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====== 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

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