Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

Alternatives: 2

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot 2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* y 2.0)))

C

double code(double x, double y) {
	return x / (y * 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (y * 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x / (y * 2.0);
}

Python

def code(x, y):
	return x / (y * 2.0)

Julia

function code(x, y)
	return Float64(x / Float64(y * 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (y * 2.0);
end

Wolfram

code[x_, y_] := N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot 2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* y 2.0)))

C

double code(double x, double y) {
	return x / (y * 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (y * 2.0d0)
end function

Java

public static double code(double x, double y) {
	return x / (y * 2.0);
}

Python

def code(x, y):
	return x / (y * 2.0)

Julia

function code(x, y)
	return Float64(x / Float64(y * 2.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (y * 2.0);
end

Wolfram

code[x_, y_] := N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{2 \cdot y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (* 2.0 y)))

C

double code(double x, double y) {
	return x / (2.0 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (2.0d0 * y)
end function

Java

public static double code(double x, double y) {
	return x / (2.0 * y);
}

Python

def code(x, y):
	return x / (2.0 * y)

Julia

function code(x, y)
	return Float64(x / Float64(2.0 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (2.0 * y);
end

Wolfram

code[x_, y_] := N[(x / N[(2.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x}{y \cdot 2} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{x}{2 \cdot y} \]
4. Add Preprocessing

Alternative 2: 15.8% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

   \[\frac{x}{y \cdot 2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-lft-identity N/A

      \[\leadsto \color{blue}{1 \cdot \frac{x}{y \cdot 2}} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{y \cdot 2}} \]

   3. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{1 \cdot x}{y \cdot 2}} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{1 \cdot x}{\color{blue}{y \cdot 2}} \]

   5. *-commutative N/A

      \[\leadsto \frac{1 \cdot x}{\color{blue}{2 \cdot y}} \]

   6. count-2-rev N/A

      \[\leadsto \frac{1 \cdot x}{\color{blue}{y + y}} \]

   7. flip-+ N/A

      \[\leadsto \frac{1 \cdot x}{\color{blue}{\frac{y \cdot y - y \cdot y}{y - y}}} \]

   8. +-inverses N/A

      \[\leadsto \frac{1 \cdot x}{\frac{\color{blue}{0}}{y - y}} \]

   9. metadata-eval N/A

      \[\leadsto \frac{1 \cdot x}{\frac{\color{blue}{0 \cdot 0}}{y - y}} \]

   10. +-inverses N/A

       \[\leadsto \frac{1 \cdot x}{\frac{0 \cdot 0}{\color{blue}{0}}} \]

   11. associate-*r/ N/A

       \[\leadsto \frac{1 \cdot x}{\color{blue}{0 \cdot \frac{0}{0}}} \]

   12. +-inverses N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \frac{\color{blue}{y \cdot y - y \cdot y}}{0}} \]

   13. +-inverses N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \frac{y \cdot y - y \cdot y}{\color{blue}{y - y}}} \]

   14. flip-+ N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \color{blue}{\left(y + y\right)}} \]

   15. count-2-rev N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \color{blue}{\left(2 \cdot y\right)}} \]

   16. *-commutative N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \color{blue}{\left(y \cdot 2\right)}} \]

   17. lift-*.f64 N/A

       \[\leadsto \frac{1 \cdot x}{0 \cdot \color{blue}{\left(y \cdot 2\right)}} \]

   18. mul0-lft N/A

       \[\leadsto \frac{1 \cdot x}{\color{blue}{0}} \]

   19. associate-*l/ N/A

       \[\leadsto \color{blue}{\frac{1}{0} \cdot x} \]

   20. associate-/r/ N/A

       \[\leadsto \color{blue}{\frac{1}{\frac{0}{x}}} \]

   21. metadata-eval N/A

       \[\leadsto \frac{1}{\frac{\color{blue}{\mathsf{neg}\left(0\right)}}{x}} \]

   22. remove-double-neg N/A

       \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(0\right)}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)}}} \]

   23. frac-2neg N/A

       \[\leadsto \frac{1}{\color{blue}{\frac{0}{\mathsf{neg}\left(x\right)}}} \]

   24. div0 N/A

       \[\leadsto \frac{1}{\color{blue}{0}} \]

   25. mul0-lft N/A

       \[\leadsto \frac{1}{\color{blue}{0 \cdot \left(y \cdot 2\right)}} \]

   26. lift-*.f64 N/A

       \[\leadsto \frac{1}{0 \cdot \color{blue}{\left(y \cdot 2\right)}} \]

   27. *-commutative N/A

       \[\leadsto \frac{1}{0 \cdot \color{blue}{\left(2 \cdot y\right)}} \]

   28. count-2-rev N/A

       \[\leadsto \frac{1}{0 \cdot \color{blue}{\left(y + y\right)}} \]

   29. flip-+ N/A

       \[\leadsto \frac{1}{0 \cdot \color{blue}{\frac{y \cdot y - y \cdot y}{y - y}}} \]

   30. +-inverses N/A

       \[\leadsto \frac{1}{0 \cdot \frac{\color{blue}{0}}{y - y}} \]

   31. +-inverses N/A

       \[\leadsto \frac{1}{0 \cdot \frac{0}{\color{blue}{0}}} \]

   32. associate-*r/ N/A

       \[\leadsto \frac{1}{\color{blue}{\frac{0 \cdot 0}{0}}} \]

   33. metadata-eval N/A

       \[\leadsto \frac{1}{\frac{\color{blue}{0}}{0}} \]

   34. +-inverses N/A

       \[\leadsto \frac{1}{\frac{\color{blue}{y \cdot y - y \cdot y}}{0}} \]

   35. +-inverses N/A

       \[\leadsto \frac{1}{\frac{y \cdot y - y \cdot y}{\color{blue}{y - y}}} \]

4. Applied rewrites 16.3%

   \[\leadsto \color{blue}{0} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024298 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, C"
  :precision binary64
  (/ x (* y 2.0)))