Average Error: 0.2 → 0.2
Time: 21.2s
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 r323323 = x;
        double r323324 = 1.0;
        double r323325 = B;
        double r323326 = tan(r323325);
        double r323327 = r323324 / r323326;
        double r323328 = r323323 * r323327;
        double r323329 = -r323328;
        double r323330 = sin(r323325);
        double r323331 = r323324 / r323330;
        double r323332 = r323329 + r323331;
        return r323332;
}
↓
double f(double B, double x) {
        double r323333 = 1.0;
        double r323334 = B;
        double r323335 = cos(r323334);
        double r323336 = x;
        double r323337 = r323335 * r323336;
        double r323338 = r323333 - r323337;
        double r323339 = sin(r323334);
        double r323340 = r323338 / r323339;
        return r323340;
}

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

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

  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 2019153 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))