make the stabilization optimization of log(erfc(x)) work.

theano/tensor/opt.py

@@ -2707,6 +2707,10 @@ def local_grad_log_erfc_neg(node):
         sqr = neg.owner.inputs[0]
         x = sqr.owner.inputs[0]
     elif exp.owner.inputs[0].owner.op == T.mul:
+        #We should compare that -(erfc_x**2) is equivalent to mul_neg
+        #Their is currently not easy way to do this in the general case
+        #So we implement some common case for now.
+
         #in many case the neg are replaced by mul in the graph.
         #This also allow to stabilize log(erfc(cst*x))
         mul_neg = exp.owner.inputs[0]
@@ -2735,11 +2739,10 @@ def local_grad_log_erfc_neg(node):
         mul_neg = T.mul(*mul_inputs)
         
         try:
-            cst = get_constant_value(mul_neg.owner.inputs[0])
+            cst2 = get_constant_value(mul_neg.owner.inputs[0])
         except TypeError:
             return False
-        if cst!=-1:
-            return False#todo implement that case
+
         if len(mul_neg.owner.inputs) == 2:
             if not mul_neg.owner.inputs[1].owner or mul_neg.owner.inputs[1].owner.op != T.sqr:
                 return False
@@ -2752,6 +2755,26 @@ def local_grad_log_erfc_neg(node):
         else:
             return False
 
+        if cst2!=-1:
+            if (not erfc_x.owner or erfc_x.owner.op != T.mul 
+                or len(erfc_x.owner.inputs)!=2):
+                #todo implement that case
+                return False
+            if erfc_x.owner.inputs[1] is not mul_neg.owner.inputs[1]:
+                return False
+            
+            x = erfc_x
+            try:                
+                cst = get_constant_value(erfc_x.owner.inputs[0])
+            except TypeError:
+                return False
+            if cst2 != -cst*2:
+                return False
+            
+            #The constant is valid. Must check that the
+        elif erfc_x is not x: 
+                return False
+            
     else:
         return False
 
@@ -2759,8 +2782,6 @@ def local_grad_log_erfc_neg(node):
         #We use that flag to don't apply the optimization recursively
         return False
 
-    if erfc_x is not x: 
-        return False
 
     #we move the y outside the div.
     true_div_no_mul = T.true_div(exp,erfc)

theano/tensor/tests/test_opt.py

@@ -1863,6 +1863,13 @@ class T_local_erfc(unittest.TestCase):
         assert f.maker.env.outputs[0].dtype==theano.config.floatX
         assert all(numpy.isfinite(f(val)))
 
+        #test that it work correctly if x is x*2 in the graph.
+        f = theano.function([x],T.grad(T.log(T.erfc(2*x)),x), mode=mode)
+        #theano.printing.debugprint(f)
+        assert len(f.maker.env.nodes)==23, len(f.maker.env.nodes)
+        assert numpy.isfinite(f(val)).all()
+        assert f.maker.env.outputs[0].dtype==theano.config.floatX
+
         f = theano.function([x],T.grad(T.log(T.erfc(x)),x), mode=mode_fusion)
         assert len(f.maker.env.nodes)==1, len(f.maker.env.nodes)
         assert f.maker.env.outputs[0].dtype==theano.config.floatX