Average Error: 0.2 → 0.2
Time: 21.6s
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 r1275629 = x;
        double r1275630 = 1.0;
        double r1275631 = B;
        double r1275632 = tan(r1275631);
        double r1275633 = r1275630 / r1275632;
        double r1275634 = r1275629 * r1275633;
        double r1275635 = -r1275634;
        double r1275636 = sin(r1275631);
        double r1275637 = r1275630 / r1275636;
        double r1275638 = r1275635 + r1275637;
        return r1275638;
}
↓
double f(double B, double x) {
        double r1275639 = 1.0;
        double r1275640 = B;
        double r1275641 = cos(r1275640);
        double r1275642 = x;
        double r1275643 = r1275641 * r1275642;
        double r1275644 = r1275639 - r1275643;
        double r1275645 = sin(r1275640);
        double r1275646 = r1275644 / r1275645;
        return r1275646;
}

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. Simplified0.2

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

  3. Taylor expanded around -inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]
  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 2019132 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))