Average Error: 0.2 → 0.2
Time: 5.4s
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 r40932 = x;
        double r40933 = 1.0;
        double r40934 = B;
        double r40935 = tan(r40934);
        double r40936 = r40933 / r40935;
        double r40937 = r40932 * r40936;
        double r40938 = -r40937;
        double r40939 = sin(r40934);
        double r40940 = r40933 / r40939;
        double r40941 = r40938 + r40940;
        return r40941;
}
↓
double f(double B, double x) {
        double r40942 = 1.0;
        double r40943 = 1.0;
        double r40944 = B;
        double r40945 = sin(r40944);
        double r40946 = r40943 / r40945;
        double r40947 = x;
        double r40948 = cos(r40944);
        double r40949 = r40947 * r40948;
        double r40950 = r40949 / r40945;
        double r40951 = r40946 - r40950;
        double r40952 = r40942 * r40951;
        return r40952;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))