Average Error: 0.2 → 0.2
Time: 20.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{1 \cdot x}}
double f(double B, double x) {
        double r961124 = x;
        double r961125 = 1.0;
        double r961126 = B;
        double r961127 = tan(r961126);
        double r961128 = r961125 / r961127;
        double r961129 = r961124 * r961128;
        double r961130 = -r961129;
        double r961131 = sin(r961126);
        double r961132 = r961125 / r961131;
        double r961133 = r961130 + r961132;
        return r961133;
}
↓
double f(double B, double x) {
        double r961134 = 1.0;
        double r961135 = B;
        double r961136 = sin(r961135);
        double r961137 = r961134 / r961136;
        double r961138 = 1.0;
        double r961139 = tan(r961135);
        double r961140 = x;
        double r961141 = r961134 * r961140;
        double r961142 = r961139 / r961141;
        double r961143 = r961138 / r961142;
        double r961144 = r961137 - r961143;
        return r961144;
}

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. Using strategy rm

  4. Applied clear-num0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))