Average Error: 0.2 → 0.2
Time: 34.0s
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 r604530 = x;
        double r604531 = 1.0;
        double r604532 = B;
        double r604533 = tan(r604532);
        double r604534 = r604531 / r604533;
        double r604535 = r604530 * r604534;
        double r604536 = -r604535;
        double r604537 = sin(r604532);
        double r604538 = r604531 / r604537;
        double r604539 = r604536 + r604538;
        return r604539;
}
↓
double f(double B, double x) {
        double r604540 = 1.0;
        double r604541 = B;
        double r604542 = cos(r604541);
        double r604543 = x;
        double r604544 = r604542 * r604543;
        double r604545 = r604540 - r604544;
        double r604546 = sin(r604541);
        double r604547 = r604545 / r604546;
        return r604547;
}

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 2019120 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))