Average Error: 10.4 → 0.3
Time: 18.3s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[x \cdot \left(3 \cdot \left(x \cdot y\right)\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(3 \cdot \left(x \cdot y\right)\right)
double f(double x, double y) {
        double r949654 = x;
        double r949655 = 3.0;
        double r949656 = r949654 * r949655;
        double r949657 = r949656 * r949654;
        double r949658 = y;
        double r949659 = r949657 * r949658;
        return r949659;
}
↓
double f(double x, double y) {
        double r949660 = x;
        double r949661 = 3.0;
        double r949662 = y;
        double r949663 = r949660 * r949662;
        double r949664 = r949661 * r949663;
        double r949665 = r949660 * r949664;
        return r949665;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.4
Target0.2
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.4

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 +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))