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 r479068 = x;
        double r479069 = 2.0;
        double r479070 = r479068 * r479069;
        double r479071 = r479068 * r479068;
        double r479072 = r479070 + r479071;
        double r479073 = y;
        double r479074 = r479073 * r479073;
        double r479075 = r479072 + r479074;
        return r479075;
}
↓
double f(double x, double y) {
        double r479076 = y;
        double r479077 = r479076 * r479076;
        double r479078 = x;
        double r479079 = 2.0;
        double r479080 = r479079 + r479078;
        double r479081 = r479078 * r479080;
        double r479082 = r479077 + r479081;
        return r479082;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2020021 
(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)))