Average Error: 0.3 → 0.3
Time: 4.0s
Precision: binary64
Cost: 448
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[y \cdot \left(y \cdot \left(x \cdot 3\right)\right)\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
y \cdot \left(y \cdot \left(x \cdot 3\right)\right)
(FPCore (x y) :precision binary64 (* (* (* x 3.0) y) y))
↓
(FPCore (x y) :precision binary64 (* y (* y (* x 3.0))))
double code(double x, double y) {
	return ((x * 3.0) * y) * y;
}
↓
double code(double x, double y) {
	return y * (y * (x * 3.0));
}

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

Alternatives

Alternative 1
Error0.2
Cost448
\[y \cdot \left(x \cdot \left(y \cdot 3\right)\right)\]
Alternative 2
Error10.2
Cost448
\[x \cdot \left(3 \cdot \left(y \cdot y\right)\right)\]
Alternative 3
Error41.1
Cost64
\[0\]
Alternative 4
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.3

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

  2. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2021044 
(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))