Average Error: 10.8 → 0.2
Time: 17.2s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[x \cdot \left(\left(3 \cdot x\right) \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(\left(3 \cdot x\right) \cdot y\right)
double f(double x, double y) {
        double r413991305 = x;
        double r413991306 = 3.0;
        double r413991307 = r413991305 * r413991306;
        double r413991308 = r413991307 * r413991305;
        double r413991309 = y;
        double r413991310 = r413991308 * r413991309;
        return r413991310;
}
↓
double f(double x, double y) {
        double r413991311 = x;
        double r413991312 = 3.0;
        double r413991313 = r413991312 * r413991311;
        double r413991314 = y;
        double r413991315 = r413991313 * r413991314;
        double r413991316 = r413991311 * r413991315;
        return r413991316;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.8
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(x \cdot 3\right) \cdot \left(x \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*l*0.3

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot \left(x \cdot y\right)\right)}\]
  6. Using strategy rm

  7. Applied associate-*r*0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"

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

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