Average Error: 0.4 → 0.5
Time: 15.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) - 1\right)\right)\]
\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(\left(y + \sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}}\right) - 1\right)\right)
double f(double x, double y) {
        double r334410 = 3.0;
        double r334411 = x;
        double r334412 = sqrt(r334411);
        double r334413 = r334410 * r334412;
        double r334414 = y;
        double r334415 = 1.0;
        double r334416 = 9.0;
        double r334417 = r334411 * r334416;
        double r334418 = r334415 / r334417;
        double r334419 = r334414 + r334418;
        double r334420 = r334419 - r334415;
        double r334421 = r334413 * r334420;
        return r334421;
}
↓
double f(double x, double y) {
        double r334422 = 3.0;
        double r334423 = x;
        double r334424 = sqrt(r334423);
        double r334425 = y;
        double r334426 = 1.0;
        double r334427 = 9.0;
        double r334428 = r334423 * r334427;
        double r334429 = r334426 / r334428;
        double r334430 = sqrt(r334429);
        double r334431 = r334430 * r334430;
        double r334432 = r334425 + r334431;
        double r334433 = r334432 - r334426;
        double r334434 = r334424 * r334433;
        double r334435 = r334422 * r334434;
        return r334435;
}

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-*l*0.4

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

  5. Applied add-sqr-sqrt0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019305 
(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)))