Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\left(x \cdot \left(x + y\right)\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\left(x \cdot \left(x + y\right)\right) \cdot 2
double f(double x, double y) {
        double r531133 = 2.0;
        double r531134 = x;
        double r531135 = r531134 * r531134;
        double r531136 = y;
        double r531137 = r531134 * r531136;
        double r531138 = r531135 + r531137;
        double r531139 = r531133 * r531138;
        return r531139;
}
↓
double f(double x, double y) {
        double r531140 = x;
        double r531141 = y;
        double r531142 = r531140 + r531141;
        double r531143 = r531140 * r531142;
        double r531144 = 2.0;
        double r531145 = r531143 * r531144;
        return r531145;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +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))))