Average Error: 0.1 → 0.1
Time: 12.8s
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 r25564520 = x;
        double r25564521 = r25564520 * r25564520;
        double r25564522 = y;
        double r25564523 = r25564522 * r25564522;
        double r25564524 = r25564521 + r25564523;
        double r25564525 = r25564524 + r25564523;
        double r25564526 = r25564525 + r25564523;
        return r25564526;
}
↓
double f(double x, double y) {
        double r25564527 = 3.0;
        double r25564528 = y;
        double r25564529 = r25564527 * r25564528;
        double r25564530 = r25564529 * r25564528;
        double r25564531 = x;
        double r25564532 = r25564531 * r25564531;
        double r25564533 = r25564530 + r25564532;
        return r25564533;
}

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 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 2019170 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"

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

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