diff --git a/autograd/numpy/numpy_tjps.py b/autograd/numpy/numpy_tjps.py
index 97174681..bdf965b9 100644
--- a/autograd/numpy/numpy_tjps.py
+++ b/autograd/numpy/numpy_tjps.py
@@ -88,23 +88,25 @@
 # ----- Trickier grads -----
 
 def tjp_dot_arg0(ans, vs, out_vs, A, B):
-    if anp.ndim(B) == 0 or anp.ndim(B) == 1 or anp.ndim(A) == 0:
-        contract_dims = max(0, anp.ndim(B) - (anp.ndim(A) != 0))
-        return lambda G: anp.tensordot(G, B, contract_dims)
+    A_ndim, B_ndim = vs.ndim, anp.ndim(B)
+    if B_ndim == 0 or B_ndim == 1 or A_ndim == 0:
+        contract_num = max(0, B_ndim - (A_ndim != 0))
+        return lambda G: anp.tensordot(G, B, contract_num)
     else:
-        return lambda G: anp.tensordot(G, anp.swapaxes(B, -1, -2), anp.ndim(B) - 1)
+        return lambda G: anp.tensordot(G, anp.swapaxes(B, -1, -2), B_ndim - 1)
 deftjp(anp.dot, tjp_dot_arg0)
 
 def tjp_dot_arg1(ans, vs, out_vs, A, B):
-    needs_transpose = anp.ndim(B) > 1 and anp.ndim(A) != 0
+    A_ndim, B_ndim = anp.ndim(A), vs.ndim
+    needs_transpose = B_ndim > 1 and A_ndim != 0
     swap = (lambda x: anp.swapaxes(x, -1, -2)) if needs_transpose else (lambda x: x)
-    if anp.ndim(A) == 0 or anp.ndim(A) == 1 or anp.ndim(B) == 0:
-        contract_dims = max(0, anp.ndim(A) - (anp.ndim(B) != 0))
+    if A_ndim == 0 or A_ndim == 1 or B_ndim == 0:
+        contract_dims = max(0, A_ndim - (B_ndim != 0))
         return lambda G: swap(anp.tensordot(G, A, contract_dims))
     else:
         return lambda G: swap(anp.tensordot(
-            G, A, [range(-anp.ndim(A) - anp.ndim(B) + 2, -anp.ndim(B) + 1),
-                   range(anp.ndim(A) - 1)]))
+            G, A, [range(-A_ndim - B_ndim + 2, -B_ndim + 1),
+                   range(A_ndim - 1)]))
 deftjp(anp.dot, tjp_dot_arg1, argnum=1)
 
 def tjp_transpose(ans, in_vs, out_vs, x, axes=None):