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

Percentage Accurate: 87.9% → 99.7%

Time: 4.7s

Alternatives: 2

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 87.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. associate-*r* N/A

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

   8. sqr-neg-rev N/A

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

   9. associate-*l* N/A

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

   10. associate-*r* N/A

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

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

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

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

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

   13. rem-square-sqrt N/A

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

   14. sqrt-prod N/A

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

   15. sqr-neg-rev N/A

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

   16. pow2 N/A

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

   17. sqrt-pow1 N/A

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

   18. metadata-eval N/A

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

   19. unpow1 N/A

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

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

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

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

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

   22. *-commutative N/A

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

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

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

   24. distribute-lft-neg-out N/A

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

   25. remove-double-neg N/A

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

   26. rem-square-sqrt N/A

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

   27. sqrt-prod N/A

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

   28. rem-sqrt-square-rev N/A

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

4. Applied rewrites 44.2%

   \[\leadsto \color{blue}{\left({x}^{1.5} \cdot y\right) \cdot \left(\sqrt{x} \cdot 3\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-pow.f64 N/A

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

   4. sqr-pow N/A

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

   5. associate-*r* N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lower-pow.f64 N/A

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

   9. metadata-eval N/A

      \[\leadsto \left({x}^{\color{blue}{\frac{3}{4}}} \cdot \left(y \cdot {x}^{\left(\frac{\frac{3}{2}}{2}\right)}\right)\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   10. *-commutative N/A

       \[\leadsto \left({x}^{\frac{3}{4}} \cdot \color{blue}{\left({x}^{\left(\frac{\frac{3}{2}}{2}\right)} \cdot y\right)}\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left({x}^{\frac{3}{4}} \cdot \color{blue}{\left({x}^{\left(\frac{\frac{3}{2}}{2}\right)} \cdot y\right)}\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   12. lower-pow.f64 N/A

       \[\leadsto \left({x}^{\frac{3}{4}} \cdot \left(\color{blue}{{x}^{\left(\frac{\frac{3}{2}}{2}\right)}} \cdot y\right)\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   13. metadata-eval 46.3

       \[\leadsto \left({x}^{0.75} \cdot \left({x}^{\color{blue}{0.75}} \cdot y\right)\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

6. Applied rewrites 46.3%

   \[\leadsto \color{blue}{\left({x}^{0.75} \cdot \left({x}^{0.75} \cdot y\right)\right)} \cdot \left(\sqrt{x} \cdot 3\right) \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left({x}^{\frac{3}{4}} \cdot \left({x}^{\frac{3}{4}} \cdot y\right)\right) \cdot \left(\sqrt{x} \cdot 3\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left({x}^{\frac{3}{4}} \cdot \left({x}^{\frac{3}{4}} \cdot y\right)\right)} \cdot \left(\sqrt{x} \cdot 3\right) \]

   3. lift-*.f64 N/A

      \[\leadsto \left({x}^{\frac{3}{4}} \cdot \color{blue}{\left({x}^{\frac{3}{4}} \cdot y\right)}\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(\left({x}^{\frac{3}{4}} \cdot {x}^{\frac{3}{4}}\right) \cdot y\right)} \cdot \left(\sqrt{x} \cdot 3\right) \]

   5. lift-pow.f64 N/A

      \[\leadsto \left(\left(\color{blue}{{x}^{\frac{3}{4}}} \cdot {x}^{\frac{3}{4}}\right) \cdot y\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   6. lift-pow.f64 N/A

      \[\leadsto \left(\left({x}^{\frac{3}{4}} \cdot \color{blue}{{x}^{\frac{3}{4}}}\right) \cdot y\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   7. pow-prod-up N/A

      \[\leadsto \left(\color{blue}{{x}^{\left(\frac{3}{4} + \frac{3}{4}\right)}} \cdot y\right) \cdot \left(\sqrt{x} \cdot 3\right) \]

   8. metadata-eval N/A

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

   9. metadata-eval N/A

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

   10. pow-plus N/A

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

   11. pow1/2 N/A

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

   12. lift-sqrt.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. associate-*l* N/A

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. associate-*l* N/A

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

   19. associate-*r* N/A

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

   20. *-commutative N/A

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

   21. lower-*.f64 N/A

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

8. Applied rewrites 99.7%

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

Alternative 2: 87.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-*r* N/A

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

   6. *-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. associate-*r* N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. associate-*l* N/A

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

   12. fabs-sqr N/A

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

   13. sqr-neg-rev N/A

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

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

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

   15. fabs-neg N/A

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

   16. rem-sqrt-square N/A

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

   17. sqrt-prod N/A

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

   18. rem-square-sqrt N/A

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

   19. *-commutative N/A

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

   20. *-commutative N/A

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

   21. *-commutative N/A

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

   22. *-commutative N/A

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

   23. lower-*.f64 N/A

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

   24. *-commutative N/A

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

   25. lower-*.f64 N/A

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

   26. rem-square-sqrt N/A

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

   27. sqrt-prod N/A

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

   28. rem-sqrt-square N/A

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

   29. fabs-neg N/A

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

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

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

   31. sqr-neg-rev N/A

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

4. Applied rewrites 90.0%

   \[\leadsto \color{blue}{\left(y \cdot 3\right) \cdot \left(x \cdot x\right)} \]
5. 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 2024343 
(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))