Average Error: 0.2 → 0.2
Time: 17.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B} \cdot 1\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B} \cdot 1
double f(double B, double x) {
        double r812881 = x;
        double r812882 = 1.0;
        double r812883 = B;
        double r812884 = tan(r812883);
        double r812885 = r812882 / r812884;
        double r812886 = r812881 * r812885;
        double r812887 = -r812886;
        double r812888 = sin(r812883);
        double r812889 = r812882 / r812888;
        double r812890 = r812887 + r812889;
        return r812890;
}
↓
double f(double B, double x) {
        double r812891 = 1.0;
        double r812892 = B;
        double r812893 = sin(r812892);
        double r812894 = r812891 / r812893;
        double r812895 = x;
        double r812896 = cos(r812892);
        double r812897 = r812895 * r812896;
        double r812898 = r812897 / r812893;
        double r812899 = r812898 * r812891;
        double r812900 = r812894 - r812899;
        return r812900;
}

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

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

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

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