Average Error: 0.2 → 0.2
Time: 14.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\tan B}
double f(double B, double x) {
        double r23339 = x;
        double r23340 = 1.0;
        double r23341 = B;
        double r23342 = tan(r23341);
        double r23343 = r23340 / r23342;
        double r23344 = r23339 * r23343;
        double r23345 = -r23344;
        double r23346 = sin(r23341);
        double r23347 = r23340 / r23346;
        double r23348 = r23345 + r23347;
        return r23348;
}
↓
double f(double B, double x) {
        double r23349 = 1.0;
        double r23350 = B;
        double r23351 = sin(r23350);
        double r23352 = r23349 / r23351;
        double r23353 = x;
        double r23354 = r23353 * r23349;
        double r23355 = tan(r23350);
        double r23356 = r23354 / r23355;
        double r23357 = r23352 - r23356;
        return r23357;
}

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/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019294 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))