Average Error: 29.9 → 0.0
Time: 12.8s
Precision: 64
Internal Precision: 2432
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]

Error

Bits error versus x

Target

Original29.9
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.9

    \[\frac{1 - \cos x}{\sin x}\]

  2. Applied simplify0.0

    \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)}\]

Runtime

Time bar (total: 12.8s)Debug logProfile

herbie shell --seed '#(1070386091 2509006183 1430610344 1025408621 36622005 1425925650)' +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

  :herbie-target
  (tan (/ x 2))

  (/ (- 1 (cos x)) (sin x)))