Average Error: 0.2 → 0.2
Time: 18.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \frac{1 - x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \frac{1 - x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r35713 = x;
        double r35714 = 1.0;
        double r35715 = B;
        double r35716 = tan(r35715);
        double r35717 = r35714 / r35716;
        double r35718 = r35713 * r35717;
        double r35719 = -r35718;
        double r35720 = sin(r35715);
        double r35721 = r35714 / r35720;
        double r35722 = r35719 + r35721;
        return r35722;
}
↓
double f(double B, double x) {
        double r35723 = 1.0;
        double r35724 = 1.0;
        double r35725 = x;
        double r35726 = B;
        double r35727 = cos(r35726);
        double r35728 = r35725 * r35727;
        double r35729 = r35724 - r35728;
        double r35730 = sin(r35726);
        double r35731 = r35729 / r35730;
        double r35732 = r35723 * r35731;
        return r35732;
}

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/0.1

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

  8. Applied *-un-lft-identity0.2

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

  9. Applied *-un-lft-identity0.2

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

  10. Applied distribute-lft-out0.2

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

  11. Simplified0.2

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

  13. Applied sub-div0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))