Average Error: 0.0 → 0.0
Time: 4.1s
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 r743905 = x;
        double r743906 = 2.0;
        double r743907 = r743905 * r743906;
        double r743908 = r743905 * r743905;
        double r743909 = r743907 + r743908;
        double r743910 = y;
        double r743911 = r743910 * r743910;
        double r743912 = r743909 + r743911;
        return r743912;
}
↓
double f(double x, double y) {
        double r743913 = y;
        double r743914 = r743913 * r743913;
        double r743915 = x;
        double r743916 = 2.0;
        double r743917 = r743916 + r743915;
        double r743918 = r743915 * r743917;
        double r743919 = r743914 + r743918;
        return r743919;
}

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 2020042 
(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)))