Average Error: 0.2 → 0.2
Time: 22.3s
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 r1787353 = x;
        double r1787354 = 1.0;
        double r1787355 = B;
        double r1787356 = tan(r1787355);
        double r1787357 = r1787354 / r1787356;
        double r1787358 = r1787353 * r1787357;
        double r1787359 = -r1787358;
        double r1787360 = sin(r1787355);
        double r1787361 = r1787354 / r1787360;
        double r1787362 = r1787359 + r1787361;
        return r1787362;
}
↓
double f(double B, double x) {
        double r1787363 = 1.0;
        double r1787364 = B;
        double r1787365 = cos(r1787364);
        double r1787366 = x;
        double r1787367 = r1787365 * r1787366;
        double r1787368 = r1787363 - r1787367;
        double r1787369 = sin(r1787364);
        double r1787370 = r1787368 / r1787369;
        return r1787370;
}

Error

Bits error versus B

Bits error versus x

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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. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
  6. Using strategy rm

  7. Applied associate-*l/0.2

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

  8. Applied sub-div0.2

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

  9. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot x}{\sin B}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))