Average Error: 0.2 → 0.2
Time: 21.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r291746 = x;
        double r291747 = 1.0;
        double r291748 = B;
        double r291749 = tan(r291748);
        double r291750 = r291747 / r291749;
        double r291751 = r291746 * r291750;
        double r291752 = -r291751;
        double r291753 = sin(r291748);
        double r291754 = r291747 / r291753;
        double r291755 = r291752 + r291754;
        return r291755;
}
↓
double f(double B, double x) {
        double r291756 = 1.0;
        double r291757 = B;
        double r291758 = sin(r291757);
        double r291759 = r291756 / r291758;
        double r291760 = x;
        double r291761 = r291760 / r291758;
        double r291762 = cos(r291757);
        double r291763 = r291761 * r291762;
        double r291764 = r291759 - r291763;
        return r291764;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019155 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))