Average Error: 0.1 → 0.1
Time: 38.1s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + \left(3 \cdot y\right) \cdot y\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + \left(3 \cdot y\right) \cdot y
double f(double x, double y) {
        double r594534 = x;
        double r594535 = r594534 * r594534;
        double r594536 = y;
        double r594537 = r594536 * r594536;
        double r594538 = r594535 + r594537;
        double r594539 = r594538 + r594537;
        double r594540 = r594539 + r594537;
        return r594540;
}
↓
double f(double x, double y) {
        double r594541 = x;
        double r594542 = r594541 * r594541;
        double r594543 = 3.0;
        double r594544 = y;
        double r594545 = r594543 * r594544;
        double r594546 = r594545 * r594544;
        double r594547 = r594542 + r594546;
        return r594547;
}

Error

Bits error versus x

Bits error versus y

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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 *-un-lft-identity0.1

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

  5. Applied associate-*l*0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))