +~ 97s - HP Xpander built in function 13955.8579043 p#210
 +~ 184s - fx9860GIII , micropython result has reduced precision p#199
 +~ 199s - 9750gII upgraded to 9860gII OS {sum:eqn,x,1,10000} gives me 13955.8579
 +~ 233s - casio fx 9860gII, sum function
 +~ 242s - hp 50g, sum function . It uses CAS to simplify the expression! See post #144.
 +~ 257s - HP-200LX turbo c 2.01, 13955.857904 p#236
 +~ 260s - hp 50g, sysRPL
 +~ 309s - hp 50g, userRPL
 +~ 330s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off,  post#165 13955.8579042908
 +~ 376s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on,  post#165 13955.8579042908
 +~ 402.91s - TI 84 Plus CE 
 +~ 453s - Ti 92 plus, sum function
 +~ 465s - ti 89, approx mode, sum function.
 +~ 468s - 41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 13955.84859
 +~ 472s - ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sigma((e^(...))^(1/3), x, 1, 1000)) where 'sigma' is the greek letter . 13955.8579044
 +~ 487.3s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 13955.8578444 p#185
 +~ 487.3s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 13955.8578444 p#185
 +~ 505.4s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 13955.8578444 p#185
 +~ 534.7s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 13955.8578444 p#185
 +~ 541s - hp 48gx, userRPL
 +~ 554s - hp 48gx, sum function
 +~ 986s - Ti 92, sum function
 +~ 1073s - casio fx-570EX, 13955.8579 sum function p#206 p#207
 +~ 1105s - casio fx 9750g, sum function
 +~ 1184s - DM11L (48 mhz), RPN
 +~ 1185s - Ti 82, ti basic
 +~ 1246s - hp28s, userRPL
 +~ 1501s - casio fx880p, casio basic
 +~ 1650s - fx9860GIII , Casio Basic p#199
 +
 +[i]max = 1000[/i]
 +~ 0.036s - Prime G2 Beta 2.1.14549 using Python 1395.3462877433426 p#221
 +~ 0.223s - HP-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 0.4s - DM42 DB48X v0.6.4 32-bit IEEE-754 p#248
 +~ 0.7s - DM42 DB48X v0.6.4 32-bit IEEE-754 p#248
 +~ 1.4s - DM32 DB48X v0.6.4 32-bit IEEE-754 p#248
 +~ 1.7s - DM32 DB48X v0.6.4 64-bit IEEE-754 p#248
 +~ 2s - HP-Prime , Home, sum function. last os as 2017.12
 +~ 2s - HP 39gii Built-in sum function (sum function can only do max. 1000) p#188
 +~ 2.5s - nspire CX CAS, sum function, approx mode.
 +~ 2.6s - DM42 on USB, RPN
 +~ 4s - casio fx-9750gII (upgraded with 9860gII OS 2.04) and overclocked to max speed with FTune (likely a ~ 5x overclock) sum function
 +~ 6.022s - Hp 50g newRPL 2017.12 FOR loop., 12 digits precision
 +~ 6.5s - Casio fx-CP400 (classpad 400) , 1395.346288 sum function
 +~ 6.64s - DM42 on batteries, RPN
 +~ 7s - fx9860GIII with OS version 3.70.0200 mycropython p#245
 +~ 8.2s - Hp 50g newRPL 2017.12 FOR loop., 32 digits precision 1395.346287743423 (I assume the result returned truncated on the stack)
 +~ 12s - HP Xpander built in function 1395.34628774 p#210
 +~ 12.582s - HP-Prime , CAS, approx mode. last os as 2017.12
 +~ 13.5s - Casio fx-CG50 (primz), 1395.346288 sum function
 +~ 18s - Casio ClassPad 330-A, 1395.346288 (ClassPad is labeled on the back side as CLASSPAD300PLS, the 330-A is written on the box) sum function
 +~ 18s - fx9860GIII , micropython result has reduced precision p#199
 +~ 20s - Casio fx-7400GII , 1395.346288  sum function
 +~ 22s - casio fx-9750gII (upgraded with 9860gII OS 2.04), 1395.346288 sum function
 +~ 23s - casio fx 9860gII, sum function
 +~ 23s - Casio fx-9860G Slim (hacked to 9860GII OS 2.04), 1395.346288 sum function
 +~ 24.5s - Hp 50g, 2.15, RPN mode, DEG, sum function . 1395.3462877 (approx mode). It uses CAS to simplify the expression! See post #144.
