Average Error: 0.2 → 0.2
Time: 44.1s
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 r3622398 = x;
        double r3622399 = 1.0;
        double r3622400 = B;
        double r3622401 = tan(r3622400);
        double r3622402 = r3622399 / r3622401;
        double r3622403 = r3622398 * r3622402;
        double r3622404 = -r3622403;
        double r3622405 = sin(r3622400);
        double r3622406 = r3622399 / r3622405;
        double r3622407 = r3622404 + r3622406;
        return r3622407;
}
↓
double f(double B, double x) {
        double r3622408 = 1.0;
        double r3622409 = B;
        double r3622410 = cos(r3622409);
        double r3622411 = x;
        double r3622412 = r3622410 * r3622411;
        double r3622413 = r3622408 - r3622412;
        double r3622414 = sin(r3622409);
        double r3622415 = r3622413 / r3622414;
        return r3622415;
}

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 2019128 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))