Average Error: 40.4 → 0.5
Time: 16.9s
Precision: 64
Internal Precision: 1408
\[\frac{e^{x}}{e^{x} - 1}\]
↓
\[\frac{1}{\frac{(e^{x} - 1)^*}{e^{x}}}\]

Error

Bits error versus x

Target

Original40.4
Target39.9
Herbie0.5
\[\frac{1}{1 - e^{-x}}\]

Derivation

  1. Initial program 40.4

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

  2. Applied simplify0.5

    \[\leadsto \color{blue}{\frac{e^{x}}{(e^{x} - 1)^*}}\]
  3. Using strategy rm

  4. Applied clear-num0.5

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

Runtime

Time bar (total: 16.9s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (x)
  :name "expq2 (section 3.11)"

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

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