Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)
double f(double B, double x) {
        double r12726 = x;
        double r12727 = 1.0;
        double r12728 = B;
        double r12729 = tan(r12728);
        double r12730 = r12727 / r12729;
        double r12731 = r12726 * r12730;
        double r12732 = -r12731;
        double r12733 = sin(r12728);
        double r12734 = r12727 / r12733;
        double r12735 = r12732 + r12734;
        return r12735;
}
↓
double f(double B, double x) {
        double r12736 = 1.0;
        double r12737 = B;
        double r12738 = sin(r12737);
        double r12739 = r12736 / r12738;
        double r12740 = x;
        double r12741 = cos(r12737);
        double r12742 = r12739 * r12741;
        double r12743 = r12740 * r12742;
        double r12744 = r12739 - r12743;
        return r12744;
}

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 tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Applied associate-*r*0.3

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

  8. Applied associate-*l*0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))