Average Error: 0.2 → 0.2
Time: 26.8s
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 r1223522 = x;
        double r1223523 = 1.0;
        double r1223524 = B;
        double r1223525 = tan(r1223524);
        double r1223526 = r1223523 / r1223525;
        double r1223527 = r1223522 * r1223526;
        double r1223528 = -r1223527;
        double r1223529 = sin(r1223524);
        double r1223530 = r1223523 / r1223529;
        double r1223531 = r1223528 + r1223530;
        return r1223531;
}
↓
double f(double B, double x) {
        double r1223532 = 1.0;
        double r1223533 = B;
        double r1223534 = cos(r1223533);
        double r1223535 = x;
        double r1223536 = r1223534 * r1223535;
        double r1223537 = r1223532 - r1223536;
        double r1223538 = sin(r1223533);
        double r1223539 = r1223537 / r1223538;
        return r1223539;
}

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 2019141 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))