Average Error: 30.2 → 0
Time: 11.7s
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 r2007577 = 1.0;
        double r2007578 = x;
        double r2007579 = cos(r2007578);
        double r2007580 = r2007577 - r2007579;
        double r2007581 = sin(r2007578);
        double r2007582 = r2007580 / r2007581;
        return r2007582;
}
↓
double f(double x) {
        double r2007583 = x;
        double r2007584 = 2.0;
        double r2007585 = r2007583 / r2007584;
        double r2007586 = tan(r2007585);
        return r2007586;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 30.2

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

  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 2019107 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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