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

Percentage Accurate: 88.1% → 99.7%

Time: 6.3s

Alternatives: 4

Speedup: 1.0×

• 24.8% 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: 88.1% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. unpow2 N/A

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

   3. associate-*l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.7

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

5. Simplified 99.7%

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

Alternative 2: 21.2% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

4. Applied egg-rr 19.5%

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

5. Final simplification 19.5%

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

Alternative 3: 21.1% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 N/A

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

   2. unpow2 N/A

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

   3. associate-*l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.7

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

5. Simplified 99.7%

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

7. Applied egg-rr 19.5%

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

Alternative 4: 5.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ 3 \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

4. Applied egg-rr 4.8%

   \[\leadsto \color{blue}{y \cdot 3} \]

5. Final simplification 4.8%

   \[\leadsto 3 \cdot y \]
6. Add Preprocessing

Developer Target 1: 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 2024207 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* (* x 3) (* x y)))

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