Average Error: 11.0 → 0.2
Time: 1.5s
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 r1315399 = x;
        double r1315400 = 3.0;
        double r1315401 = r1315399 * r1315400;
        double r1315402 = r1315401 * r1315399;
        double r1315403 = y;
        double r1315404 = r1315402 * r1315403;
        return r1315404;
}
↓
double f(double x, double y) {
        double r1315405 = x;
        double r1315406 = 3.0;
        double r1315407 = r1315406 * r1315405;
        double r1315408 = y;
        double r1315409 = r1315407 * r1315408;
        double r1315410 = r1315405 * r1315409;
        return r1315410;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.0
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 11.0

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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*0.2

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot \left(x \cdot y\right)\right)}\]
  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 2020025 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3) (* x y))

  (* (* (* x 3) x) y))