Average Error: 0.2 → 0.2
Time: 26.9s
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 r598554 = x;
        double r598555 = 1.0;
        double r598556 = B;
        double r598557 = tan(r598556);
        double r598558 = r598555 / r598557;
        double r598559 = r598554 * r598558;
        double r598560 = -r598559;
        double r598561 = sin(r598556);
        double r598562 = r598555 / r598561;
        double r598563 = r598560 + r598562;
        return r598563;
}
↓
double f(double B, double x) {
        double r598564 = 1.0;
        double r598565 = B;
        double r598566 = cos(r598565);
        double r598567 = x;
        double r598568 = r598566 * r598567;
        double r598569 = r598564 - r598568;
        double r598570 = sin(r598565);
        double r598571 = r598569 / r598570;
        return r598571;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}}\]
  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 2019134 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))