Average Error: 0.3 → 0.2
Time: 15.9s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(\left(y \cdot 3\right) \cdot x\right) \cdot y\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(\left(y \cdot 3\right) \cdot x\right) \cdot y
double f(double x, double y) {
        double r40084106 = x;
        double r40084107 = 3.0;
        double r40084108 = r40084106 * r40084107;
        double r40084109 = y;
        double r40084110 = r40084108 * r40084109;
        double r40084111 = r40084110 * r40084109;
        return r40084111;
}
↓
double f(double x, double y) {
        double r40084112 = y;
        double r40084113 = 3.0;
        double r40084114 = r40084112 * r40084113;
        double r40084115 = x;
        double r40084116 = r40084114 * r40084115;
        double r40084117 = r40084116 * r40084112;
        return r40084117;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \cdot y\]

  4. Final simplification0.2

    \[\leadsto \left(\left(y \cdot 3\right) \cdot x\right) \cdot y\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))