Average Error: 0.2 → 0.9
Time: 30.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{\frac{1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}}{\sqrt[3]{\sin B}} - \frac{x}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{\frac{1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}}{\sqrt[3]{\sin B}} - \frac{x}{\tan B}
double f(double B, double x) {
        double r3717924 = x;
        double r3717925 = 1.0;
        double r3717926 = B;
        double r3717927 = tan(r3717926);
        double r3717928 = r3717925 / r3717927;
        double r3717929 = r3717924 * r3717928;
        double r3717930 = -r3717929;
        double r3717931 = sin(r3717926);
        double r3717932 = r3717925 / r3717931;
        double r3717933 = r3717930 + r3717932;
        return r3717933;
}
↓
double f(double B, double x) {
        double r3717934 = 1.0;
        double r3717935 = B;
        double r3717936 = sin(r3717935);
        double r3717937 = cbrt(r3717936);
        double r3717938 = r3717937 * r3717937;
        double r3717939 = r3717934 / r3717938;
        double r3717940 = r3717939 / r3717937;
        double r3717941 = x;
        double r3717942 = tan(r3717935);
        double r3717943 = r3717941 / r3717942;
        double r3717944 = r3717940 - r3717943;
        return r3717944;
}

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. Simplified0.2

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

  4. Applied add-cube-cbrt0.9

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}\right) \cdot \sqrt[3]{\sin B}}} - \frac{x}{\tan B}\]

  5. Applied associate-/r*0.9

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}}{\sqrt[3]{\sin B}}} - \frac{x}{\tan B}\]

  6. Final simplification0.9

    \[\leadsto \frac{\frac{1}{\sqrt[3]{\sin B} \cdot \sqrt[3]{\sin B}}}{\sqrt[3]{\sin B}} - \frac{x}{\tan B}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))