Average Error: 0.2 → 0.2
Time: 5.5s
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 r42769 = x;
        double r42770 = 1.0;
        double r42771 = B;
        double r42772 = tan(r42771);
        double r42773 = r42770 / r42772;
        double r42774 = r42769 * r42773;
        double r42775 = -r42774;
        double r42776 = sin(r42771);
        double r42777 = r42770 / r42776;
        double r42778 = r42775 + r42777;
        return r42778;
}
↓
double f(double B, double x) {
        double r42779 = x;
        double r42780 = 1.0;
        double r42781 = r42779 * r42780;
        double r42782 = B;
        double r42783 = sin(r42782);
        double r42784 = r42781 / r42783;
        double r42785 = cos(r42782);
        double r42786 = r42784 * r42785;
        double r42787 = -r42786;
        double r42788 = r42780 / r42783;
        double r42789 = r42787 + r42788;
        return r42789;
}

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 2019353 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))