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

Percentage Accurate: 99.7% → 99.7%

Time: 4.0s

Alternatives: 3

Speedup: 1.0×

• 25.0% 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

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

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]

Derivation

1. Initial program 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. lift-*.f64 N/A

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

   2. rem-square-sqrt N/A

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

   3. sqrt-prod N/A

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

   4. sqr-neg-rev N/A

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

   5. pow2 N/A

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

   6. sqrt-pow1 N/A

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

   7. metadata-eval N/A

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

   8. unpow1 N/A

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

   9. distribute-rgt-neg-out N/A

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

   10. lift-*.f64 N/A

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

   11. associate-*l* N/A

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

   12. distribute-lft-neg-in N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 N/A

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

   15. rem-square-sqrt N/A

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

   16. sqrt-prod N/A

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

   17. sqr-neg-rev N/A

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

   18. pow2 N/A

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

   19. sqrt-pow1 N/A

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

   20. metadata-eval N/A

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

   21. unpow1 N/A

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

   22. distribute-rgt-neg-out N/A

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

   23. distribute-lft-neg-in N/A

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

   24. lower-*.f64 N/A

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

   25. metadata-eval N/A

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

   26. lower-neg.f64 99.7

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

4. Applied rewrites 99.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*r* N/A

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

   6. associate-*l* N/A

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

   7. *-commutative N/A

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

   8. lift-neg.f64 N/A

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

   9. distribute-rgt-neg-out N/A

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

   10. distribute-lft-neg-in N/A

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

   11. metadata-eval N/A

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

   12. lift-*.f64 N/A

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

   13. sqr-neg-rev N/A

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

   14. associate-*r* N/A

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

   15. *-commutative N/A

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. associate-*r* N/A

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

   19. distribute-lft-neg-in N/A

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

   20. distribute-rgt-neg-out N/A

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

   21. lift-neg.f64 N/A

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

   22. unpow1 N/A

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

   23. metadata-eval N/A

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

   24. sqrt-pow1 N/A

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

   25. pow2 N/A

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

   26. sqr-neg-rev N/A

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

   27. sqrt-prod N/A

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

   28. rem-square-sqrt N/A

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

6. Applied rewrites 99.7%

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

Alternative 3: 88.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. *-commutative N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. unpow2 N/A

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

   7. lower-*.f64 90.1

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

5. Applied rewrites 90.1%

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

Developer Target 1: 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 2024329 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

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

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