Average Error: 0.1 → 0.1
Time: 14.7s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(y \cdot 3\right) + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot \left(y \cdot 3\right) + x \cdot x
double f(double x, double y) {
        double r21625158 = x;
        double r21625159 = r21625158 * r21625158;
        double r21625160 = y;
        double r21625161 = r21625160 * r21625160;
        double r21625162 = r21625159 + r21625161;
        double r21625163 = r21625162 + r21625161;
        double r21625164 = r21625163 + r21625161;
        return r21625164;
}
↓
double f(double x, double y) {
        double r21625165 = y;
        double r21625166 = 3.0;
        double r21625167 = r21625165 * r21625166;
        double r21625168 = r21625165 * r21625167;
        double r21625169 = x;
        double r21625170 = r21625169 * r21625169;
        double r21625171 = r21625168 + r21625170;
        return r21625171;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {y}^{2}} + x \cdot x\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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)))