Average Error: 0.2 → 0.2
Time: 1.7m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r625137 = x;
        double r625138 = 1.0;
        double r625139 = B;
        double r625140 = tan(r625139);
        double r625141 = r625138 / r625140;
        double r625142 = r625137 * r625141;
        double r625143 = -r625142;
        double r625144 = sin(r625139);
        double r625145 = r625138 / r625144;
        double r625146 = r625143 + r625145;
        return r625146;
}
↓
double f(double B, double x) {
        double r625147 = 1.0;
        double r625148 = B;
        double r625149 = sin(r625148);
        double r625150 = r625147 / r625149;
        double r625151 = x;
        double r625152 = cos(r625148);
        double r625153 = r625151 * r625152;
        double r625154 = r625153 / r625149;
        double r625155 = r625150 - r625154;
        return r625155;
}

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

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

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))