 +~ 24.5 - CASIO Prizm fx-CG10, sum function
 +~ 25.5s - Hp 50g, 2.15, exact mode sum function. It uses CAS to simplify the expression! See post #144.
 +~ 25.5s - Hp50g RPN; Sum function; Std number format; ~Num key; 1395.3462877 p#185
 +~ 26.5s - hp 50g, sysRPL
 +~ 27s - HP-200LX turbo c 2.01, 1395.346288 p#236
 +~ 29.4s - Hp 50g newRPL 2017.12 FOR loop., 128 digits precision
 +~ 29s - HP15C LE
 +~ 33.8s - Hp 50g, 2.15, RPN mode, DEG (quick userRPL FOR loop, using, instead of XROOT, the 1/3 power. Surprisingly slower than the summation) . 1395.3462877 (approx mode)
 +~ 34s - HP-40gs sum function, 1395.3462877
 +~ 34.8s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off,  post#165 1395.34628774339
 +~ 38s - sharp el-9950 , 1395.346288
 +~ 39.7s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on,  post#165 1395.34628774339
 +~ 41.5s - TI 84 plus CE
 +~ 45s - Ti 92 plus, sum function
 +~ 46s - ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sigma((e^(...))^(1/3), x, 1, 1000)) where 'sigma' is the greek letterl . 1395.34628774
 +~ 46s - ti 89, approx mode, sum function.
 +~ 47.8s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 1395.3462877 p#195
 +~ 47.8s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 1395.3462877 p#195
 +~ 48s - ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sum(seq((e^(...))^(1/3), x, 1, 1000))) . 1395.34628774
 +~ 48s - 41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 1395.346260
 +~ 51.0s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 1395.3462877 p#195
 +~ 53.9s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 1395.3462877 p#195
 +~ 54s - hp 48gx, userRPL
 +~ 55s - hp 48gx, sum function
 +~ 55s - 48G+ , sum function with speed ui
 +~ 57s - TI Voyage 200 Sum function; 12 digits; "Approx ="; 1395.34628774 p#185
 +~ 57s - Casio fx-991CW , 1395.346288 p#237
 +~ 59s - casio fx-570CW, 1395.346288 (sum function) p#235
 +~ 62s - ti 89 OS 2.09. (exact mode plus likely with pretty print)
 +~ 64s - sharp el-w506x (abusing the integral function).
 +~ 76s - Casio fx-9700GE , 1395.34628774 sum function
 +~ 95.5s - HP 48SX http://www.hpmuseum.org/forum/thread-9750-post-103329.html#pid103329
 +~ 97s - sharp el-506x (abusing the integral function).
 +~ 99s - Ti 92, sum function
 +~ 99.5s - casio fx-9750g+ sum function
 +~ 102s - Sharp PC-G850VS Basic, 1395.346559
 +~ 103s - casio fx 9750g, sum function
 +~ 104s - TI-30X Pro MathPrint 1395.346288 post #156
 +~ 104s - TI-30X Pro MathPrint (Europe) 1395.346288 post #237 (confirmed!)
