Average Error: 0.1 → 0.1
Time: 3.5s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + 3 \cdot \left(y \cdot y\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + 3 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r303740 = x;
        double r303741 = r303740 * r303740;
        double r303742 = y;
        double r303743 = r303742 * r303742;
        double r303744 = r303741 + r303743;
        double r303745 = r303744 + r303743;
        double r303746 = r303745 + r303743;
        return r303746;
}
↓
double f(double x, double y) {
        double r303747 = x;
        double r303748 = r303747 * r303747;
        double r303749 = 3.0;
        double r303750 = y;
        double r303751 = r303750 * r303750;
        double r303752 = r303749 * r303751;
        double r303753 = r303748 + r303752;
        return r303753;
}

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 +-commutative0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))