Average Error: 0.0 → 0.0
Time: 3.1s
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 r331958 = x;
        double r331959 = 2.0;
        double r331960 = r331958 * r331959;
        double r331961 = r331958 * r331958;
        double r331962 = r331960 + r331961;
        double r331963 = y;
        double r331964 = r331963 * r331963;
        double r331965 = r331962 + r331964;
        return r331965;
}
↓
double f(double x, double y) {
        double r331966 = y;
        double r331967 = r331966 * r331966;
        double r331968 = x;
        double r331969 = 2.0;
        double r331970 = r331969 + r331968;
        double r331971 = r331968 * r331970;
        double r331972 = r331967 + r331971;
        return r331972;
}

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 2019326 
(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)))