Average Error: 0.2 → 0.2
Time: 8.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r17881 = x;
        double r17882 = 1.0;
        double r17883 = B;
        double r17884 = tan(r17883);
        double r17885 = r17882 / r17884;
        double r17886 = r17881 * r17885;
        double r17887 = -r17886;
        double r17888 = sin(r17883);
        double r17889 = r17882 / r17888;
        double r17890 = r17887 + r17889;
        return r17890;
}
↓
double f(double B, double x) {
        double r17891 = 1.0;
        double r17892 = 1.0;
        double r17893 = B;
        double r17894 = sin(r17893);
        double r17895 = r17892 / r17894;
        double r17896 = x;
        double r17897 = cos(r17893);
        double r17898 = r17896 * r17897;
        double r17899 = r17898 / r17894;
        double r17900 = r17895 - r17899;
        double r17901 = r17891 * r17900;
        return r17901;
}

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. Taylor expanded around inf 0.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))