Average Error: 0.2 → 0.2
Time: 21.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(1 \cdot \frac{-1}{\frac{\sin B}{x}}\right) \cdot \cos B + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(1 \cdot \frac{-1}{\frac{\sin B}{x}}\right) \cdot \cos B + \frac{1}{\sin B}
double f(double B, double x) {
        double r40296 = x;
        double r40297 = 1.0;
        double r40298 = B;
        double r40299 = tan(r40298);
        double r40300 = r40297 / r40299;
        double r40301 = r40296 * r40300;
        double r40302 = -r40301;
        double r40303 = sin(r40298);
        double r40304 = r40297 / r40303;
        double r40305 = r40302 + r40304;
        return r40305;
}
↓
double f(double B, double x) {
        double r40306 = 1.0;
        double r40307 = -1.0;
        double r40308 = B;
        double r40309 = sin(r40308);
        double r40310 = x;
        double r40311 = r40309 / r40310;
        double r40312 = r40307 / r40311;
        double r40313 = r40306 * r40312;
        double r40314 = cos(r40308);
        double r40315 = r40313 * r40314;
        double r40316 = r40306 / r40309;
        double r40317 = r40315 + r40316;
        return r40317;
}

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. Using strategy rm

  3. Applied tan-quot0.2

    \[\leadsto \left(-x \cdot \frac{1}{\color{blue}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B}\]

  4. Applied associate-/r/0.2

    \[\leadsto \left(-x \cdot \color{blue}{\left(\frac{1}{\sin B} \cdot \cos B\right)}\right) + \frac{1}{\sin B}\]

  5. Applied associate-*r*0.2

    \[\leadsto \left(-\color{blue}{\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B}\right) + \frac{1}{\sin B}\]

  6. Simplified0.2

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

  8. Applied clear-num0.2

    \[\leadsto \left(-\left(1 \cdot \color{blue}{\frac{1}{\frac{\sin B}{x}}}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]

  9. Final simplification0.2

    \[\leadsto \left(1 \cdot \frac{-1}{\frac{\sin B}{x}}\right) \cdot \cos B + \frac{1}{\sin B}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))