Average Error: 0.2 → 0.2
Time: 4.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \frac{1 - x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \frac{1 - x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r55457 = x;
        double r55458 = 1.0;
        double r55459 = B;
        double r55460 = tan(r55459);
        double r55461 = r55458 / r55460;
        double r55462 = r55457 * r55461;
        double r55463 = -r55462;
        double r55464 = sin(r55459);
        double r55465 = r55458 / r55464;
        double r55466 = r55463 + r55465;
        return r55466;
}
↓
double f(double B, double x) {
        double r55467 = 1.0;
        double r55468 = 1.0;
        double r55469 = x;
        double r55470 = B;
        double r55471 = cos(r55470);
        double r55472 = r55469 * r55471;
        double r55473 = r55468 - r55472;
        double r55474 = sin(r55470);
        double r55475 = r55473 / r55474;
        double r55476 = r55467 * r55475;
        return r55476;
}

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. Taylor expanded around inf 0.2

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

  3. Simplified0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))