Average Error: 0.2 → 0.2
Time: 25.1s
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 r782713 = x;
        double r782714 = 1.0;
        double r782715 = B;
        double r782716 = tan(r782715);
        double r782717 = r782714 / r782716;
        double r782718 = r782713 * r782717;
        double r782719 = -r782718;
        double r782720 = sin(r782715);
        double r782721 = r782714 / r782720;
        double r782722 = r782719 + r782721;
        return r782722;
}
↓
double f(double B, double x) {
        double r782723 = 1.0;
        double r782724 = B;
        double r782725 = cos(r782724);
        double r782726 = x;
        double r782727 = r782725 * r782726;
        double r782728 = r782723 - r782727;
        double r782729 = sin(r782724);
        double r782730 = r782728 / r782729;
        return r782730;
}

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 2019162 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))