(/ (* (- 1) (- (exp x) (exp (- x)))) (- (exp x) (- (exp x) (exp (- x)))))

Average Error: 58.3 → 57.5

Time: 3.3s

Precision: binary64

• could not determine a ground truth for program body

  1. x = 127140.91663662092

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 58.3

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

2. Simplified 57.5

   \[\leadsto \color{blue}{1 - \left(e^{x} \cdot 1\right) \cdot e^{x}}\]

3. Final simplification 57.5

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

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (* (- 1) (- (exp x) (exp (- x)))) (- (exp x) (- (exp x) (exp (- x)))))"
  :precision binary64
  (/ (* (neg 1.0) (- (exp x) (exp (neg x)))) (- (exp x) (- (exp x) (exp (neg x))))))