Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r60496 = x;
        double r60497 = 1.0;
        double r60498 = B;
        double r60499 = tan(r60498);
        double r60500 = r60497 / r60499;
        double r60501 = r60496 * r60500;
        double r60502 = -r60501;
        double r60503 = sin(r60498);
        double r60504 = r60497 / r60503;
        double r60505 = r60502 + r60504;
        return r60505;
}
↓
double f(double B, double x) {
        double r60506 = 1.0;
        double r60507 = x;
        double r60508 = B;
        double r60509 = cos(r60508);
        double r60510 = r60507 * r60509;
        double r60511 = sin(r60508);
        double r60512 = r60510 / r60511;
        double r60513 = r60506 * r60512;
        double r60514 = -r60513;
        double r60515 = r60506 / r60511;
        double r60516 = r60514 + r60515;
        return r60516;
}

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

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))