Average Error: 0.2 → 0.3
Time: 6.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r17748 = x;
        double r17749 = 1.0;
        double r17750 = B;
        double r17751 = tan(r17750);
        double r17752 = r17749 / r17751;
        double r17753 = r17748 * r17752;
        double r17754 = -r17753;
        double r17755 = sin(r17750);
        double r17756 = r17749 / r17755;
        double r17757 = r17754 + r17756;
        return r17757;
}
↓
double f(double B, double x) {
        double r17758 = x;
        double r17759 = 1.0;
        double r17760 = B;
        double r17761 = sin(r17760);
        double r17762 = r17759 / r17761;
        double r17763 = r17758 * r17762;
        double r17764 = cos(r17760);
        double r17765 = r17763 * r17764;
        double r17766 = -r17765;
        double r17767 = r17766 + r17762;
        return r17767;
}

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 tan-quot0.2

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

  4. Applied associate-/r/0.2

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

  5. Applied associate-*r*0.3

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

  6. Final simplification0.3

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

Reproduce

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