Average Error: 0.0 → 0.0
Time: 1.8s
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 r657249 = 2.0;
        double r657250 = x;
        double r657251 = r657250 * r657250;
        double r657252 = y;
        double r657253 = r657250 * r657252;
        double r657254 = r657251 + r657253;
        double r657255 = r657249 * r657254;
        return r657255;
}
↓
double f(double x, double y) {
        double r657256 = 2.0;
        double r657257 = x;
        double r657258 = r657256 * r657257;
        double r657259 = y;
        double r657260 = r657257 + r657259;
        double r657261 = r657258 * r657260;
        return r657261;
}

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 2020034 +o rules:numerics
(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))))