Average Error: 0.2 → 0.2
Time: 19.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}
double f(double B, double x) {
        double r1922599 = x;
        double r1922600 = 1.0;
        double r1922601 = B;
        double r1922602 = tan(r1922601);
        double r1922603 = r1922600 / r1922602;
        double r1922604 = r1922599 * r1922603;
        double r1922605 = -r1922604;
        double r1922606 = sin(r1922601);
        double r1922607 = r1922600 / r1922606;
        double r1922608 = r1922605 + r1922607;
        return r1922608;
}
↓
double f(double B, double x) {
        double r1922609 = 1.0;
        double r1922610 = B;
        double r1922611 = sin(r1922610);
        double r1922612 = r1922609 / r1922611;
        double r1922613 = 1.0;
        double r1922614 = tan(r1922610);
        double r1922615 = x;
        double r1922616 = r1922609 * r1922615;
        double r1922617 = r1922614 / r1922616;
        double r1922618 = r1922613 / r1922617;
        double r1922619 = r1922612 - r1922618;
        return r1922619;
}

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

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

  4. Applied clear-num0.2

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

  5. Final simplification0.2

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

Reproduce

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