Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(x \cdot x + y \cdot y\right) + y \cdot \left(y + y\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(x \cdot x + y \cdot y\right) + y \cdot \left(y + y\right)
double f(double x, double y) {
        double r592287 = x;
        double r592288 = r592287 * r592287;
        double r592289 = y;
        double r592290 = r592289 * r592289;
        double r592291 = r592288 + r592290;
        double r592292 = r592291 + r592290;
        double r592293 = r592292 + r592290;
        return r592293;
}
↓
double f(double x, double y) {
        double r592294 = x;
        double r592295 = r592294 * r592294;
        double r592296 = y;
        double r592297 = r592296 * r592296;
        double r592298 = r592295 + r592297;
        double r592299 = r592296 + r592296;
        double r592300 = r592296 * r592299;
        double r592301 = r592298 + r592300;
        return r592301;
}

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. Using strategy rm

  3. Applied associate-+l+0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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)))