Average Error: 0.2 → 0.2
Time: 18.5s
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 r710545 = x;
        double r710546 = 1.0;
        double r710547 = B;
        double r710548 = tan(r710547);
        double r710549 = r710546 / r710548;
        double r710550 = r710545 * r710549;
        double r710551 = -r710550;
        double r710552 = sin(r710547);
        double r710553 = r710546 / r710552;
        double r710554 = r710551 + r710553;
        return r710554;
}
↓
double f(double B, double x) {
        double r710555 = 1.0;
        double r710556 = B;
        double r710557 = cos(r710556);
        double r710558 = x;
        double r710559 = r710557 * r710558;
        double r710560 = r710555 - r710559;
        double r710561 = sin(r710556);
        double r710562 = r710560 / r710561;
        return r710562;
}

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