Average Error: 0.0 → 0.0
Time: 11.0s
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 r348378 = x;
        double r348379 = 2.0;
        double r348380 = r348378 * r348379;
        double r348381 = r348378 * r348378;
        double r348382 = r348380 + r348381;
        double r348383 = y;
        double r348384 = r348383 * r348383;
        double r348385 = r348382 + r348384;
        return r348385;
}
↓
double f(double x, double y) {
        double r348386 = y;
        double r348387 = r348386 * r348386;
        double r348388 = x;
        double r348389 = 2.0;
        double r348390 = r348389 + r348388;
        double r348391 = r348388 * r348390;
        double r348392 = r348387 + r348391;
        return r348392;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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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)))