Average Error: 0.2 → 0.2
Time: 10.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\frac{\sin B}{1 - x \cdot \cos B}}
double f(double B, double x) {
        double r17330 = x;
        double r17331 = 1.0;
        double r17332 = B;
        double r17333 = tan(r17332);
        double r17334 = r17331 / r17333;
        double r17335 = r17330 * r17334;
        double r17336 = -r17335;
        double r17337 = sin(r17332);
        double r17338 = r17331 / r17337;
        double r17339 = r17336 + r17338;
        return r17339;
}
↓
double f(double B, double x) {
        double r17340 = 1.0;
        double r17341 = B;
        double r17342 = sin(r17341);
        double r17343 = 1.0;
        double r17344 = x;
        double r17345 = cos(r17341);
        double r17346 = r17344 * r17345;
        double r17347 = r17343 - r17346;
        double r17348 = r17342 / r17347;
        double r17349 = r17340 / r17348;
        return r17349;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))