Average Error: 0.0 → 0.0
Time: 2.9s
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 r583199 = x;
        double r583200 = 2.0;
        double r583201 = r583199 * r583200;
        double r583202 = r583199 * r583199;
        double r583203 = r583201 + r583202;
        double r583204 = y;
        double r583205 = r583204 * r583204;
        double r583206 = r583203 + r583205;
        return r583206;
}
↓
double f(double x, double y) {
        double r583207 = y;
        double r583208 = r583207 * r583207;
        double r583209 = x;
        double r583210 = 2.0;
        double r583211 = r583210 + r583209;
        double r583212 = r583209 * r583211;
        double r583213 = r583208 + r583212;
        return r583213;
}

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 2020060 
(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)))