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

Percentage Accurate: 88.0% → 99.7%

Time: 7.8s

Alternatives: 5

Speedup: 1.0×

• 25.5% 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: 88.0% 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

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

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]

Derivation

1. Initial program 89.5%

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

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. *-commutative 89.5%

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

   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. Add Preprocessing

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

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(x * Float64(3.0 * Float64(x * y)))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. associate-*l* 99.8%

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

   2. associate-*l* 99.7%

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

3. Simplified 99.7%

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

Alternative 4: 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 89.5%

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

   1. associate-*l* 99.8%

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

   2. associate-*l* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around 0 89.5%

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

   1. add-sqr-sqrt 61.7%

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

   2. pow2 61.7%

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

   3. sqrt-prod 50.3%

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

   4. sqrt-pow1 56.7%

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

   5. metadata-eval 56.7%

      \[\leadsto 3 \cdot {\left({x}^{\color{blue}{1}} \cdot \sqrt{y}\right)}^{2} \]

   6. pow1 56.7%

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

7. Applied egg-rr 56.7%

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

   1. unpow2 56.7%

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

   2. *-commutative 56.7%

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

   3. associate-*r* 56.8%

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

   4. associate-*r* 56.7%

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

   5. add-sqr-sqrt 99.7%

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

9. Applied egg-rr 99.7%

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

10. Final simplification 99.7%

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

Alternative 5: 88.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.5%

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

   1. associate-*l* 99.8%

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

   2. associate-*l* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around 0 89.5%

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

   1. unpow2 89.5%

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

7. Applied egg-rr 89.5%

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

8. Final simplification 89.5%

   \[\leadsto 3 \cdot \left(y \cdot \left(x \cdot x\right)\right) \]
9. 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 2024143 
(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))