Average Error: 0.2 → 0.2
Time: 27.6s
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 r2848614 = x;
        double r2848615 = 1.0;
        double r2848616 = B;
        double r2848617 = tan(r2848616);
        double r2848618 = r2848615 / r2848617;
        double r2848619 = r2848614 * r2848618;
        double r2848620 = -r2848619;
        double r2848621 = sin(r2848616);
        double r2848622 = r2848615 / r2848621;
        double r2848623 = r2848620 + r2848622;
        return r2848623;
}
↓
double f(double B, double x) {
        double r2848624 = 1.0;
        double r2848625 = B;
        double r2848626 = cos(r2848625);
        double r2848627 = x;
        double r2848628 = r2848626 * r2848627;
        double r2848629 = r2848624 - r2848628;
        double r2848630 = sin(r2848625);
        double r2848631 = r2848629 / r2848630;
        return r2848631;
}

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 2019104 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))