Average Error: 0.4 → 0.5
Time: 23.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(y + \sqrt{\frac{\frac{1}{x}}{9}} \cdot \sqrt{\frac{\frac{1}{x}}{9}}\right)\right) + \left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(y + \sqrt{\frac{\frac{1}{x}}{9}} \cdot \sqrt{\frac{\frac{1}{x}}{9}}\right)\right) + \left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r338340 = 3.0;
        double r338341 = x;
        double r338342 = sqrt(r338341);
        double r338343 = r338340 * r338342;
        double r338344 = y;
        double r338345 = 1.0;
        double r338346 = 9.0;
        double r338347 = r338341 * r338346;
        double r338348 = r338345 / r338347;
        double r338349 = r338344 + r338348;
        double r338350 = r338349 - r338345;
        double r338351 = r338343 * r338350;
        return r338351;
}
↓
double f(double x, double y) {
        double r338352 = 3.0;
        double r338353 = x;
        double r338354 = sqrt(r338353);
        double r338355 = y;
        double r338356 = 1.0;
        double r338357 = r338356 / r338353;
        double r338358 = 9.0;
        double r338359 = r338357 / r338358;
        double r338360 = sqrt(r338359);
        double r338361 = r338360 * r338360;
        double r338362 = r338355 + r338361;
        double r338363 = r338354 * r338362;
        double r338364 = r338352 * r338363;
        double r338365 = -r338356;
        double r338366 = r338352 * r338354;
        double r338367 = r338365 * r338366;
        double r338368 = r338364 + r338367;
        return r338368;
}

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
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-/r*0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{\frac{1}{x}}{9}}\right) - 1\right)\]
  4. Using strategy rm

  5. Applied sub-neg0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\left(y + \frac{\frac{1}{x}}{9}\right) + \left(-1\right)\right)}\]

  6. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(3 \cdot \sqrt{x}\right) \cdot \left(-1\right)}\]

  7. Simplified0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \color{blue}{\left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)}\]
  8. Using strategy rm

  9. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{\frac{1}{x}}{9}\right)\right)} + \left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.5

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(y + \color{blue}{\sqrt{\frac{\frac{1}{x}}{9}} \cdot \sqrt{\frac{\frac{1}{x}}{9}}}\right)\right) + \left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]

  12. Final simplification0.5

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(y + \sqrt{\frac{\frac{1}{x}}{9}} \cdot \sqrt{\frac{\frac{1}{x}}{9}}\right)\right) + \left(-1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))