Average Error: 0.2 → 0.2
Time: 23.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r44675 = x;
        double r44676 = 1.0;
        double r44677 = B;
        double r44678 = tan(r44677);
        double r44679 = r44676 / r44678;
        double r44680 = r44675 * r44679;
        double r44681 = -r44680;
        double r44682 = sin(r44677);
        double r44683 = r44676 / r44682;
        double r44684 = r44681 + r44683;
        return r44684;
}
↓
double f(double B, double x) {
        double r44685 = 1.0;
        double r44686 = B;
        double r44687 = sin(r44686);
        double r44688 = r44685 / r44687;
        double r44689 = x;
        double r44690 = r44689 * r44688;
        double r44691 = cos(r44686);
        double r44692 = r44690 * r44691;
        double r44693 = r44688 - r44692;
        return r44693;
}

Error

Bits error versus B

Bits error versus x

Try it out

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

    \[\leadsto \frac{1}{\sin B} - x \cdot \frac{1}{\color{blue}{\frac{\sin B}{\cos B}}}\]

  5. Applied associate-/r/0.2

    \[\leadsto \frac{1}{\sin B} - x \cdot \color{blue}{\left(\frac{1}{\sin B} \cdot \cos B\right)}\]

  6. Applied associate-*r*0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B}\]

  7. Final simplification0.2

    \[\leadsto \frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))