Average Error: 0.2 → 0.2
Time: 57.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r1082865 = x;
        double r1082866 = 1.0;
        double r1082867 = B;
        double r1082868 = tan(r1082867);
        double r1082869 = r1082866 / r1082868;
        double r1082870 = r1082865 * r1082869;
        double r1082871 = -r1082870;
        double r1082872 = sin(r1082867);
        double r1082873 = r1082866 / r1082872;
        double r1082874 = r1082871 + r1082873;
        return r1082874;
}
↓
double f(double B, double x) {
        double r1082875 = 1.0;
        double r1082876 = B;
        double r1082877 = sin(r1082876);
        double r1082878 = r1082875 / r1082877;
        double r1082879 = x;
        double r1082880 = r1082879 / r1082877;
        double r1082881 = cos(r1082876);
        double r1082882 = r1082880 * r1082881;
        double r1082883 = r1082878 - r1082882;
        return r1082883;
}

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. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019152 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))