Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(2 + x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + x \cdot \left(2 + x\right)
double f(double x, double y) {
        double r293291 = x;
        double r293292 = 2.0;
        double r293293 = r293291 * r293292;
        double r293294 = r293291 * r293291;
        double r293295 = r293293 + r293294;
        double r293296 = y;
        double r293297 = r293296 * r293296;
        double r293298 = r293295 + r293297;
        return r293298;
}
↓
double f(double x, double y) {
        double r293299 = y;
        double r293300 = r293299 * r293299;
        double r293301 = x;
        double r293302 = 2.0;
        double r293303 = r293302 + r293301;
        double r293304 = r293301 * r293303;
        double r293305 = r293300 + r293304;
        return r293305;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot y + x \cdot \left(2 + x\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot y + x \cdot \left(2 + x\right)\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2 x) (* x x)))

  (+ (+ (* x 2) (* x x)) (* y y)))