Average Error: 40.2 → 0.3
Time: 22.0s
Precision: 64
Internal Precision: 1344
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[\frac{e^{x}}{(e^{x} - 1)^*}\]

Error

Bits error versus x

Target

Original40.2
Target39.9
Herbie0.3
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 40.2

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

  2. Applied simplify0.3

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

Runtime

Time bar (total: 22.0s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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