Average Error: 0.2 → 0.2
Time: 4.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r47960 = x;
        double r47961 = 1.0;
        double r47962 = B;
        double r47963 = tan(r47962);
        double r47964 = r47961 / r47963;
        double r47965 = r47960 * r47964;
        double r47966 = -r47965;
        double r47967 = sin(r47962);
        double r47968 = r47961 / r47967;
        double r47969 = r47966 + r47968;
        return r47969;
}
↓
double f(double B, double x) {
        double r47970 = x;
        double r47971 = 1.0;
        double r47972 = r47970 * r47971;
        double r47973 = B;
        double r47974 = sin(r47973);
        double r47975 = r47972 / r47974;
        double r47976 = cos(r47973);
        double r47977 = r47975 * r47976;
        double r47978 = -r47977;
        double r47979 = r47971 / r47974;
        double r47980 = r47978 + r47979;
        return r47980;
}

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. Using strategy rm

  3. Applied associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

    \[\leadsto \left(-\frac{x \cdot 1}{\color{blue}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B}\]

  6. Applied associate-/r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\sin B} \cdot \cos B}\right) + \frac{1}{\sin B}\]

  7. Final simplification0.2

    \[\leadsto \left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))