Average Error: 0.2 → 0.2
Time: 5.8s
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 r13734 = x;
        double r13735 = 1.0;
        double r13736 = B;
        double r13737 = tan(r13736);
        double r13738 = r13735 / r13737;
        double r13739 = r13734 * r13738;
        double r13740 = -r13739;
        double r13741 = sin(r13736);
        double r13742 = r13735 / r13741;
        double r13743 = r13740 + r13742;
        return r13743;
}
↓
double f(double B, double x) {
        double r13744 = 1.0;
        double r13745 = x;
        double r13746 = B;
        double r13747 = cos(r13746);
        double r13748 = r13745 * r13747;
        double r13749 = sin(r13746);
        double r13750 = r13748 / r13749;
        double r13751 = r13744 * r13750;
        double r13752 = -r13751;
        double r13753 = r13744 / r13749;
        double r13754 = r13752 + r13753;
        return r13754;
}

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