Average Error: 0.2 → 0.2
Time: 4.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r9793 = x;
        double r9794 = 1.0;
        double r9795 = B;
        double r9796 = tan(r9795);
        double r9797 = r9794 / r9796;
        double r9798 = r9793 * r9797;
        double r9799 = -r9798;
        double r9800 = sin(r9795);
        double r9801 = r9794 / r9800;
        double r9802 = r9799 + r9801;
        return r9802;
}
↓
double f(double B, double x) {
        double r9803 = x;
        double r9804 = 1.0;
        double r9805 = r9803 * r9804;
        double r9806 = B;
        double r9807 = sin(r9806);
        double r9808 = r9805 / r9807;
        double r9809 = cos(r9806);
        double r9810 = r9808 * r9809;
        double r9811 = -r9810;
        double r9812 = r9804 / r9807;
        double r9813 = r9811 + r9812;
        return r9813;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))