Average Error: 0.2 → 0.2
Time: 16.2s
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 r1674524 = x;
        double r1674525 = 1.0;
        double r1674526 = B;
        double r1674527 = tan(r1674526);
        double r1674528 = r1674525 / r1674527;
        double r1674529 = r1674524 * r1674528;
        double r1674530 = -r1674529;
        double r1674531 = sin(r1674526);
        double r1674532 = r1674525 / r1674531;
        double r1674533 = r1674530 + r1674532;
        return r1674533;
}
↓
double f(double B, double x) {
        double r1674534 = 1.0;
        double r1674535 = B;
        double r1674536 = sin(r1674535);
        double r1674537 = r1674534 / r1674536;
        double r1674538 = x;
        double r1674539 = cos(r1674535);
        double r1674540 = r1674538 * r1674539;
        double r1674541 = r1674540 / r1674536;
        double r1674542 = r1674541 * r1674534;
        double r1674543 = r1674537 - r1674542;
        return r1674543;
}

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 2019172 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))