Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r59749 = x;
        double r59750 = 1.0;
        double r59751 = B;
        double r59752 = tan(r59751);
        double r59753 = r59750 / r59752;
        double r59754 = r59749 * r59753;
        double r59755 = -r59754;
        double r59756 = sin(r59751);
        double r59757 = r59750 / r59756;
        double r59758 = r59755 + r59757;
        return r59758;
}
↓
double f(double B, double x) {
        double r59759 = x;
        double r59760 = 1.0;
        double r59761 = B;
        double r59762 = sin(r59761);
        double r59763 = r59760 / r59762;
        double r59764 = cos(r59761);
        double r59765 = r59763 * r59764;
        double r59766 = r59759 * r59765;
        double r59767 = -r59766;
        double r59768 = r59767 + r59763;
        return r59768;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))