Average Error: 0.2 → 0.2
Time: 17.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B} \cdot 1\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B} \cdot 1
double f(double B, double x) {
        double r871569 = x;
        double r871570 = 1.0;
        double r871571 = B;
        double r871572 = tan(r871571);
        double r871573 = r871570 / r871572;
        double r871574 = r871569 * r871573;
        double r871575 = -r871574;
        double r871576 = sin(r871571);
        double r871577 = r871570 / r871576;
        double r871578 = r871575 + r871577;
        return r871578;
}
↓
double f(double B, double x) {
        double r871579 = 1.0;
        double r871580 = B;
        double r871581 = sin(r871580);
        double r871582 = r871579 / r871581;
        double r871583 = x;
        double r871584 = cos(r871580);
        double r871585 = r871583 * r871584;
        double r871586 = r871585 / r871581;
        double r871587 = r871586 * r871579;
        double r871588 = r871582 - r871587;
        return r871588;
}

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

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

  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

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

Reproduce

herbie shell --seed 2019192 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))