Average Error: 0.2 → 0.2
Time: 18.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}
double f(double B, double x) {
        double r2116799 = x;
        double r2116800 = 1.0;
        double r2116801 = B;
        double r2116802 = tan(r2116801);
        double r2116803 = r2116800 / r2116802;
        double r2116804 = r2116799 * r2116803;
        double r2116805 = -r2116804;
        double r2116806 = sin(r2116801);
        double r2116807 = r2116800 / r2116806;
        double r2116808 = r2116805 + r2116807;
        return r2116808;
}
↓
double f(double B, double x) {
        double r2116809 = 1.0;
        double r2116810 = B;
        double r2116811 = cos(r2116810);
        double r2116812 = x;
        double r2116813 = r2116809 * r2116812;
        double r2116814 = r2116811 * r2116813;
        double r2116815 = r2116809 - r2116814;
        double r2116816 = sin(r2116810);
        double r2116817 = r2116815 / r2116816;
        return r2116817;
}

Error

Bits error versus B

Bits error versus x

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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

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

  4. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{1 \cdot x}{\sin B} \cdot \cos B}\]
  5. Using strategy rm

  6. Applied associate-*l/0.2

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

  7. Applied sub-div0.2

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

  8. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))