Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, F

Percentage Accurate: 99.6% → 99.6%

Time: 1.1s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 27\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 27.0) y))

C

double code(double x, double y) {
	return (x * 27.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 27.0d0) * y
end function

Java

public static double code(double x, double y) {
	return (x * 27.0) * y;
}

Python

def code(x, y):
	return (x * 27.0) * y

Julia

function code(x, y)
	return Float64(Float64(x * 27.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 27.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(x * 27.0), $MachinePrecision] * y), $MachinePrecision]

Initial Program: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 27\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x 27.0) y))

C

double code(double x, double y) {
	return (x * 27.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 27.0d0) * y
end function

Java

public static double code(double x, double y) {
	return (x * 27.0) * y;
}

Python

def code(x, y):
	return (x * 27.0) * y

Julia

function code(x, y)
	return Float64(Float64(x * 27.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 27.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(x * 27.0), $MachinePrecision] * y), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y\right) \cdot 27 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x y) 27.0))

C

double code(double x, double y) {
	return (x * y) * 27.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) * 27.0d0
end function

Java

public static double code(double x, double y) {
	return (x * y) * 27.0;
}

Python

def code(x, y):
	return (x * y) * 27.0

Julia

function code(x, y)
	return Float64(Float64(x * y) * 27.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) * 27.0;
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] * 27.0), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(x \cdot 27\right) \cdot y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 27\right)} \cdot y \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{y \cdot \left(x \cdot 27\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto y \cdot \color{blue}{\left(x \cdot 27\right)} \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 27} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 27} \]

   6. *-commutative N/A

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot 27 \]

   7. lower-*.f64 99.7

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot 27 \]

4. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 27} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 27\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y (* x 27.0)))

C

double code(double x, double y) {
	return y * (x * 27.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (x * 27.0d0)
end function

Java

public static double code(double x, double y) {
	return y * (x * 27.0);
}

Python

def code(x, y):
	return y * (x * 27.0)

Julia

function code(x, y)
	return Float64(y * Float64(x * 27.0))
end

MATLAB

function tmp = code(x, y)
	tmp = y * (x * 27.0);
end

Wolfram

code[x_, y_] := N[(y * N[(x * 27.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(x \cdot 27\right) \cdot y \]
2. Add Preprocessing

3. Final simplification 99.7%

   \[\leadsto y \cdot \left(x \cdot 27\right) \]
4. Add Preprocessing

Alternative 3: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y \cdot 27\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (* y 27.0)))

C

double code(double x, double y) {
	return x * (y * 27.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y * 27.0d0)
end function

Java

public static double code(double x, double y) {
	return x * (y * 27.0);
}

Python

def code(x, y):
	return x * (y * 27.0)

Julia

function code(x, y)
	return Float64(x * Float64(y * 27.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (y * 27.0);
end

Wolfram

code[x_, y_] := N[(x * N[(y * 27.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\left(x \cdot 27\right) \cdot y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto \color{blue}{x \cdot \left(27 \cdot y\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\left(27 \cdot y\right) \cdot x} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(27 \cdot y\right) \cdot x} \]

   4. lower-*.f64 99.7

      \[\leadsto \color{blue}{\left(27 \cdot y\right)} \cdot x \]

4. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\left(27 \cdot y\right) \cdot x} \]

5. Final simplification 99.7%

   \[\leadsto x \cdot \left(y \cdot 27\right) \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))