Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + \left(2 + x\right) \cdot x\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + \left(2 + x\right) \cdot x
double f(double x, double y) {
        double r310917 = x;
        double r310918 = 2.0;
        double r310919 = r310917 * r310918;
        double r310920 = r310917 * r310917;
        double r310921 = r310919 + r310920;
        double r310922 = y;
        double r310923 = r310922 * r310922;
        double r310924 = r310921 + r310923;
        return r310924;
}
↓
double f(double x, double y) {
        double r310925 = y;
        double r310926 = r310925 * r310925;
        double r310927 = 2.0;
        double r310928 = x;
        double r310929 = r310927 + r310928;
        double r310930 = r310929 * r310928;
        double r310931 = r310926 + r310930;
        return r310931;
}

Error

Bits error versus x

Bits error versus y

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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

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))