Average Error: 0.2 → 0.2
Time: 46.2s
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 r1216741 = x;
        double r1216742 = 1.0;
        double r1216743 = B;
        double r1216744 = tan(r1216743);
        double r1216745 = r1216742 / r1216744;
        double r1216746 = r1216741 * r1216745;
        double r1216747 = -r1216746;
        double r1216748 = sin(r1216743);
        double r1216749 = r1216742 / r1216748;
        double r1216750 = r1216747 + r1216749;
        return r1216750;
}
↓
double f(double B, double x) {
        double r1216751 = 1.0;
        double r1216752 = B;
        double r1216753 = cos(r1216752);
        double r1216754 = x;
        double r1216755 = r1216753 * r1216754;
        double r1216756 = r1216751 - r1216755;
        double r1216757 = sin(r1216752);
        double r1216758 = r1216756 / r1216757;
        return r1216758;
}

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))))