Average Error: 0.4 → 0.4
Time: 11.3s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)
double f(double x, double y) {
        double r7393335 = 3.0;
        double r7393336 = x;
        double r7393337 = sqrt(r7393336);
        double r7393338 = r7393335 * r7393337;
        double r7393339 = y;
        double r7393340 = 1.0;
        double r7393341 = 9.0;
        double r7393342 = r7393336 * r7393341;
        double r7393343 = r7393340 / r7393342;
        double r7393344 = r7393339 + r7393343;
        double r7393345 = r7393344 - r7393340;
        double r7393346 = r7393338 * r7393345;
        return r7393346;
}
↓
double f(double x, double y) {
        double r7393347 = 3.0;
        double r7393348 = x;
        double r7393349 = sqrt(r7393348);
        double r7393350 = y;
        double r7393351 = 1.0;
        double r7393352 = r7393351 / r7393348;
        double r7393353 = 9.0;
        double r7393354 = r7393352 / r7393353;
        double r7393355 = r7393350 + r7393354;
        double r7393356 = r7393355 - r7393351;
        double r7393357 = r7393349 * r7393356;
        double r7393358 = r7393347 * r7393357;
        return r7393358;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-/r*0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - 1.0\right)\right)\]

  6. Final simplification0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1.0}{x}}{9.0}\right) - 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))