Average Error: 0.3 → 0.2
Time: 3.4s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(x \cdot \left(3 \cdot y\right)\right) \cdot y
double f(double x, double y) {
        double r790400 = x;
        double r790401 = 3.0;
        double r790402 = r790400 * r790401;
        double r790403 = y;
        double r790404 = r790402 * r790403;
        double r790405 = r790404 * r790403;
        return r790405;
}
↓
double f(double x, double y) {
        double r790406 = x;
        double r790407 = 3.0;
        double r790408 = y;
        double r790409 = r790407 * r790408;
        double r790410 = r790406 * r790409;
        double r790411 = r790410 * r790408;
        return r790411;
}

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

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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