Average Error: 0.2 → 0.2
Time: 18.0s
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 r788334 = x;
        double r788335 = 1.0;
        double r788336 = B;
        double r788337 = tan(r788336);
        double r788338 = r788335 / r788337;
        double r788339 = r788334 * r788338;
        double r788340 = -r788339;
        double r788341 = sin(r788336);
        double r788342 = r788335 / r788341;
        double r788343 = r788340 + r788342;
        return r788343;
}
↓
double f(double B, double x) {
        double r788344 = 1.0;
        double r788345 = B;
        double r788346 = cos(r788345);
        double r788347 = x;
        double r788348 = r788346 * r788347;
        double r788349 = r788344 - r788348;
        double r788350 = sin(r788345);
        double r788351 = r788349 / r788350;
        return r788351;
}

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 2019154 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))