Average Error: 0.2 → 0.2
Time: 20.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r39325 = x;
        double r39326 = 1.0;
        double r39327 = B;
        double r39328 = tan(r39327);
        double r39329 = r39326 / r39328;
        double r39330 = r39325 * r39329;
        double r39331 = -r39330;
        double r39332 = sin(r39327);
        double r39333 = r39326 / r39332;
        double r39334 = r39331 + r39333;
        return r39334;
}
↓
double f(double B, double x) {
        double r39335 = 1.0;
        double r39336 = B;
        double r39337 = sin(r39336);
        double r39338 = r39335 / r39337;
        double r39339 = x;
        double r39340 = r39339 * r39335;
        double r39341 = r39340 / r39337;
        double r39342 = cos(r39336);
        double r39343 = r39341 * r39342;
        double r39344 = r39338 - r39343;
        return r39344;
}

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. Using strategy rm

  4. Applied associate-*r/0.1

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))