Average Error: 0.2 → 0.2
Time: 18.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(\cos B \cdot x\right) \cdot 1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(\cos B \cdot x\right) \cdot 1}{\sin B}
double f(double B, double x) {
        double r2539783 = x;
        double r2539784 = 1.0;
        double r2539785 = B;
        double r2539786 = tan(r2539785);
        double r2539787 = r2539784 / r2539786;
        double r2539788 = r2539783 * r2539787;
        double r2539789 = -r2539788;
        double r2539790 = sin(r2539785);
        double r2539791 = r2539784 / r2539790;
        double r2539792 = r2539789 + r2539791;
        return r2539792;
}
↓
double f(double B, double x) {
        double r2539793 = 1.0;
        double r2539794 = B;
        double r2539795 = cos(r2539794);
        double r2539796 = x;
        double r2539797 = r2539795 * r2539796;
        double r2539798 = r2539797 * r2539793;
        double r2539799 = r2539793 - r2539798;
        double r2539800 = sin(r2539794);
        double r2539801 = r2539799 / r2539800;
        return r2539801;
}

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

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

  3. Taylor expanded around inf 0.2

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

  5. Applied associate-*r/0.2

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

  6. Applied sub-div0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))