(/ (- (+ (* (- x) (exp x)) (exp x)) 1) (pow (- (exp x) 1) 2))

Average Error: 41.9 → 41.9

Time: 3.4s

Precision: binary64

Math

\[\frac{\left(\left(-x\right) \cdot e^{x} + e^{x}\right) - 1}{{\left(e^{x} - 1\right)}^{2}}\]

↓

\[\frac{\left(\left(-x\right) \cdot e^{x} + e^{x}\right) - 1}{{\left(e^{x} - 1\right)}^{2}}\]

Error

Bits error versus x

Derivation

1. Initial program 41.9

   \[\frac{\left(\left(-x\right) \cdot e^{x} + e^{x}\right) - 1}{{\left(e^{x} - 1\right)}^{2}}\]

2. Final simplification 41.9

   \[\leadsto \frac{\left(\left(-x\right) \cdot e^{x} + e^{x}\right) - 1}{{\left(e^{x} - 1\right)}^{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (- (+ (* (- x) (exp x)) (exp x)) 1) (pow (- (exp x) 1) 2))"
  :precision binary64
  (/ (- (+ (* (neg x) (exp x)) (exp x)) 1.0) (pow (- (exp x) 1.0) 2.0)))