Average Error: 0.2 → 0.2
Time: 18.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}
double f(double B, double x) {
        double r21966 = x;
        double r21967 = 1.0;
        double r21968 = B;
        double r21969 = tan(r21968);
        double r21970 = r21967 / r21969;
        double r21971 = r21966 * r21970;
        double r21972 = -r21971;
        double r21973 = sin(r21968);
        double r21974 = r21967 / r21973;
        double r21975 = r21972 + r21974;
        return r21975;
}
↓
double f(double B, double x) {
        double r21976 = 1.0;
        double r21977 = B;
        double r21978 = sin(r21977);
        double r21979 = 1.0;
        double r21980 = x;
        double r21981 = cos(r21977);
        double r21982 = r21980 * r21981;
        double r21983 = r21979 - r21982;
        double r21984 = r21978 / r21983;
        double r21985 = r21976 / r21984;
        return r21985;
}

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

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

Reproduce

herbie shell --seed 2019291 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))