Average Error: 0.1 → 0.1
Time: 13.7s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[3 \cdot \left(y \cdot y\right) + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
3 \cdot \left(y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r321162 = x;
        double r321163 = r321162 * r321162;
        double r321164 = y;
        double r321165 = r321164 * r321164;
        double r321166 = r321163 + r321165;
        double r321167 = r321166 + r321165;
        double r321168 = r321167 + r321165;
        return r321168;
}
↓
double f(double x, double y) {
        double r321169 = 3.0;
        double r321170 = y;
        double r321171 = r321170 * r321170;
        double r321172 = r321169 * r321171;
        double r321173 = x;
        double r321174 = r321173 * r321173;
        double r321175 = r321172 + r321174;
        return r321175;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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)))