Average Error: 0.2 → 0.2
Time: 17.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}
double f(double B, double x) {
        double r26812 = x;
        double r26813 = 1.0;
        double r26814 = B;
        double r26815 = tan(r26814);
        double r26816 = r26813 / r26815;
        double r26817 = r26812 * r26816;
        double r26818 = -r26817;
        double r26819 = sin(r26814);
        double r26820 = r26813 / r26819;
        double r26821 = r26818 + r26820;
        return r26821;
}
↓
double f(double B, double x) {
        double r26822 = 1.0;
        double r26823 = B;
        double r26824 = sin(r26823);
        double r26825 = 1.0;
        double r26826 = x;
        double r26827 = cos(r26823);
        double r26828 = r26826 * r26827;
        double r26829 = r26825 - r26828;
        double r26830 = r26824 / r26829;
        double r26831 = r26822 / r26830;
        return r26831;
}

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. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019297 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))