Average Error: 0.2 → 0.2
Time: 33.9s
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 r1271411 = x;
        double r1271412 = 1.0;
        double r1271413 = B;
        double r1271414 = tan(r1271413);
        double r1271415 = r1271412 / r1271414;
        double r1271416 = r1271411 * r1271415;
        double r1271417 = -r1271416;
        double r1271418 = sin(r1271413);
        double r1271419 = r1271412 / r1271418;
        double r1271420 = r1271417 + r1271419;
        return r1271420;
}
↓
double f(double B, double x) {
        double r1271421 = 1.0;
        double r1271422 = B;
        double r1271423 = cos(r1271422);
        double r1271424 = x;
        double r1271425 = r1271423 * r1271424;
        double r1271426 = r1271421 - r1271425;
        double r1271427 = sin(r1271422);
        double r1271428 = r1271426 / r1271427;
        return r1271428;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019129 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))