Average Error: 0.0 → 0.0
Time: 13.4s
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 r340200 = 2.0;
        double r340201 = x;
        double r340202 = r340201 * r340201;
        double r340203 = y;
        double r340204 = r340201 * r340203;
        double r340205 = r340202 + r340204;
        double r340206 = r340200 * r340205;
        return r340206;
}
↓
double f(double x, double y) {
        double r340207 = 2.0;
        double r340208 = x;
        double r340209 = r340207 * r340208;
        double r340210 = y;
        double r340211 = r340208 + r340210;
        double r340212 = r340209 * r340211;
        return r340212;
}

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 2019322 
(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))))