Average Error: 0.2 → 0.2
Time: 37.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r647811 = x;
        double r647812 = 1.0;
        double r647813 = B;
        double r647814 = tan(r647813);
        double r647815 = r647812 / r647814;
        double r647816 = r647811 * r647815;
        double r647817 = -r647816;
        double r647818 = sin(r647813);
        double r647819 = r647812 / r647818;
        double r647820 = r647817 + r647819;
        return r647820;
}
↓
double f(double B, double x) {
        double r647821 = 1.0;
        double r647822 = B;
        double r647823 = cos(r647822);
        double r647824 = x;
        double r647825 = r647823 * r647824;
        double r647826 = r647821 - r647825;
        double r647827 = sin(r647822);
        double r647828 = r647826 / r647827;
        return r647828;
}

Error

Bits error versus B

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.2

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]

  5. Applied associate-/r/0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
  6. Using strategy rm

  7. Applied associate-*l/0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]

  8. Applied sub-div0.2

    \[\leadsto \color{blue}{\frac{1 - x \cdot \cos B}{\sin B}}\]

  9. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot x}{\sin B}\]

Reproduce

herbie shell --seed 2019121 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))