Average Error: 0.4 → 0.4
Time: 20.4s
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 r20488513 = 3.0;
        double r20488514 = x;
        double r20488515 = sqrt(r20488514);
        double r20488516 = r20488513 * r20488515;
        double r20488517 = y;
        double r20488518 = 1.0;
        double r20488519 = 9.0;
        double r20488520 = r20488514 * r20488519;
        double r20488521 = r20488518 / r20488520;
        double r20488522 = r20488517 + r20488521;
        double r20488523 = r20488522 - r20488518;
        double r20488524 = r20488516 * r20488523;
        return r20488524;
}
↓
double f(double x, double y) {
        double r20488525 = 3.0;
        double r20488526 = x;
        double r20488527 = sqrt(r20488526);
        double r20488528 = y;
        double r20488529 = 1.0;
        double r20488530 = r20488529 / r20488526;
        double r20488531 = 9.0;
        double r20488532 = r20488530 / r20488531;
        double r20488533 = r20488528 + r20488532;
        double r20488534 = r20488533 - r20488529;
        double r20488535 = r20488527 * r20488534;
        double r20488536 = r20488525 * r20488535;
        return r20488536;
}

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 2019164 +o rules:numerics
(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)))