Average Error: 0.2 → 0.2
Time: 11.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} \cdot \left(1 - x \cdot \cos B\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} \cdot \left(1 - x \cdot \cos B\right)
double f(double B, double x) {
        double r61596 = x;
        double r61597 = 1.0;
        double r61598 = B;
        double r61599 = tan(r61598);
        double r61600 = r61597 / r61599;
        double r61601 = r61596 * r61600;
        double r61602 = -r61601;
        double r61603 = sin(r61598);
        double r61604 = r61597 / r61603;
        double r61605 = r61602 + r61604;
        return r61605;
}
↓
double f(double B, double x) {
        double r61606 = 1.0;
        double r61607 = B;
        double r61608 = sin(r61607);
        double r61609 = r61606 / r61608;
        double r61610 = 1.0;
        double r61611 = x;
        double r61612 = cos(r61607);
        double r61613 = r61611 * r61612;
        double r61614 = r61610 - r61613;
        double r61615 = r61609 * r61614;
        return r61615;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

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