Average Error: 0.2 → 0.2
Time: 19.9s
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 r794926 = x;
        double r794927 = 1.0;
        double r794928 = B;
        double r794929 = tan(r794928);
        double r794930 = r794927 / r794929;
        double r794931 = r794926 * r794930;
        double r794932 = -r794931;
        double r794933 = sin(r794928);
        double r794934 = r794927 / r794933;
        double r794935 = r794932 + r794934;
        return r794935;
}
↓
double f(double B, double x) {
        double r794936 = 1.0;
        double r794937 = B;
        double r794938 = cos(r794937);
        double r794939 = x;
        double r794940 = r794938 * r794939;
        double r794941 = r794936 - r794940;
        double r794942 = sin(r794937);
        double r794943 = r794941 / r794942;
        return r794943;
}

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. Taylor expanded around inf 0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))