Average Error: 0.2 → 0.2
Time: 22.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r40680 = x;
        double r40681 = 1.0;
        double r40682 = B;
        double r40683 = tan(r40682);
        double r40684 = r40681 / r40683;
        double r40685 = r40680 * r40684;
        double r40686 = -r40685;
        double r40687 = sin(r40682);
        double r40688 = r40681 / r40687;
        double r40689 = r40686 + r40688;
        return r40689;
}
↓
double f(double B, double x) {
        double r40690 = 1.0;
        double r40691 = B;
        double r40692 = sin(r40691);
        double r40693 = r40690 / r40692;
        double r40694 = x;
        double r40695 = r40694 * r40690;
        double r40696 = r40695 / r40692;
        double r40697 = cos(r40691);
        double r40698 = r40696 * r40697;
        double r40699 = r40693 - r40698;
        return r40699;
}

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. Using strategy rm

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))