Average Error: 0.2 → 0.3
Time: 10.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r17883 = x;
        double r17884 = 1.0;
        double r17885 = B;
        double r17886 = tan(r17885);
        double r17887 = r17884 / r17886;
        double r17888 = r17883 * r17887;
        double r17889 = -r17888;
        double r17890 = sin(r17885);
        double r17891 = r17884 / r17890;
        double r17892 = r17889 + r17891;
        return r17892;
}
↓
double f(double B, double x) {
        double r17893 = x;
        double r17894 = 1.0;
        double r17895 = B;
        double r17896 = sin(r17895);
        double r17897 = r17894 / r17896;
        double r17898 = r17893 * r17897;
        double r17899 = cos(r17895);
        double r17900 = r17898 * r17899;
        double r17901 = -r17900;
        double r17902 = r17901 + r17897;
        return r17902;
}

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 tan-quot0.2

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

  4. Applied associate-/r/0.2

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

  5. Applied associate-*r*0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))