Average Error: 39.5 → 0.3
Time: 26.9s
Precision: 64
Internal Precision: 1344
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[\frac{e^{x}}{(e^{x} - 1)^*}\]

Error

Bits error versus x

Target

Original39.5
Target39.2
Herbie0.3
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 39.5

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

  2. Applied simplify0.3

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

Runtime

Time bar (total: 26.9s)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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