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benchmarks:sum_trig_exp_root [2018/04/07 03:37]
pier4r
benchmarks:sum_trig_exp_root [2018/04/07 03:39] (current)
pier4r
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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 calculator apps =====
 +<​file>​
 +[i]max = 100000[/i]
 +~ 7.9s - Free42 iphone SE and 6s  http://​www.hpmuseum.org/​forum/​thread-9750-post-94029.html#​pid94029
 +</​file>​
 +
 +===== Physical calculators =====
 +
 +<​file>​
 +[i]max = 100000[/i]
 +~ 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 - HW-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 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
 +~ 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
 +~ 84s - numworks 2017.12 python
 +~ 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
 +~ 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
 +
 +[i]max = 10000[/i]
 +~ 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 - HW-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
 +~ 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
 +~ 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 - HW-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
 +~ 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
 +~ 260s - hp 50g, sysRPL
 +~ 309s - hp 50g, userRPL
 +~ 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
 +~ 541s - hp 48gx, userRPL
 +~ 554s - hp 48gx, sum function
 +~ 986s - Ti 92, sum function
 +~ 1105s - casio fx 9750g, sum function
 +~ 1184s - DM11L (48 mhz), RPN
 +~ 1185s - Ti 82, ti basic
 +~ 1246s - hp28s, userRPL
 +~ 1501s - casio fx880p, casio basic
 +
 +[i]max = 1000[/i]
 +~ 0.223s - HW-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 2s - HW-Prime , Home, sum function. last os as 2017.12
 +~ 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
 +~ 8.2s - Hp 50g newRPL 2017.12 FOR loop., 32 digits precision 1395.346287743423 (I assume the result returned truncated on the stack)
 +~ 12.582s - HW-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
 +~ 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)
 +~ 24.5 - CASIO Prizm fx-CG10, sum function
 +~ 25.5s - Hp 50g, 2.15, exact mode sum function
 +~ 26.5s - hp 50g, sysRPL
 +~ 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
 +~ 38s - sharp el-9950 , 1395.346288
 +~ 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.
 +~ 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
 +~ 54s - hp 48gx, userRPL
 +~ 55s - hp 48gx, sum function
 +~ 55s - 48G+ , sum function with speed ui
 +~ 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
 +~ 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
 +~ 108s - casio fx991 version , 1395.346288 (the fast batch reported by some users) sum function
 +~ 121s - Ti 82, ti basic
 +~ 125s - DM11L (48 mhz), RPN
 +~ 130s - hp28s, userRPL
 +~ 131s - casio fx991 version , 1395.346288 (the slow batch reported by some users) sum function
 +~ 133s - 136s - DM15L , 48 mhz (interesting the difference with the 41L), 1395.346288
 +~ 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).
 +~ 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
 +~ 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
 +~ 404.93s - DM41L 48 mhz , RPN program
 +~ 502.2s - Sharp 516X sum function
 +~ 525s  - Casio fx-115ES Plus: 1395.346288 sum function
 +~ 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
 +
 +[i]max = 100[/i]
 +~ 0.036s - HW-Prime , Home, Teval(), HP PPL. last os as 2017.12
 +~ 0.2s - HW-Prime , Home, sum function. last os as 2017.12
 +~ 0.28s - DM42 on USB, RPN
 +~ 0.6s - DM42 on batteries, RPN
 +~ 2.5s - casio fx 9860gII, sum function
 +~ 2.7s - hp 50g, sum function
 +~ 2.8s - hp 50g, sysRPL
 +~ 3.3s - hp 50g, userRPL
 +~ 4s - ti 89, approx mode, sum function.
 +~ 5s - Ti 92 plus, sum function
 +~ 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
 +~ 10s - Ti 92, sum function
 +~ 11s - casio fx 9750g, sum function
 +~ 11s - Sharp PC-G850VS Basic, 139.2971873
 +~ 13s - Ti 82, ti basic
 +~ 14s - DM11L (48 mhz), RPN
 +~ 14s - dm15L 48 mhz, RPN, 139.2971874
 +~ 14s - casio fx991 version , 1395.346288 (the slow batch reported by other users) sum function
 +~ 14s - hp28s, userRPL ​
 +~ 15s - HP-41CL / x50 speed: 100 iterations (139.2926) RPN 
 +~ 16s - casio fx880p, casio basic
 +~ 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
 +~ 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
 +~ 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
 +~ 42.23s - DM41L 48 mhz , RPN program
 +~ 63s - dm15L 12mhz , RPN, 139.2971874
 +~ 65s - Casio fx-991ES PLUS sum function
 +~ 91s - Sharp PC-1401 Basic, 139.2971873
 +~ 91s - Olivetti M10, basic
 +~ 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
 +~ 313- 320s - hp15C , RPN ,  139.2971874
 +~ 329s - hp-65 N=100, Result= 139.2971873
 +~ 340s - HP-67. RPN (139.2925695)
 +~ 434s - HP 55 , RPN program 139.2971873
 +
 +[i]max = 10[/i]
 +~ 1< seconds - Hp 50g, 2.15, RPN mode 13.7118350167 (approx mode)
 +~ 2s - Epson Hx-20 . max 7 digits precision. 13.7118
 +~ 2s - Epson Hx-20 . max 16 digits precision. 13.71183562278748
 +~ 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
 +~ 6s - dm15C 12mhz , RPN, 13.71183502
 +~ 9s - Sharp PC-1401 Basic, 13.71183501
 +~ 9.5s - Olivetti M10, basic
 +~ 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
 +~ 29s - HP-25C (Woodstock):​ N=10, Result=13.71183501
 +~ 32s - hp15C , RPN, 13.71183502
 +~ 32s - hp-65, Time= 32 sec, Result= 13.71183501
 +~ 35s - HP-29C (Woodstock) N=10, Result=13.71183501
 +~ 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 .
 +~ 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>​
benchmarks/sum_trig_exp_root.txt · Last modified: 2018/04/07 03:39 by pier4r