Average Error: 30.5 → 0.0
Time: 11.5s
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 r983406 = 1.0;
        double r983407 = x;
        double r983408 = cos(r983407);
        double r983409 = r983406 - r983408;
        double r983410 = sin(r983407);
        double r983411 = r983409 / r983410;
        return r983411;
}
↓
double f(double x) {
        double r983412 = x;
        double r983413 = 2.0;
        double r983414 = r983412 / r983413;
        double r983415 = tan(r983414);
        return r983415;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original30.5
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.5

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

  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 2019154 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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