Average Error: 0.2 → 0.2
Time: 15.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{-\cos B}{\frac{\sin B}{x}} \cdot 1 + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{-\cos B}{\frac{\sin B}{x}} \cdot 1 + \frac{1}{\sin B}
double f(double B, double x) {
        double r36843 = x;
        double r36844 = 1.0;
        double r36845 = B;
        double r36846 = tan(r36845);
        double r36847 = r36844 / r36846;
        double r36848 = r36843 * r36847;
        double r36849 = -r36848;
        double r36850 = sin(r36845);
        double r36851 = r36844 / r36850;
        double r36852 = r36849 + r36851;
        return r36852;
}
↓
double f(double B, double x) {
        double r36853 = B;
        double r36854 = cos(r36853);
        double r36855 = -r36854;
        double r36856 = sin(r36853);
        double r36857 = x;
        double r36858 = r36856 / r36857;
        double r36859 = r36855 / r36858;
        double r36860 = 1.0;
        double r36861 = r36859 * r36860;
        double r36862 = r36860 / r36856;
        double r36863 = r36861 + r36862;
        return r36863;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

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

  4. Taylor expanded around inf 0.2

    \[\leadsto \left(-\color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\right) + \frac{1}{\sin B}\]

  5. Simplified0.2

    \[\leadsto \left(-\color{blue}{\frac{\cos B}{\frac{\sin B}{x}} \cdot 1}\right) + \frac{1}{\sin B}\]

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))