torture test: trigs

round #1: accuracy of tan(355/226)

this test is to compute the tangent of 355/226 (radians) which is very close to pi/2 and tan(pi/2) = infinity. the accuracy of this test depends on the accuracy of the tangent implementation and the number of internal significant figures used in the calculation.

correct answer, tan(355/226) = -7497258.18532558711290507183

calculator displayed result relative error
palm pilot (rom calculator ieee-754) -7497258.1916213 8.40x10-10
hp35 -7462586.567 4.61x10^-3
hp65 -7.518796992e6 2.87x10^-3
hp29c, hp32e, 15c, 41cx -7507225.705 1.33x10^-3
hp20s, 32sii -7497089.06508 2.26x10^-5
hp25 -7518796.992 2.87x10-3
hp 28c, hp48G -7497089.06508 2.26x10^-5
hp30s, hp9g -7497258.185 0
sumlock 322G scientist -7497239.623 2.48x10^-6
casio fx-10 E  
casio fx-19, fx-29 -13698630 way out
casio fx-101, fx-31, fx-39, fx-82, fx-120 -7518797 2.87x10^-3
casio fx-1 -7498465.796 1.61x10^-4
casio fx-201p -7507507.5 1.37x10^-3
casio fx-100, fx-3900pv, fx-451m -7501875.469 6.16x10^-4
casio fx-3500p, fx-180p -7501875.46 6.16x10^-4
casio fx-361, fx-911m, fx-82l, fx-85m, fx-350, fx-920 -7501875.5 6.16x10^-4
casio fx-300h, fx-85v -7497938.1 9.07x10^-5
casio fx-100d, fx-4000p, fx-5500l, fx-50f -7497938.067 9.07x10^-5
casio fx-992v -7497263.49882 7.09x10^-7
casio fx-4800p -7497258.44 3.40x10^-8
boots 425 (casio fx-31) -7518797 2.87x10^-3
national semiconductor 4640 -7496700.103 7.44x10^-5
commodore sr-4148R & 1540 -7497396.771 1.85x10^-5
commodore sr-1800 -7497396.7(71) 1.85x10^-5
commodore sr-9190r -7498432.938 1.57x10^-4
sharp pc-1001 -7496251.874 1.34x10^-4
sharp el-512 -7497484.888 3.02x10^-5
sharp el-545h, el-5020 -7497681.111 5.28x10^-5
sharp el-531p -7497656.982 5.32x10^-5
sharp el-9900 -7497264.141 7.96x10^-7
sharp pc-1251 pocket computer -7497484.888 3.02x10^-5
sinclair enterprise -9708737.9 way out
canon f-73 -7499447.58 2.92x10^-4
ti sr-50 & ti-58, ti-59 -7497385.261 1.70x10^-5
ti-55, ti-51-III -7496251.9 1.34x10^-4
ti-57 (1978) -7501875.5 6.16x10^-4
ti-52 -7497094.876 2.18x10^-5
ti-30x iiB -7497263.499 7.09x10^-7
ti-30 -7543377.2 6.15x10^-3
ti-30 lcd -7512430 2.02x10^-3
ti-89 (current) -7497257.87793 4.10x10^-8
ti-30s -7499447.6 2.92x10^-4
sharp el520w -7497264.149 7.95x10^-7
casio fx-991es, fx-570es -7497258.44 3.40x10^-8


  • it is interesting that the SR-50 from 1973 is twice as accurate as the top of the line HP.
  • the casio fx-1 beats many more modern casio machines (and it has no native radian mode).
  • the fx-4800p just beats the ti89 because it works with 15 digits.
  • all the new casio models like the fx-991es are the same 15 digit accuracy as the fx-4800p.