Average Error: 30.1 → 0
Time: 9.2s
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 r1658572 = 1.0;
        double r1658573 = x;
        double r1658574 = cos(r1658573);
        double r1658575 = r1658572 - r1658574;
        double r1658576 = sin(r1658573);
        double r1658577 = r1658575 / r1658576;
        return r1658577;
}
↓
double f(double x) {
        double r1658578 = x;
        double r1658579 = 2.0;
        double r1658580 = r1658578 / r1658579;
        double r1658581 = tan(r1658580);
        return r1658581;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.1
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.1

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

  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 2019168 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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