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

Percentage Accurate: 88.5% → 99.7%

Time: 4.2s

Alternatives: 3

Speedup: 1.0×

• 25.2% 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: 88.5% 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 88.8%

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
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. Final simplification 99.8%

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

Alternative 2: 88.5% 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 88.8%

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

   1. *-commutative 88.8%

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

   2. associate-*l* 88.7%

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

   3. associate-*l* 88.7%

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

3. Simplified 88.7%

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

4. Final simplification 88.7%

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

Alternative 3: 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 88.8%

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

   1. *-commutative 88.8%

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

   2. associate-*l* 88.7%

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

   3. associate-*l* 88.7%

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

3. Simplified 88.7%

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

   1. add-sqr-sqrt 53.2%

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

   2. pow2 53.2%

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

   3. *-commutative 53.2%

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

   4. associate-*r* 53.2%

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

   5. *-commutative 53.2%

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

   6. sqrt-prod 40.9%

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

   7. sqrt-prod 21.4%

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

   8. add-sqr-sqrt 46.7%

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

   9. *-commutative 46.7%

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

5. Applied egg-rr 46.7%

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

   1. unpow2 46.7%

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

   2. swap-sqr 40.9%

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

   3. add-sqr-sqrt 88.7%

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

   4. associate-*l* 99.7%

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

   5. *-commutative 99.7%

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

   6. *-commutative 99.7%

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

7. Applied egg-rr 99.7%

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

   1. add-sqr-sqrt 53.0%

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

   2. sqrt-unprod 53.3%

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

   3. rem-sqrt-square 60.0%

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

   4. associate-*r* 59.9%

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

   5. *-commutative 59.9%

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

9. Applied egg-rr 59.9%

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

10. Taylor expanded in y around 0 59.9%

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

    1. associate-*r* 59.9%

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

    2. *-commutative 59.9%

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

    3. *-commutative 59.9%

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

    4. unpow1 59.9%

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

    5. sqr-pow 52.9%

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

    6. fabs-sqr 52.9%

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

    7. sqr-pow 99.7%

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

    8. unpow1 99.7%

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

    9. associate-*l* 99.8%

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

    10. associate-*r* 99.7%

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

    11. *-commutative 99.7%

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

12. Simplified 99.7%

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

13. Final simplification 99.7%

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

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 2023301 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3.0) (* x y))

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