Average Error: 0.2 → 0.2
Time: 17.4s
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 r2337902 = x;
        double r2337903 = 1.0;
        double r2337904 = B;
        double r2337905 = tan(r2337904);
        double r2337906 = r2337903 / r2337905;
        double r2337907 = r2337902 * r2337906;
        double r2337908 = -r2337907;
        double r2337909 = sin(r2337904);
        double r2337910 = r2337903 / r2337909;
        double r2337911 = r2337908 + r2337910;
        return r2337911;
}
↓
double f(double B, double x) {
        double r2337912 = 1.0;
        double r2337913 = B;
        double r2337914 = cos(r2337913);
        double r2337915 = x;
        double r2337916 = r2337914 * r2337915;
        double r2337917 = r2337916 * r2337912;
        double r2337918 = r2337912 - r2337917;
        double r2337919 = sin(r2337913);
        double r2337920 = r2337918 / r2337919;
        return r2337920;
}

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 2019169 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))