Average Error: 0.1 → 0.1
Time: 10.9s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot y + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(3 \cdot y\right) \cdot y + x \cdot x
double f(double x, double y) {
        double r556469 = x;
        double r556470 = r556469 * r556469;
        double r556471 = y;
        double r556472 = r556471 * r556471;
        double r556473 = r556470 + r556472;
        double r556474 = r556473 + r556472;
        double r556475 = r556474 + r556472;
        return r556475;
}
↓
double f(double x, double y) {
        double r556476 = 3.0;
        double r556477 = y;
        double r556478 = r556476 * r556477;
        double r556479 = r556478 * r556477;
        double r556480 = x;
        double r556481 = r556480 * r556480;
        double r556482 = r556479 + r556481;
        return r556482;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right)\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(y \cdot y\right) + x \cdot x}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(3 \cdot y\right) \cdot y} + x \cdot x\]

  5. Final simplification0.1

    \[\leadsto \left(3 \cdot y\right) \cdot y + x \cdot x\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

  :herbie-target
  (+ (* x x) (* y (+ y (+ y y))))

  (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))