Average Error: 0.2 → 0.2
Time: 4.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r41517 = x;
        double r41518 = 1.0;
        double r41519 = B;
        double r41520 = tan(r41519);
        double r41521 = r41518 / r41520;
        double r41522 = r41517 * r41521;
        double r41523 = -r41522;
        double r41524 = sin(r41519);
        double r41525 = r41518 / r41524;
        double r41526 = r41523 + r41525;
        return r41526;
}
↓
double f(double B, double x) {
        double r41527 = 1.0;
        double r41528 = B;
        double r41529 = sin(r41528);
        double r41530 = r41527 / r41529;
        double r41531 = x;
        double r41532 = cos(r41528);
        double r41533 = r41531 * r41532;
        double r41534 = r41533 / r41529;
        double r41535 = r41527 * r41534;
        double r41536 = r41530 - r41535;
        return r41536;
}

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

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

  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

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

Reproduce

herbie shell --seed 2020059 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))