Average Error: 0.0 → 0.0
Time: 9.0s
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 r32033886 = 2.0;
        double r32033887 = x;
        double r32033888 = r32033887 * r32033887;
        double r32033889 = y;
        double r32033890 = r32033887 * r32033889;
        double r32033891 = r32033888 + r32033890;
        double r32033892 = r32033886 * r32033891;
        return r32033892;
}
↓
double f(double x, double y) {
        double r32033893 = 2.0;
        double r32033894 = x;
        double r32033895 = r32033893 * r32033894;
        double r32033896 = y;
        double r32033897 = r32033894 + r32033896;
        double r32033898 = r32033895 * r32033897;
        return r32033898;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))