Average Error: 0.0 → 0.0
Time: 4.6s
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 r573094 = 2.0;
        double r573095 = x;
        double r573096 = r573095 * r573095;
        double r573097 = y;
        double r573098 = r573095 * r573097;
        double r573099 = r573096 + r573098;
        double r573100 = r573094 * r573099;
        return r573100;
}
↓
double f(double x, double y) {
        double r573101 = x;
        double r573102 = y;
        double r573103 = r573101 + r573102;
        double r573104 = r573101 * r573103;
        double r573105 = 2.0;
        double r573106 = r573104 * r573105;
        return r573106;
}

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 
(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))))