Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(2 \cdot x\right) \cdot \left(x + y\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(2 \cdot x\right) \cdot \left(x + y\right)
double f(double x, double y) {
        double r480811 = 2.0;
        double r480812 = x;
        double r480813 = r480812 * r480812;
        double r480814 = y;
        double r480815 = r480812 * r480814;
        double r480816 = r480813 + r480815;
        double r480817 = r480811 * r480816;
        return r480817;
}
↓
double f(double x, double y) {
        double r480818 = 2.0;
        double r480819 = x;
        double r480820 = r480818 * r480819;
        double r480821 = y;
        double r480822 = r480819 + r480821;
        double r480823 = r480820 * r480822;
        return r480823;
}

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

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-out0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2) (+ x y))

  (* 2 (+ (* x x) (* x y))))