(exp (- (- x) (* 2 (log1p (exp (- x))))))

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: binary64

• could not determine a ground truth for program body

  1. x = -61476344590.049736

Math

\[e^{\left(-x\right) - 2 \cdot \mathsf{log1p}\left(e^{-x}\right)}\]

↓

\[e^{\left(-x\right) - 2 \cdot \mathsf{log1p}\left(e^{-x}\right)}\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[e^{\left(-x\right) - 2 \cdot \mathsf{log1p}\left(e^{-x}\right)}\]

2. Final simplification 0.0

   \[\leadsto e^{\left(-x\right) - 2 \cdot \mathsf{log1p}\left(e^{-x}\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(exp (- (- x) (* 2 (log1p (exp (- x))))))"
  :precision binary64
  (exp (- (neg x) (* 2.0 (log1p (exp (neg x)))))))