Average Error: 40.5 → 0.5
Time: 13.2s
Precision: 64
Internal Precision: 1408
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[\frac{e^{x}}{(e^{x} - 1)^*}\]

Error

Bits error versus x

Target

Original40.5
Target40.1
Herbie0.5
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 40.5

    \[\frac{e^{x}}{e^{x} - 1}\]

  2. Applied simplify0.5

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

Runtime

Time bar (total: 13.2s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

  :herbie-target
  (/ 1 (- 1 (exp (- x))))

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