Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r37546 = x;
        double r37547 = 1.0;
        double r37548 = B;
        double r37549 = tan(r37548);
        double r37550 = r37547 / r37549;
        double r37551 = r37546 * r37550;
        double r37552 = -r37551;
        double r37553 = sin(r37548);
        double r37554 = r37547 / r37553;
        double r37555 = r37552 + r37554;
        return r37555;
}
↓
double f(double B, double x) {
        double r37556 = 1.0;
        double r37557 = 1.0;
        double r37558 = B;
        double r37559 = sin(r37558);
        double r37560 = r37557 / r37559;
        double r37561 = x;
        double r37562 = cos(r37558);
        double r37563 = r37561 * r37562;
        double r37564 = r37563 / r37559;
        double r37565 = r37560 - r37564;
        double r37566 = r37556 * r37565;
        return r37566;
}

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. Using strategy rm

  3. Applied associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  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. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))