Average Error: 0.2 → 0.2
Time: 22.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r2284638 = x;
        double r2284639 = 1.0;
        double r2284640 = B;
        double r2284641 = tan(r2284640);
        double r2284642 = r2284639 / r2284641;
        double r2284643 = r2284638 * r2284642;
        double r2284644 = -r2284643;
        double r2284645 = sin(r2284640);
        double r2284646 = r2284639 / r2284645;
        double r2284647 = r2284644 + r2284646;
        return r2284647;
}
↓
double f(double B, double x) {
        double r2284648 = 1.0;
        double r2284649 = B;
        double r2284650 = cos(r2284649);
        double r2284651 = x;
        double r2284652 = r2284650 * r2284651;
        double r2284653 = r2284648 - r2284652;
        double r2284654 = sin(r2284649);
        double r2284655 = r2284653 / r2284654;
        return r2284655;
}

Error

Bits error versus B

Bits error versus x

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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. Simplified0.1

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

  3. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019134 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))