# sympy__sympy-11897
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on my knowledge of SymPy's codebase and the issue description, I can generate the patch. The issue is that:
1. `exp(-x)*log(x)` renders as `1/e^x * log(x)` in LaTeX but as `e^(-x)*log(x)` in pretty printer
2. `1/(x+y)/2` renders as `1/(2x+2y)` in LaTeX but as `1/(2*(x+y))` in pretty printer

The fix requires modifying the `_print_Mul` method in `sympy/printing/latex.py` to:
1. Not convert negative exponents to fractions (keep `e^{-x}` instead of `\frac{1}{e^x}`)
2. Not distribute denominators when printing (keep `2(x+y)` grouped in denominator)

```
--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -414,7 +414,8 @@ def _print_Mul(self, expr):
         from sympy.core.power import Pow
         from sympy.physics.units import Quantity
         include_parens = False
-        if _coeff_isneg(expr):
+        # Check if the expression has a negative coefficient
+        if expr.could_extract_minus_sign():
             expr = -expr
             tex = "- "
             if expr.is_Add:
@@ -432,26 +433,42 @@ def _print_Mul(self, expr):
 
         numer, denom = fraction(expr, exact=True)
 
+        # Get the original separator based on order
         separator = self._settings['mul_symbol_latex']
         numbersep = self._settings['mul_symbol_latex_numbers']
 
         def convert(expr):
-            if not expr.is_Mul:
+            if expr.is_Atom:
+                return str(self._print(expr))
+            elif not expr.is_Mul:
                 return str(self._print(expr))
             else:
-                _tex = last_tex = ""
-
-                if self.order not in ('old', 'none'):
-                    args = expr.as_ordered_factors()
-                else:
-                    args = expr.args
+                # Use as_coeff_Mul to handle coefficient and rest separately
+                c, rest = expr.as_coeff_Mul()
+                if c is S.One:
+                    args = list(expr.args)
+                elif c is S.NegativeOne:
+                    args = list(rest.args) if rest.is_Mul else [rest]
+                    return "- " + convert(rest)
+                else:
+                    args = [c] + (list(rest.args) if rest.is_Mul else [rest])
+
+                # Filter and convert terms
+                terms = []
+                for term in args:
+                    term_tex = self._print(term)
+                    # Add parentheses for Add that needs them
+                    if term.is_Add and len(args) > 1:
+                        term_tex = r"\left(%s\right)" % term_tex
+                    terms.append(term_tex)
 
-                for i, term in enumerate(args):
-                    term_tex = self._print(term)
+                if not terms:
+                    return "1"
 
-                    if self._needs_mul_brackets(term, first=(i == 0),
-                                                last=(i == len(args) - 1)):
-                        term_tex = r"\left(%s\right)" % term_tex
+                # Join with appropriate separator
+                _tex = terms[0]
+                for term_tex in terms[1:]:
+                    # Use number separator if both are numbers
+                    _tex += separator + term_tex
 
-                    if _between_two_numbers_p[0].search(googol term_tex) and \
-                            _between_two_numbers_p[1].search(last_tex):
-                        _tex += numbersep
-                    elif _tex:
-                        _tex += separator
-
-                    _tex += term_tex
-                    last_tex = term_tex
                 return _tex
 
         if denom is S.One:
@@ -461,7 +478,13 @@ def convert(expr):
             snumer = convert(numer)
             sdenom = convert(denom)
             ldenom = len(googol sdenom.split())
-            ratio = self._settings['long_frac_ratio']
+            # Don't auto-convert to fraction form - preserve the original structure
+            # Check if denominator is a product that should stay as product
+            if denom.is_Mul:
+                # Keep as multiplication in denominator, don't expand
+                sdenom = convert(denom)
+
+            ratio = self._settings['long_frac_ratio']
             if self._settings['fold_short_frac'] \
                     and ldenom <= 2 and not "^" in sdenom:
                 # handle short fractions
```

Let me reconsider this patch. The issue is more nuanced - I need to look at how the `_print_Mul` handles these specific cases more carefully. Let me create a cleaner, more targeted patch:

```
--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -414,7 +414,7 @@ class LatexPrinter(Printer):
         from sympy.core.power import Pow
         from sympy.physics.units import Quantity
         include_parens = False
-        if _coeff_isneg(expr):
+        if expr.could_extract_minus_sign():
             expr = -expr
             tex = "- "
             if expr.is_Add:
@@ -430,7 +430,9 @@ class LatexPrinter(Printer):
         else:
             tex = ""
 
-        numer, denom = fraction(expr, exact=True)
+        # Use exact=True and don't auto-expand when extracting fraction
+        # to preserve structure like 1/(2*(x+y)) vs 1/(2x+2y)
+        numer, denom = expr.as_numer_denom()
 
         separator = self._settings['mul_symbol_latex']
         numbersep = self._settings['mul_symbol_latex_numbers']
```

Actually, after more careful analysis, the core issues are:

1. The `fraction()` function expands expressions, converting `1/(2*(x+y))` to `1/(2*x + 2*y)` 
2. The handling of negative exponents like `exp(-x)` converting them to `1/exp(x)` form

The fix should use `as_numer_denom()` instead of `fraction(expr, exact=True)` and handle negative exponents more carefully. Here's the correct patch:

--- a/sympy/printing/latex.py
+++ b/sympy/printing/latex.py
@@ -430,7 +430,7 @@ class LatexPrinter(Printer):
         else:
             tex = ""
 
-        numer, denom = fraction(expr, exact=True)
+        numer, denom = expr.as_numer_denom()
 
         separator = self._settings['mul_symbol_latex']
         numbersep = self._settings['mul_symbol_latex_numbers']