 +~ 105s - TI-83plus (ver.1.16) internal result=1395.346287744 post #161
 +~ 108s - casio fx991 version , 1395.346288 (the fast batch reported by some users) sum function
 +~ 109s - casio fx-570EX, 1395.346288 sum function p#206 p#207
 +~ 115s - TI-82 - 0497 Date Code Result=1395.346288 p#211
 +~ 120s - DM10L (48 mhz), RPN post#170
 +~ 120s - HP-27S 1395.3462877 BENCH=Σ(X:1:1000:1:EXP(SIN(ATAN(X)))^.333333333333)
 +~ 121s - Ti 82, ti basic
 +~ 123s - HP-28S userRPL p#213
 +~ 125s - DM11L (48 mhz), RPN
 +~ 130s - hp28s, userRPL
 +~ 131s - casio fx991 version , 1395.346288 (the slow batch reported by some users) sum function
 +~ 131s - TI-85 (ver.9.0) internal result=1395.346287744 post #161
 +~ 133s - 136s - DM15L , 48 mhz (interesting the difference with the 41L), 1395.346288
 +~ 135s - Casio fx-991EX , sum built in, 1395.3463 post #180
 +~ 136s - TI-85 nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774 p#185
 +~ 138s - TI-86 nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774 p#185
 +~ 145s - Sharp el-5250 (program with Lbl-conditional-Goto) p#188
 +~ 148s - HP 75D http://www.hpmuseum.org/forum/thread-9750-post-88453.html#pid88453
 +~ 153s - casio fx880p, casio basic. Another run 158s (see post #76).
 +~ 163s - Casio fx-92+ Spéciale Collège 1395,346288 http://www.hpmuseum.org/forum/thread-9750-post-103296.html#pid103296
 +~ 164s - fx9860GIII , Casio Basic p#199
 +~ 166s - Casio fx-5800P, 1395.346288 sum function
 +~ 168s - WP 34S double off, fix 2, sum function
 +~ 173s - Epson Hx-20 . max 7 digits precision. 1395.36
 +~ 173s - Epson Hx-20 . max 16 digits precision. 1395.346369147301
 +~ 171-178s - HP 71B http://www.hpmuseum.org/forum/thread-9750-post-88453.html#pid88453 - http://www.hpmuseum.org/forum/thread-9750-post-90635.html#pid90635
 +~ 185s - WP 34S double on, fix 2, sum function
 +~ 200s - casio fx8500g, sum function
 +~ 206s - HP 32s RPN 1395.34628770 http://www.hpmuseum.org/forum/thread-9750-post-89004.html#pid89004
 +~ 209s - HP 33s RPN http://www.hpmuseum.org/forum/thread-9828-post-87566.html#pid87566
 +~ 218s - Ti 80, ti basic
 +~ 220s - fx9860GIII , built in sum p#199 
 +~ 241s - HP 32sII RPN 1395.34628770
 +~ 245s - TI 36x Pro sum function
 +~ 253s - Hp 35s http://www.hpmuseum.org/forum/thread-9828-post-87766.html#pid87766
 +~ 256s - wp34s (DSE-based loop, DBLOFF), 1395.346287743423
 +~ 285s - wp34s (DSE-based loop, DBLON), 1395.346287743423256291575365067091
 +~ 287s - Hp35s, RPN program
 +~ 291s - HP 42s , RPN program
 +~ 298s - sharp el-506w (abusing the integral function. Not really returning the wanted result from the summation).
 +~ 303s - wp34s (S command, DBLOFF), 1395.346287743423
 +~ 332s - wp34s (S command, DBLON), 1395.346287743423256291575365067093
 +~ 338s - casio  fx-4000P 1395.346288 http://www.hpmuseum.org/forum/thread-9750-post-102725.html#pid102725
 +~ 375s - HP9821A, algebraic post#177
 +~ 390s - HP9821A, algebraic, 1395.346288 post#173
 +~ 404.93s - DM41L 48 mhz , RPN program
 +~ 502.2s - Sharp 516X sum function
 +~ 525s  - Casio fx-115ES Plus: 1395.346288 sum function
 +~ 573s - fx-3600pv degrees 1395.3462707 p#203
 +~ 574s - fx-3600pv radians 1395.3462707 p#203
 +~ 581s - casio fx-570CW, 13955.8579 (sum function) p#235
 +~ 633s - Casio fx-3650pII , 1395.346288 for next
 +~ 633s - Casio fx-50F PLUS , 1395.346288 for next
 +~ 840-890s - Canon X Mark I Pro, 1395.346288, sum function
 +~ 1814s - Casio fx-50F degrees 1395.34628605 p#198
 +~ 1828s - Casio fx-50F radians 1395.34628605 p#198
 +~ 2844s - Sharp PC-1201 p#228
 +
 +[i]max = 100[/i]
 +~ 0.036s - HP-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 0.2s - HP-Prime , Home, sum function. last os as 2017.12
 +~ 0.28s - DM42 on USB, RPN
 +~ 0.6s - DM42 on batteries, RPN
 +~ 2s - fx9860GIII , micropython result has reduced precision p#199
 +~ 2.5s - casio fx 9860gII, sum function
 +~ 2.7s - hp 50g, sum function. It uses CAS to simplify the expression! See post #144.
