Average Error: 0.2 → 0.2
Time: 8.2s
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 r22037 = x;
        double r22038 = 1.0;
        double r22039 = B;
        double r22040 = tan(r22039);
        double r22041 = r22038 / r22040;
        double r22042 = r22037 * r22041;
        double r22043 = -r22042;
        double r22044 = sin(r22039);
        double r22045 = r22038 / r22044;
        double r22046 = r22043 + r22045;
        return r22046;
}
↓
double f(double B, double x) {
        double r22047 = 1.0;
        double r22048 = x;
        double r22049 = B;
        double r22050 = cos(r22049);
        double r22051 = r22048 * r22050;
        double r22052 = sin(r22049);
        double r22053 = r22051 / r22052;
        double r22054 = r22047 * r22053;
        double r22055 = -r22054;
        double r22056 = r22047 / r22052;
        double r22057 = r22055 + r22056;
        return r22057;
}

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 2019322 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))