Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B

Average Accuracy: 99.5% → 99.6%

Time: 3.1s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (* (* (* x 3.0) y) y))

↓

(FPCore (x y) :precision binary64 (* (* y x) (* y 3.0)))

C

double code(double x, double y) {
	return ((x * 3.0) * y) * y;
}

↓

double code(double x, double y) {
	return (y * x) * (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 3.0d0) * y) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * x) * (y * 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((x * 3.0) * y) * y;
}

↓

public static double code(double x, double y) {
	return (y * x) * (y * 3.0);
}

Python

def code(x, y):
	return ((x * 3.0) * y) * y

↓

def code(x, y):
	return (y * x) * (y * 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 3.0) * y) * y)
end

↓

function code(x, y)
	return Float64(Float64(y * x) * Float64(y * 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 3.0) * y) * y;
end

↓

function tmp = code(x, y)
	tmp = (y * x) * (y * 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision]

↓

code[x_, y_] := N[(N[(y * x), $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

Target

Original	99.5%
Target	99.6%
Herbie	99.6%

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

Derivation

1. Initial program 99.5%

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

2. Simplified 84.1%

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

   [Start] 99.5	\[ \left(\left(x \cdot 3\right) \cdot y\right) \cdot y \]
   associate-*l* [=>] 84.1	\[ \color{blue}{\left(x \cdot 3\right) \cdot \left(y \cdot y\right)} \]

3. Taylor expanded in x around 0 84.1%

   \[\leadsto \color{blue}{3 \cdot \left({y}^{2} \cdot x\right)} \]

4. Simplified 99.6%

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

   [Start] 84.1	\[ 3 \cdot \left({y}^{2} \cdot x\right) \]
   *-commutative [=>] 84.1	\[ \color{blue}{\left({y}^{2} \cdot x\right) \cdot 3} \]
   unpow2 [=>] 84.1	\[ \left(\color{blue}{\left(y \cdot y\right)} \cdot x\right) \cdot 3 \]
   *-commutative [=>] 84.1	\[ \color{blue}{\left(x \cdot \left(y \cdot y\right)\right)} \cdot 3 \]
   associate-*r* [=>] 99.6	\[ \color{blue}{\left(\left(x \cdot y\right) \cdot y\right)} \cdot 3 \]
   associate-*r* [<=] 99.6	\[ \color{blue}{\left(x \cdot y\right) \cdot \left(y \cdot 3\right)} \]
   *-commutative [=>] 99.6	\[ \color{blue}{\left(y \cdot x\right)} \cdot \left(y \cdot 3\right) \]
   *-commutative [=>] 99.6	\[ \left(y \cdot x\right) \cdot \color{blue}{\left(3 \cdot y\right)} \]

5. Final simplification 99.6%

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

Alternatives

Alternative 1
Accuracy	99.6%
Cost	448

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

Reproduce

herbie shell --seed 2023151 
(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))