Average Error: 0.2 → 0.2
Time: 5.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r42688 = x;
        double r42689 = 1.0;
        double r42690 = B;
        double r42691 = tan(r42690);
        double r42692 = r42689 / r42691;
        double r42693 = r42688 * r42692;
        double r42694 = -r42693;
        double r42695 = sin(r42690);
        double r42696 = r42689 / r42695;
        double r42697 = r42694 + r42696;
        return r42697;
}
↓
double f(double B, double x) {
        double r42698 = 1.0;
        double r42699 = B;
        double r42700 = sin(r42699);
        double r42701 = r42698 / r42700;
        double r42702 = x;
        double r42703 = r42702 * r42698;
        double r42704 = r42703 / r42700;
        double r42705 = cos(r42699);
        double r42706 = r42704 * r42705;
        double r42707 = r42701 - r42706;
        return r42707;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))