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

Percentage Accurate: 88.2% → 99.7%

Time: 5.7s

Alternatives: 4

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 3\right) \cdot x\right) \cdot y \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(x \cdot y\right)\right) \cdot 3 \end{array} \]

FPCore

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

C

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 * (x * y)) * 3.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. associate-*l* 99.7%

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

   2. associate-*l* 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{x \cdot \left(3 \cdot \left(x \cdot y\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-sqr-sqrt 60.7%

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

   2. pow2 60.7%

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

   3. associate-*r* 60.7%

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

   4. *-commutative 60.7%

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

   5. associate-*r* 60.7%

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

   6. associate-*r* 57.6%

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

   7. sqrt-prod 43.3%

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

   8. sqrt-unprod 24.0%

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

   9. add-sqr-sqrt 46.6%

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

6. Applied egg-rr 46.6%

   \[\leadsto \color{blue}{{\left(x \cdot \sqrt{3 \cdot y}\right)}^{2}} \]
7. Step-by-step derivation

   1. unpow2 46.6%

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

   2. swap-sqr 43.3%

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

   3. add-sqr-sqrt 89.4%

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

   4. associate-*l* 99.7%

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

   5. *-commutative 99.7%

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

   6. associate-*l* 99.6%

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

   7. associate-*r* 99.7%

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

8. Applied egg-rr 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y\right) \cdot \left(x \cdot 3\right) \end{array} \]

FPCore

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

C

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 * y) * (x * 3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. associate-*l* 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

   \[\leadsto \left(x \cdot y\right) \cdot \left(x \cdot 3\right) \]
6. Add Preprocessing

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(x \cdot \left(y \cdot 3\right)\right) \end{array} \]

FPCore

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

C

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 * (x * (y * 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. *-commutative 89.4%

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

   2. associate-*l* 99.7%

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

   3. associate-*r* 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

   \[\leadsto x \cdot \left(x \cdot \left(y \cdot 3\right)\right) \]
6. Add Preprocessing

Alternative 4: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\left(x \cdot y\right) \cdot 3\right) \end{array} \]

FPCore

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

C

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 * ((x * y) * 3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
2. Step-by-step derivation

   1. associate-*l* 99.7%

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

   2. associate-*l* 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

   \[\leadsto x \cdot \left(\left(x \cdot y\right) \cdot 3\right) \]
6. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot \left(x \cdot y\right) \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024098 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (* (* x 3.0) (* x y))

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