Average Error: 0.2 → 0.2
Time: 19.7s
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 r1922597 = x;
        double r1922598 = 1.0;
        double r1922599 = B;
        double r1922600 = tan(r1922599);
        double r1922601 = r1922598 / r1922600;
        double r1922602 = r1922597 * r1922601;
        double r1922603 = -r1922602;
        double r1922604 = sin(r1922599);
        double r1922605 = r1922598 / r1922604;
        double r1922606 = r1922603 + r1922605;
        return r1922606;
}
↓
double f(double B, double x) {
        double r1922607 = 1.0;
        double r1922608 = B;
        double r1922609 = sin(r1922608);
        double r1922610 = r1922607 / r1922609;
        double r1922611 = 1.0;
        double r1922612 = tan(r1922608);
        double r1922613 = x;
        double r1922614 = r1922607 * r1922613;
        double r1922615 = r1922612 / r1922614;
        double r1922616 = r1922611 / r1922615;
        double r1922617 = r1922610 - r1922616;
        return r1922617;
}

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))))