Average Error: 30.7 → 0
Time: 11.1s
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 r2226603 = 1.0;
        double r2226604 = x;
        double r2226605 = cos(r2226604);
        double r2226606 = r2226603 - r2226605;
        double r2226607 = sin(r2226604);
        double r2226608 = r2226606 / r2226607;
        return r2226608;
}
↓
double f(double x) {
        double r2226609 = x;
        double r2226610 = 2.0;
        double r2226611 = r2226609 / r2226610;
        double r2226612 = tan(r2226611);
        return r2226612;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.7
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.7

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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