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

Average Error: 0.4 → 0.4

Time: 911.0ms

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.4

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

2. Final simplification 0.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (- x) (* 2 (log1p (exp (- x)))))"
  :precision binary64
  (- (neg x) (* 2.0 (log1p (exp (neg x))))))