Average Error: 0.1 → 0.1
Time: 12.2s
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 r585887 = x;
        double r585888 = r585887 * r585887;
        double r585889 = y;
        double r585890 = r585889 * r585889;
        double r585891 = r585888 + r585890;
        double r585892 = r585891 + r585890;
        double r585893 = r585892 + r585890;
        return r585893;
}
↓
double f(double x, double y) {
        double r585894 = 3.0;
        double r585895 = y;
        double r585896 = r585894 * r585895;
        double r585897 = r585896 * r585895;
        double r585898 = x;
        double r585899 = r585898 * r585898;
        double r585900 = r585897 + r585899;
        return r585900;
}

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 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)))