Average Error: 0.2 → 0.2
Time: 6.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r15887 = x;
        double r15888 = 1.0;
        double r15889 = B;
        double r15890 = tan(r15889);
        double r15891 = r15888 / r15890;
        double r15892 = r15887 * r15891;
        double r15893 = -r15892;
        double r15894 = sin(r15889);
        double r15895 = r15888 / r15894;
        double r15896 = r15893 + r15895;
        return r15896;
}
↓
double f(double B, double x) {
        double r15897 = 1.0;
        double r15898 = x;
        double r15899 = B;
        double r15900 = cos(r15899);
        double r15901 = r15898 * r15900;
        double r15902 = sin(r15899);
        double r15903 = r15901 / r15902;
        double r15904 = r15897 * r15903;
        double r15905 = -r15904;
        double r15906 = r15897 / r15902;
        double r15907 = r15905 + r15906;
        return r15907;
}

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. Taylor expanded around inf 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))