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 r38637 = x;
        double r38638 = 1.0;
        double r38639 = B;
        double r38640 = tan(r38639);
        double r38641 = r38638 / r38640;
        double r38642 = r38637 * r38641;
        double r38643 = -r38642;
        double r38644 = sin(r38639);
        double r38645 = r38638 / r38644;
        double r38646 = r38643 + r38645;
        return r38646;
}
↓
double f(double B, double x) {
        double r38647 = 1.0;
        double r38648 = B;
        double r38649 = sin(r38648);
        double r38650 = r38647 / r38649;
        double r38651 = x;
        double r38652 = r38651 * r38647;
        double r38653 = r38652 / r38649;
        double r38654 = cos(r38648);
        double r38655 = r38653 * r38654;
        double r38656 = r38650 - r38655;
        return r38656;
}

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 2020081 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))