Average Error: 0.0 → 0.0
Time: 11.4s
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 r299342 = x;
        double r299343 = 2.0;
        double r299344 = r299342 * r299343;
        double r299345 = r299342 * r299342;
        double r299346 = r299344 + r299345;
        double r299347 = y;
        double r299348 = r299347 * r299347;
        double r299349 = r299346 + r299348;
        return r299349;
}
↓
double f(double x, double y) {
        double r299350 = y;
        double r299351 = r299350 * r299350;
        double r299352 = x;
        double r299353 = 2.0;
        double r299354 = r299353 + r299352;
        double r299355 = r299352 * r299354;
        double r299356 = r299351 + r299355;
        return r299356;
}

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 2019323 
(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)))