Average Error: 30.2 → 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 r973449 = 1.0;
        double r973450 = x;
        double r973451 = cos(r973450);
        double r973452 = r973449 - r973451;
        double r973453 = sin(r973450);
        double r973454 = r973452 / r973453;
        return r973454;
}
↓
double f(double x) {
        double r973455 = x;
        double r973456 = 2.0;
        double r973457 = r973455 / r973456;
        double r973458 = tan(r973457);
        return r973458;
}

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 2019156 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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