Average Error: 0.2 → 0.2
Time: 28.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r2019881 = x;
        double r2019882 = 1.0;
        double r2019883 = B;
        double r2019884 = tan(r2019883);
        double r2019885 = r2019882 / r2019884;
        double r2019886 = r2019881 * r2019885;
        double r2019887 = -r2019886;
        double r2019888 = sin(r2019883);
        double r2019889 = r2019882 / r2019888;
        double r2019890 = r2019887 + r2019889;
        return r2019890;
}
↓
double f(double B, double x) {
        double r2019891 = 1.0;
        double r2019892 = B;
        double r2019893 = sin(r2019892);
        double r2019894 = r2019891 / r2019893;
        double r2019895 = x;
        double r2019896 = r2019895 / r2019893;
        double r2019897 = cos(r2019892);
        double r2019898 = r2019896 * r2019897;
        double r2019899 = r2019894 - r2019898;
        return r2019899;
}

Error

Bits error versus B

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))