Average Error: 0.3 → 0.4
Time: 2.1s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(\left(x \cdot \left(3 \cdot y\right)\right) \cdot \sqrt{y}\right) \cdot \sqrt{y}\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(\left(x \cdot \left(3 \cdot y\right)\right) \cdot \sqrt{y}\right) \cdot \sqrt{y}
double code(double x, double y) {
	return ((double) (((double) (((double) (x * 3.0)) * y)) * y));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (x * ((double) (3.0 * y)))) * ((double) sqrt(y)))) * ((double) sqrt(y))));
}

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

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*0.3

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

  5. Applied add-sqr-sqrt0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020162 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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