Average Error: 0.2 → 0.2
Time: 17.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22541 = x;
        double r22542 = 1.0;
        double r22543 = B;
        double r22544 = tan(r22543);
        double r22545 = r22542 / r22544;
        double r22546 = r22541 * r22545;
        double r22547 = -r22546;
        double r22548 = sin(r22543);
        double r22549 = r22542 / r22548;
        double r22550 = r22547 + r22549;
        return r22550;
}
↓
double f(double B, double x) {
        double r22551 = x;
        double r22552 = 1.0;
        double r22553 = B;
        double r22554 = cos(r22553);
        double r22555 = sin(r22553);
        double r22556 = r22554 / r22555;
        double r22557 = r22552 * r22556;
        double r22558 = r22551 * r22557;
        double r22559 = -r22558;
        double r22560 = r22552 / r22555;
        double r22561 = r22559 + r22560;
        return r22561;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019347 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))