Average Error: 0.2 → 0.2
Time: 5.1s
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 r53509 = x;
        double r53510 = 1.0;
        double r53511 = B;
        double r53512 = tan(r53511);
        double r53513 = r53510 / r53512;
        double r53514 = r53509 * r53513;
        double r53515 = -r53514;
        double r53516 = sin(r53511);
        double r53517 = r53510 / r53516;
        double r53518 = r53515 + r53517;
        return r53518;
}
↓
double f(double B, double x) {
        double r53519 = 1.0;
        double r53520 = x;
        double r53521 = r53520 * r53519;
        double r53522 = B;
        double r53523 = cos(r53522);
        double r53524 = r53521 * r53523;
        double r53525 = r53519 - r53524;
        double r53526 = sin(r53522);
        double r53527 = r53525 / r53526;
        return r53527;
}

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 2020049 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))