Average Error: 29.5 → 0.0
Time: 10.8s
Precision: 64
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]
\frac{1 - \cos x}{\sin x}
↓
\tan \left(\frac{x}{2}\right)
double f(double x) {
        double r1359667 = 1.0;
        double r1359668 = x;
        double r1359669 = cos(r1359668);
        double r1359670 = r1359667 - r1359669;
        double r1359671 = sin(r1359668);
        double r1359672 = r1359670 / r1359671;
        return r1359672;
}
↓
double f(double x) {
        double r1359673 = x;
        double r1359674 = 2.0;
        double r1359675 = r1359673 / r1359674;
        double r1359676 = tan(r1359675);
        return r1359676;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original29.5
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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