Average Error: 0.2 → 0.2
Time: 20.1s
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 r351671 = x;
        double r351672 = 1.0;
        double r351673 = B;
        double r351674 = tan(r351673);
        double r351675 = r351672 / r351674;
        double r351676 = r351671 * r351675;
        double r351677 = -r351676;
        double r351678 = sin(r351673);
        double r351679 = r351672 / r351678;
        double r351680 = r351677 + r351679;
        return r351680;
}
↓
double f(double B, double x) {
        double r351681 = 1.0;
        double r351682 = B;
        double r351683 = cos(r351682);
        double r351684 = x;
        double r351685 = r351683 * r351684;
        double r351686 = r351681 - r351685;
        double r351687 = sin(r351682);
        double r351688 = r351686 / r351687;
        return r351688;
}

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

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

  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 2019153 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))