Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)
double f(double B, double x) {
        double r18713 = x;
        double r18714 = 1.0;
        double r18715 = B;
        double r18716 = tan(r18715);
        double r18717 = r18714 / r18716;
        double r18718 = r18713 * r18717;
        double r18719 = -r18718;
        double r18720 = sin(r18715);
        double r18721 = r18714 / r18720;
        double r18722 = r18719 + r18721;
        return r18722;
}
↓
double f(double B, double x) {
        double r18723 = 1.0;
        double r18724 = B;
        double r18725 = sin(r18724);
        double r18726 = r18723 / r18725;
        double r18727 = x;
        double r18728 = cos(r18724);
        double r18729 = r18728 / r18725;
        double r18730 = r18723 * r18729;
        double r18731 = r18727 * r18730;
        double r18732 = r18726 - r18731;
        return r18732;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))