Average Error: 0.1 → 0.1
Time: 2.9s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
double f(double x, double y) {
        double r693291 = x;
        double r693292 = r693291 * r693291;
        double r693293 = y;
        double r693294 = r693293 * r693293;
        double r693295 = r693292 + r693294;
        double r693296 = r693295 + r693294;
        double r693297 = r693296 + r693294;
        return r693297;
}
↓
double f(double x, double y) {
        double r693298 = x;
        double r693299 = r693298 * r693298;
        double r693300 = y;
        double r693301 = r693300 * r693300;
        double r693302 = r693299 + r693301;
        double r693303 = r693302 + r693301;
        double r693304 = r693303 + r693301;
        return r693304;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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)))