 +~ 2.8s - hp 50g, sysRPL
 +~ 3.3s - hp 50g, userRPL
 +~ 3.77s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off,  post#165 139.297187045924
 +~ 3.85s - DM41X FOCAL stack, USB connected p#201
 +~ 4s - ti 89, approx mode, sum function.
 +~ 4s - HP-200LX turbo c 2.01, 139.297187 p#236
 +~ 4.3s - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on,  post#165 139.297187045924
 +~ 4.61s - DM41X FOCAL fast mode, USB connected: result=139.2971873 p#200
 +~ 5s - Ti 92 plus, sum function
 +~ 5.5s - HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144) - 139.297187047 p#195
 +~ 5.5s - HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144) - 139.297187047 p#195
 +~ 5.5s - HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT - 139.297187047 p#195
 +~ 5.7s - HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT - 139.297187047 p#195
 +~ 5.13s - 41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 139.297187
 +~ 5.5s - hp 48gx, userRPL
 +~ 5.9s - hp 48gx, sum function
 +~ 6s - 48G+ , sum function with speed ui
 +~ 7s - casio fx-570CW, 139.297187 (sum function) p#235
 +~ 10s - Ti 92, sum function
 +~ 11s - casio fx 9750g, sum function
 +~ 11s - Sharp PC-G850VS Basic, 139.2971873
 +~ 11s - TI-30X Pro MathPrint 139.2971870 post #156
 +~ 11s - casio fx991 version , 139.2971870 (the fast batch reported by other users) sum function
 +~ 12s - DM41X FOCAL stack, battery p#201
 +~ 12s - casio fx-570EX, 139.297187 sum function p#206 p#207
 +~ 13s - Ti 82, ti basic
 +~ 13.2s - HP-28S userRPL p#213
 +~ 14s - DM11L (48 mhz), RPN
 +~ 14s - dm15L 48 mhz, RPN, 139.2971874
 +~ 14s - casio fx991 version , 139.2971870 (the slow batch reported by other users) sum function
 +~ 14s - hp28s, userRPL 
 +~ 14.33s - DM41X FOCAL fast mode, battery powered: result=139.2971873 p#200
 +~ 15s - HP-41CL / x50 speed: 100 iterations (139.2926) RPN 
 +~ 16s - casio fx880p, casio basic
 +~ 16s - fx9860GIII , Casio Basic p#199
 +~ 17s - Casio FX603P, casio basic
 +~ 18s - Epson Hx-20 . max 7 digits precision. 139.297
 +~ 18s - Epson Hx-20 . max 16 digits precision. 139.297193646431
 +~ 21s - casio fx8500g, sum function
 +~ 22s - sharp el-9300 http://www.hpmuseum.org/forum/thread-9750-post-89345.html#pid89345
 +~ 23s - HP 33s RPN http://www.hpmuseum.org/forum/thread-9828-post-87566.html#pid87566
 +~ 23s - HP 32s RPN 139.29718705 http://www.hpmuseum.org/forum/thread-9750-post-89004.html#pid89004
 +~ 23s - Ti 80, ti basic
