Average Error: 0.2 → 0.2
Time: 20.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} + \left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right)
double f(double B, double x) {
        double r22784 = x;
        double r22785 = 1.0;
        double r22786 = B;
        double r22787 = tan(r22786);
        double r22788 = r22785 / r22787;
        double r22789 = r22784 * r22788;
        double r22790 = -r22789;
        double r22791 = sin(r22786);
        double r22792 = r22785 / r22791;
        double r22793 = r22790 + r22792;
        return r22793;
}
↓
double f(double B, double x) {
        double r22794 = 1.0;
        double r22795 = B;
        double r22796 = sin(r22795);
        double r22797 = r22794 / r22796;
        double r22798 = x;
        double r22799 = r22798 / r22796;
        double r22800 = r22794 * r22799;
        double r22801 = cos(r22795);
        double r22802 = r22800 * r22801;
        double r22803 = -r22802;
        double r22804 = r22797 + r22803;
        return r22804;
}

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*0.2

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

  7. Simplified0.2

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

  9. Applied sub-neg0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))