Average Error: 0.2 → 0.2
Time: 23.1s
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 r788040 = x;
        double r788041 = 1.0;
        double r788042 = B;
        double r788043 = tan(r788042);
        double r788044 = r788041 / r788043;
        double r788045 = r788040 * r788044;
        double r788046 = -r788045;
        double r788047 = sin(r788042);
        double r788048 = r788041 / r788047;
        double r788049 = r788046 + r788048;
        return r788049;
}
↓
double f(double B, double x) {
        double r788050 = 1.0;
        double r788051 = B;
        double r788052 = cos(r788051);
        double r788053 = x;
        double r788054 = r788052 * r788053;
        double r788055 = r788050 - r788054;
        double r788056 = sin(r788051);
        double r788057 = r788055 / r788056;
        return r788057;
}

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