Average Error: 0.2 → 0.2
Time: 11.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r39699 = x;
        double r39700 = 1.0;
        double r39701 = B;
        double r39702 = tan(r39701);
        double r39703 = r39700 / r39702;
        double r39704 = r39699 * r39703;
        double r39705 = -r39704;
        double r39706 = sin(r39701);
        double r39707 = r39700 / r39706;
        double r39708 = r39705 + r39707;
        return r39708;
}
↓
double f(double B, double x) {
        double r39709 = 1.0;
        double r39710 = B;
        double r39711 = sin(r39710);
        double r39712 = r39709 / r39711;
        double r39713 = x;
        double r39714 = cos(r39710);
        double r39715 = r39713 * r39714;
        double r39716 = r39715 / r39711;
        double r39717 = r39709 * r39716;
        double r39718 = r39712 - r39717;
        return r39718;
}

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. Using strategy rm

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

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

  8. Applied associate-*l*0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

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