# Calculator Benchmark: simple summation test that involves common trigonometric, exp/log and power/roots operations

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 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 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

## Mobile devices with programming apps having math libraries

[i]max = 1000000[/i]
~ 5.22s - Nintendo New 2DS XL (2017) with SmileBasic A=1395612.15872538 post #159

[i]max = 100000[/i]
~ 0.52s - Nintendo New 2DS XL (2017) with SmileBasic A=139560.97614105 post #159

## Mobile devices with calculator apps

[i]max = 100000[/i]
~ 7.9s - Free42 iphone SE and 6s  http://www.hpmuseum.org/forum/thread-9750-post-94029.html#pid94029

## Physical calculators

[i]max = 100000[/i]
~ 7.7s - HW-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
~ 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 - 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
~ 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
~ 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
~ 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]
~ 0.74s - HW-Prime G2 , sum function http://www.hpmuseum.org/forum/thread-9750-post-103311.html#pid103311
~ 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 . It uses CAS to simplify the expression! See post #144.
~ 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). 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.
~ 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
~ 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
~ 108s - casio fx991 version , 1395.346288 (the fast batch reported by some users) sum function
~ 120s - HP-27S 1395.3462877 BENCH=Σ(X:1:1000:1:EXP(SIN(ATAN(X)))^.333333333333)
~ 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).
~ 163s - Casio fx-92+ Spéciale Collège 1395,346288 http://www.hpmuseum.org/forum/thread-9750-post-103296.html#pid103296
~ 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
~ 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
~ 338s - casio  fx-4000P 1395.346288 http://www.hpmuseum.org/forum/thread-9750-post-102725.html#pid102725
~ 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. It uses CAS to simplify the expression! See post #144.
~ 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
~ 11s - TI-30X Pro MathPrint 139.2971870 post #156
~ 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 (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
~ 42.23s - DM41L 48 mhz , RPN program
~ 45s - CASIO PB 700 - BASIC  Result: 139.297187 post #153
~ 63s - dm15L 12mhz , RPN, 139.2971874
~ 65s - Casio fx-991ES PLUS sum function
~ 91s - Sharp PC-1401 Basic, 139.2971873
~ 91s - Olivetti M10, basic
~ 91s - CASIO FX-602P - KEYSTROKE PROGRAM Result:139.2971873 post #149
~ 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
~ 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)
~ 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.
~ 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
~ 3.5s - HP 42S - RPN PROGRAM  Result: 13.7118350166 post#149
~ 4.6s - CASIO PB 700 - BASIC  Result: 13.71183502 post #153
~ 6s - dm15C 12mhz , RPN, 13.71183502
~ 9s - Sharp PC-1401 Basic, 13.71183501
~ 9.2s - CASIO FX-602P - KEYSTROKE PROGRAM Result:13.71183502 post #149
~ 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
~ 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
~ 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