Average Error: 30.0 → 0
Time: 11.6s
Precision: 64
Internal Precision: 2368
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.0
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.0

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

  2. Applied simplify0

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

Runtime

Time bar (total: 11.6s)Debug logProfile

herbie shell --seed '#(1072936661 1621281212 3440817831 3219514234 460296804 1258167384)' +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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