Average Error: 30.8 → 29.5
Time: 6.1s
Precision: 64
Internal Precision: 128
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original30.8
Target29.5
Herbie29.5
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.8

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

  2. Initial simplification29.5

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

  3. Final simplification29.5

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

Runtime

Time bar (total: 6.1s)Debug logProfile

herbie shell --seed 2018277 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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