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

Average Error: 10.7 → 0.3

Time: 10.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return x * (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) * x) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (x * (y * 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 * (x * (y * 3.0));
}

Python

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

↓

def code(x, y):
	return x * (x * (y * 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(x * Float64(y * 3.0)))
end

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	10.7
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.7

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

2. Simplified 0.3

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

   [Start] 10.7	\[ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
   rational.json-simplify-2 [=>] 10.7	\[ \color{blue}{y \cdot \left(\left(x \cdot 3\right) \cdot x\right)} \]
   rational.json-simplify-2 [=>] 10.7	\[ y \cdot \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)} \]
   rational.json-simplify-43 [=>] 0.3	\[ \color{blue}{x \cdot \left(\left(x \cdot 3\right) \cdot y\right)} \]

3. Applied egg-rr 10.0

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

4. Applied egg-rr 0.3

   \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(x \cdot 3\right)\right) - 0} \]

5. Simplified 0.3

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

   [Start] 0.3	\[ x \cdot \left(y \cdot \left(x \cdot 3\right)\right) - 0 \]
   rational.json-simplify-5 [=>] 0.3	\[ \color{blue}{x \cdot \left(y \cdot \left(x \cdot 3\right)\right)} \]
   rational.json-simplify-43 [=>] 0.3	\[ x \cdot \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)} \]
   rational.json-simplify-2 [<=] 0.3	\[ x \cdot \left(x \cdot \color{blue}{\left(y \cdot 3\right)}\right) \]

6. Final simplification 0.3

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

Alternatives

Alternative 1
Error	0.2
Cost	448

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

Reproduce

herbie shell --seed 2023068 
(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))