Average Error: 0.2 → 0.2
Time: 25.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \cos B \cdot \frac{x \cdot 1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \cos B \cdot \frac{x \cdot 1}{\sin B}
double f(double B, double x) {
        double r770918 = x;
        double r770919 = 1.0;
        double r770920 = B;
        double r770921 = tan(r770920);
        double r770922 = r770919 / r770921;
        double r770923 = r770918 * r770922;
        double r770924 = -r770923;
        double r770925 = sin(r770920);
        double r770926 = r770919 / r770925;
        double r770927 = r770924 + r770926;
        return r770927;
}
↓
double f(double B, double x) {
        double r770928 = 1.0;
        double r770929 = B;
        double r770930 = sin(r770929);
        double r770931 = r770928 / r770930;
        double r770932 = cos(r770929);
        double r770933 = x;
        double r770934 = r770933 * r770928;
        double r770935 = r770934 / r770930;
        double r770936 = r770932 * r770935;
        double r770937 = r770931 - r770936;
        return r770937;
}

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 tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))