Average Error: 58.7 → 0.0
Time: 4.0s
Precision: 64
Internal Precision: 1408
\[e^{x} - 1\]
↓
\[(e^{x} - 1)^*\]

Error

Bits error versus x

Target

Original58.7
Target0.4
Herbie0.0
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right)\]

Derivation

  1. Initial program 58.7

    \[e^{x} - 1\]

  2. Applied simplify0.0

    \[\leadsto \color{blue}{(e^{x} - 1)^*}\]

Runtime

Time bar (total: 4.0s)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' +o rules:numerics
(FPCore (x)
  :name "expm1 (example 3.7)"
  :pre (< -0.00017 x)

  :herbie-target
  (* x (+ (+ 1 (/ x 2)) (/ (* x x) 6)))

  (- (exp x) 1))