Average Error: 0.2 → 0.2
Time: 8.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r18688 = x;
        double r18689 = 1.0;
        double r18690 = B;
        double r18691 = tan(r18690);
        double r18692 = r18689 / r18691;
        double r18693 = r18688 * r18692;
        double r18694 = -r18693;
        double r18695 = sin(r18690);
        double r18696 = r18689 / r18695;
        double r18697 = r18694 + r18696;
        return r18697;
}
↓
double f(double B, double x) {
        double r18698 = 1.0;
        double r18699 = x;
        double r18700 = B;
        double r18701 = cos(r18700);
        double r18702 = r18699 * r18701;
        double r18703 = sin(r18700);
        double r18704 = r18702 / r18703;
        double r18705 = r18698 * r18704;
        double r18706 = -r18705;
        double r18707 = r18698 / r18703;
        double r18708 = r18706 + r18707;
        return r18708;
}

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/0.1

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

  4. Taylor expanded around inf 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))