Average Error: 0.2 → 0.2
Time: 5.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r13682 = x;
        double r13683 = 1.0;
        double r13684 = B;
        double r13685 = tan(r13684);
        double r13686 = r13683 / r13685;
        double r13687 = r13682 * r13686;
        double r13688 = -r13687;
        double r13689 = sin(r13684);
        double r13690 = r13683 / r13689;
        double r13691 = r13688 + r13690;
        return r13691;
}
↓
double f(double B, double x) {
        double r13692 = x;
        double r13693 = 1.0;
        double r13694 = r13692 * r13693;
        double r13695 = B;
        double r13696 = sin(r13695);
        double r13697 = r13694 / r13696;
        double r13698 = cos(r13695);
        double r13699 = r13697 * r13698;
        double r13700 = -r13699;
        double r13701 = r13693 / r13696;
        double r13702 = r13700 + r13701;
        return r13702;
}

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. Using strategy rm

  3. Applied associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))