Average Error: 0.0 → 0.0
Time: 4.0s
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 r541376 = x;
        double r541377 = 2.0;
        double r541378 = r541376 * r541377;
        double r541379 = r541376 * r541376;
        double r541380 = r541378 + r541379;
        double r541381 = y;
        double r541382 = r541381 * r541381;
        double r541383 = r541380 + r541382;
        return r541383;
}
↓
double f(double x, double y) {
        double r541384 = y;
        double r541385 = r541384 * r541384;
        double r541386 = x;
        double r541387 = 2.0;
        double r541388 = r541387 + r541386;
        double r541389 = r541386 * r541388;
        double r541390 = r541385 + r541389;
        return r541390;
}

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 2020042 
(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)))