Average Error: 0.0 → 0.0
Time: 6.4s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + \left(2 \cdot x + x \cdot x\right)
double f(double x, double y) {
        double r616900 = x;
        double r616901 = 2.0;
        double r616902 = r616900 * r616901;
        double r616903 = r616900 * r616900;
        double r616904 = r616902 + r616903;
        double r616905 = y;
        double r616906 = r616905 * r616905;
        double r616907 = r616904 + r616906;
        return r616907;
}
↓
double f(double x, double y) {
        double r616908 = y;
        double r616909 = r616908 * r616908;
        double r616910 = 2.0;
        double r616911 = x;
        double r616912 = r616910 * r616911;
        double r616913 = r616911 * r616911;
        double r616914 = r616912 + r616913;
        double r616915 = r616909 + r616914;
        return r616915;
}

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. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto y \cdot y + \color{blue}{\left(x \cdot 2 + x \cdot x\right)}\]

  5. Simplified0.0

    \[\leadsto y \cdot y + \left(\color{blue}{2 \cdot x} + x \cdot x\right)\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))