Average Error: 0.2 → 0.2
Time: 29.3s
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 r1988889 = x;
        double r1988890 = 1.0;
        double r1988891 = B;
        double r1988892 = tan(r1988891);
        double r1988893 = r1988890 / r1988892;
        double r1988894 = r1988889 * r1988893;
        double r1988895 = -r1988894;
        double r1988896 = sin(r1988891);
        double r1988897 = r1988890 / r1988896;
        double r1988898 = r1988895 + r1988897;
        return r1988898;
}
↓
double f(double B, double x) {
        double r1988899 = 1.0;
        double r1988900 = B;
        double r1988901 = cos(r1988900);
        double r1988902 = x;
        double r1988903 = r1988901 * r1988902;
        double r1988904 = r1988899 - r1988903;
        double r1988905 = sin(r1988900);
        double r1988906 = r1988904 / r1988905;
        return r1988906;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019158 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))