Average Error: 0.2 → 0.2
Time: 10.1s
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 r33519 = x;
        double r33520 = 1.0;
        double r33521 = B;
        double r33522 = tan(r33521);
        double r33523 = r33520 / r33522;
        double r33524 = r33519 * r33523;
        double r33525 = -r33524;
        double r33526 = sin(r33521);
        double r33527 = r33520 / r33526;
        double r33528 = r33525 + r33527;
        return r33528;
}
↓
double f(double B, double x) {
        double r33529 = 1.0;
        double r33530 = B;
        double r33531 = sin(r33530);
        double r33532 = 1.0;
        double r33533 = x;
        double r33534 = cos(r33530);
        double r33535 = r33533 * r33534;
        double r33536 = r33532 - r33535;
        double r33537 = r33531 / r33536;
        double r33538 = r33529 / r33537;
        return r33538;
}

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. Taylor expanded around inf 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))