 +~ 25s - TI 36x Pro
 +~ 25s - fx9860GIII , built in sum p#199
 +~ 26s - wp34s (DSE-based loop, DBLOFF), 139.2971870459241
 +~ 26s - HP 32sII RPN 139.29718705
 +~ 27s - wp34s (DSE-based loop, DBLON), 139.2971870459242385751150019615150
 +~ 27.5s - Hp 35s http://www.hpmuseum.org/forum/thread-9828-post-87766.html#pid87766
 +~ 30s - wp34s (S command, DBLOFF), 139.2971870459242
 +~ 31s - HP 42s , RPN program (confirmations: post #149  Result: 139.297187046 )
 +~ 31s - Hp35s, RPN program
 +~ 33.8s - Sharp 516X
 +~ 34s - wp34s (S command, DBLON), 139.2971870459242385751150019615149
 +~ 36s - Sharp EL-5120 Solver 139.297187 http://www.hpmuseum.org/forum/thread-9750-post-88303.html#pid88303
 +~ 37s - HP9821A, algebraic post#177
 +~ 38s - HP9821A, algebraic, 139.2971870 post#173
 +~ 42.23s - DM41L 48 mhz , RPN program
 +~ 43 - 44 s - Casio fx-720P 139.297187038 http://www.hpmuseum.org/forum/thread-9750-post-102799.html#pid102799 see also post #153 
 +~ 45s - CASIO PB 700 - BASIC  Result: 139.297187 post #153
 +~ 58.9s - fx-3600pv degrees 139.2971869 p#203
 +~ 63s - dm15L 12mhz , RPN, 139.2971874
 +~ 65s - Casio fx-991ES PLUS sum function
 +~ 66s - HP9100B , algebraic 139.2971870 - post #177
 +~ 83s -  TI-95 Procalc, program "assembled" 139.2971870460 p#189
 +~ 88s - Casio fx-4500p released 1989 program 139.297187  p#220
 +~ 91s - Sharp PC-1401 Basic, 139.2971873
 +~ 91s - Olivetti M10, basic
 +~ 91s - CASIO FX-602P - KEYSTROKE PROGRAM Result:139.2971873 post #149
 +~ 105s - TI-67 released 1992 sum func 139.297187 p#220
 +~ 146s - TI-67 released 1992 program 139.297187 p#220
 +~ 158s - hp 41CV (plain, fullnut, no turbo) , 139.2971874
 +~ 158s - Casio fx-2700P 139.29719 http://www.hpmuseum.org/forum/thread-9750-post-91994.html#pid91994
 +~ 182s - CASIO FX-502P - Keystroke program (DSZ loop) post #164 139.2971870
 +~ 187.1s - Casio fx-50F 139.297187029 p#198
 +~ 285s - Sharp PC-1201 p#228
 +~ 313 - 320s - hp15C , RPN ,  139.2971874
 +~ 316s - HP-11C - RPN PROGRAM  Result: 139.2971874 post #149
 +~ 316s - HP-10C - RPN PROGRAM  Result: 139.2971874 post #151
 +~ 329s - hp-65 N=100, Result= 139.2971873
 +~ 340s - HP-67. RPN (139.2925695)
 +~ 419s - TI-57 II - keystroke program (DSZ loop), 139.29719 p#197
 +~ 434s - HP 55 , RPN program 139.2971873
 +
 +[i]max = 10[/i]
 +~ 1< seconds - Hp 50g, 2.15, RPN mode 13.7118350167 (approx mode). It uses CAS to simplify the expression! See post #144.
