Average Error: 0.2 → 0.2
Time: 20.2s
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 r1042807 = x;
        double r1042808 = 1.0;
        double r1042809 = B;
        double r1042810 = tan(r1042809);
        double r1042811 = r1042808 / r1042810;
        double r1042812 = r1042807 * r1042811;
        double r1042813 = -r1042812;
        double r1042814 = sin(r1042809);
        double r1042815 = r1042808 / r1042814;
        double r1042816 = r1042813 + r1042815;
        return r1042816;
}
↓
double f(double B, double x) {
        double r1042817 = 1.0;
        double r1042818 = B;
        double r1042819 = sin(r1042818);
        double r1042820 = r1042817 / r1042819;
        double r1042821 = x;
        double r1042822 = cos(r1042818);
        double r1042823 = r1042821 * r1042822;
        double r1042824 = r1042823 / r1042819;
        double r1042825 = r1042824 * r1042817;
        double r1042826 = r1042820 - r1042825;
        return r1042826;
}

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

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

  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 2019170 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))