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

Average Error: 10.6 → 0.2

Time: 5.3s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	10.6
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 10.6

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

2. Simplified 0.2

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

   [Start] 10.6	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.6	\[ \color{blue}{y \cdot \left(\left(x \cdot 3\right) \cdot x\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 10.6	\[ y \cdot \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.2	\[ \color{blue}{x \cdot \left(y \cdot \left(x \cdot 3\right)\right)} \]

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.3
Cost	448

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

Alternative 2
Error	0.3
Cost	448

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

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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