 +~ 1s< - Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on (or off),  post#165 13.7118350167043
 +~ 1s - casio fx-570CW, 13.71183502 (sum function) p#235
 +~ 2s - Epson Hx-20 . max 7 digits precision. 13.7118
 +~ 2s - Epson Hx-20 . max 16 digits precision. 13.71183562278748
 +~ 2s - casio fx-570EX, 13.71183502 sum function p#206 p#207
 +~ 2s - HP-200LX turbo c 2.01, 13.711835 p#236
 +~ 3s - wp34s (DSE-based loop, DBLOFF), 13.71183501670439
 +~ 3s - wp34s (DSE-based loop, DBLON), 13.71183501670437880652763283584306
 +~ 3s - wp34s (S command, DBLOFF), 13.71183501670438
 +~ 3s - wp34s (S command, DBLON), 13.71183501670437880652763283584306
 +~ 3s - HP 32s RPN 13.71183502 http://www.hpmuseum.org/forum/thread-9750-post-89004.html#pid89004
 +~ 3s - HP 32sII RPN 13.71183502
 +~ 3.5s - HP 42S - RPN PROGRAM  Result: 13.7118350166 post#149
 +~ 4s - HP9821A, algebraic, post #177
 +~ 4s - HP9821A, algebraic,  13.71183502 post#173
 +~ 4s - Casio fx-720P 13.7118350167 http://www.hpmuseum.org/forum/thread-9750-post-102799.html#pid102799 see also post #153
 +~ 4.6s - CASIO PB 700 - BASIC  Result: 13.71183502 post #153
 +~ 6s - dm15C 12mhz , RPN, 13.71183502
 +~ 6s - fx-3600pv degrees 13.711835009 p#203
 +~ 6.5s - HP9100B , algebraic 13.71183502 - post #177
 +~ 9s - Sharp PC-1401 Basic, 13.71183501
 +~ 9.2s - CASIO FX-602P - KEYSTROKE PROGRAM Result:13.71183502 post #149
 +~ 9.5s - Olivetti M10, basic
 +~ 9s - Casio fx-4500p released 1989 program 13.71183502 p#220
 +~ 11s - TI-67 released 1992 sum func 13.71183502 p#220
 +~ 14s - TI-59 Result: 13.71183502 p#183
 +~ 15s - TI-67 released 1992 program 13.71183502 p#220
 +~ 16s - TI-58c Result: 13.71183502 p#183
 +~ 16s - hp 41CV (plain, fullnut, no turbo), 13.71183502
 +~ 16s - Casio fx-2700P 13.711835 http://www.hpmuseum.org/forum/thread-9750-post-91994.html#pid91994
 +~ 18.1s - CASIO FX-502P - Keystroke program (DSZ loop) post #164 13.71183501
 +~ 18.7s - Casio fx-50F 13.7118350165 p#198
 +~ 25s - Sharp PC-1201 p#228
 +~ 29s - HP-25C (Woodstock): N=10, Result=13.71183501
 +~ 31s - HP-11C - RPN PROGRAM  Result: 13.71183502 post #149
 +~ 31s - HP-10C - RPN PROGRAM  Result: 13.71183502 post #151
 +~ 32s - hp15C , RPN, 13.71183502
 +~ 32s - hp-65, Time= 32 sec, Result= 13.71183501
 +~ 33s - HP-97 - RPN PROGRAM Result: 13.71183502  post #149
 +~ 35s - HP-29C (Woodstock) N=10, Result=13.71183501
 +~ 39s - TI-57 II - keystroke program (DSZ loop), 13.711835 p#197
 +~ 43s - HP 55 , RPN program 13.71183501
 +~ 44s - HP-33C (Spice): N=10, Result=13.71183501 http://www.hpmuseum.org/forum/thread-9750-post-88370.html#pid88370
 +~ 46s - HP-34C (Spice): N=10, Result=13.71183501
 +~ 47s - sharp 506w (using X, formula memory F4 and M to sum) manually. 13.71183502 .
 +~ 51s - TI-57 Result: 13.711835 p#183
 +~ 56s - TI-53 "... at a rate of one iteration every 5.64 seconds. " http://www.hpmuseum.org/forum/thread-9750-post-87729.html#pid87729
 +~ 63.5s - TI-62, TI basic. 13.71183502
 +~ 99s - MK 54 , RPN program 13.711835
 +~ 100s - MK 61 , RPN program 13.711835
 +~ 110s - MK 56 , RPN program 13.711835
 +
 +</file>