(/ (cos (pow e (- x))) (sin (pow e x)))

Average Error: 0.3 → 0.3

Time: 30.2s

Precision: binary64

• could not determine a ground truth for program body

  1. e = -61476344590.049736
  2. x = -1.2499510398585455e+92

Math

\[\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]

↓

\[\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]

Error

Bits error versus e

Bits error versus x

Derivation

1. Initial program 0.3

   \[\frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]

2. Final simplification 0.3

   \[\leadsto \frac{\cos \left({e}^{\left(-x\right)}\right)}{\sin \left({e}^{x}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (e x)
  :name "(/ (cos (pow e (- x))) (sin (pow e x)))"
  :precision binary64
  (/ (cos (pow e (neg x))) (sin (pow e x))))