Average Error: 30.6 → 0
Time: 17.0s
Precision: 64
Internal Precision: 2624
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]

Error

Bits error versus x

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Results

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Target

Original30.6
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.6

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

  2. Applied simplify0

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

Runtime

Time bar (total: 17.0s)Debug logProfile

herbie shell --seed 2018170 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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