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

Percentage Accurate: 99.7% → 99.7%

Time: 4.8s

Alternatives: 4

Speedup: 1.0×

• 25.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-*l* 89.9%

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

   2. associate-*l* 89.8%

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

3. Simplified 89.8%

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

5. Taylor expanded in x around 0 89.8%

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

   1. add-sqr-sqrt 56.4%

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

   2. pow2 56.4%

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

   3. *-commutative 56.4%

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

   4. sqrt-prod 45.7%

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

   5. unpow2 45.7%

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

   6. sqrt-prod 21.7%

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

   7. add-sqr-sqrt 50.1%

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

7. Applied egg-rr 50.1%

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

   1. unpow2 50.1%

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

   2. *-commutative 50.1%

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

   3. associate-*r* 50.1%

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

   4. associate-*r* 50.1%

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

   5. add-sqr-sqrt 99.6%

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

9. Applied egg-rr 99.6%

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

10. Final simplification 99.6%

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in x around 0 99.7%

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

4. Final simplification 99.7%

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

Alternative 4: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-*l* 89.9%

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

   2. associate-*l* 89.8%

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

3. Simplified 89.8%

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

   1. add-cube-cbrt 89.2%

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

   2. pow3 89.2%

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

   3. associate-*r* 89.1%

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

   4. *-commutative 89.1%

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

   5. associate-*l* 89.1%

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

   6. pow2 89.1%

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

6. Applied egg-rr 89.1%

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

   1. rem-cube-cbrt 89.8%

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

   2. unpow2 89.8%

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

   3. associate-*r* 99.6%

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

   4. associate-*l* 99.7%

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

   5. *-commutative 99.7%

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

   6. associate-*r* 99.7%

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

8. Applied egg-rr 99.7%

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

9. Final simplification 99.7%

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

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024048 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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