Average Error: 0.2 → 0.2
Time: 4.0m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r1587703 = x;
        double r1587704 = 1.0;
        double r1587705 = B;
        double r1587706 = tan(r1587705);
        double r1587707 = r1587704 / r1587706;
        double r1587708 = r1587703 * r1587707;
        double r1587709 = -r1587708;
        double r1587710 = sin(r1587705);
        double r1587711 = r1587704 / r1587710;
        double r1587712 = r1587709 + r1587711;
        return r1587712;
}
↓
double f(double B, double x) {
        double r1587713 = 1.0;
        double r1587714 = B;
        double r1587715 = cos(r1587714);
        double r1587716 = x;
        double r1587717 = r1587715 * r1587716;
        double r1587718 = r1587713 - r1587717;
        double r1587719 = sin(r1587714);
        double r1587720 = r1587718 / r1587719;
        return r1587720;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot x}{\sin B}\]

Reproduce

herbie shell --seed 2019144 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))