Average Error: 0.2 → 0.2
Time: 8.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r12512 = x;
        double r12513 = 1.0;
        double r12514 = B;
        double r12515 = tan(r12514);
        double r12516 = r12513 / r12515;
        double r12517 = r12512 * r12516;
        double r12518 = -r12517;
        double r12519 = sin(r12514);
        double r12520 = r12513 / r12519;
        double r12521 = r12518 + r12520;
        return r12521;
}
↓
double f(double B, double x) {
        double r12522 = 1.0;
        double r12523 = 1.0;
        double r12524 = B;
        double r12525 = sin(r12524);
        double r12526 = r12523 / r12525;
        double r12527 = x;
        double r12528 = cos(r12524);
        double r12529 = r12527 * r12528;
        double r12530 = r12529 / r12525;
        double r12531 = r12526 - r12530;
        double r12532 = r12522 * r12531;
        return r12532;
}

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

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))