Average Error: 0.2 → 0.2
Time: 13.8s
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 r29553 = x;
        double r29554 = 1.0;
        double r29555 = B;
        double r29556 = tan(r29555);
        double r29557 = r29554 / r29556;
        double r29558 = r29553 * r29557;
        double r29559 = -r29558;
        double r29560 = sin(r29555);
        double r29561 = r29554 / r29560;
        double r29562 = r29559 + r29561;
        return r29562;
}
↓
double f(double B, double x) {
        double r29563 = 1.0;
        double r29564 = B;
        double r29565 = sin(r29564);
        double r29566 = 1.0;
        double r29567 = x;
        double r29568 = cos(r29564);
        double r29569 = r29567 * r29568;
        double r29570 = r29566 - r29569;
        double r29571 = r29565 / r29570;
        double r29572 = r29563 / r29571;
        return r29572;
}

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 2019304 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))