Average Error: 0.2 → 0.2
Time: 20.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r45687 = x;
        double r45688 = 1.0;
        double r45689 = B;
        double r45690 = tan(r45689);
        double r45691 = r45688 / r45690;
        double r45692 = r45687 * r45691;
        double r45693 = -r45692;
        double r45694 = sin(r45689);
        double r45695 = r45688 / r45694;
        double r45696 = r45693 + r45695;
        return r45696;
}
↓
double f(double B, double x) {
        double r45697 = 1.0;
        double r45698 = x;
        double r45699 = r45698 * r45697;
        double r45700 = B;
        double r45701 = cos(r45700);
        double r45702 = r45699 * r45701;
        double r45703 = r45697 - r45702;
        double r45704 = sin(r45700);
        double r45705 = r45703 / r45704;
        return r45705;
}

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

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

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  9. Applied associate-*l/0.2

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

  10. Applied sub-div0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))