diff --git a/tinygrad/tensor.py b/tinygrad/tensor.py
index 7e7fafbc02..442c08fd83 100644
--- a/tinygrad/tensor.py
+++ b/tinygrad/tensor.py
@@ -2414,24 +2414,23 @@ class Tensor:
       # simple pow identities
       if x < 0: return self.reciprocal().pow(-x)
       if x == 0: return 1 + self * 0
-      if x in [3,2,1]: return functools.reduce(lambda acc,_: acc * self, range(int(x)-1), self)
-      if x == 0.5: return self.sqrt()
+      if int(x - 0.5) + 0.5 == x: return self.pow(int(x - 0.5)) * self.sqrt()
+      if int(x) == x: return self.pow(x // 2).square() * (1 if x % 2 == 0 else self)
+
+    # positive const ** self
     if not isinstance(x, Tensor) and reverse and x > 0: return self.mul(math.log(x)).exp()
 
     base, exponent = self._broadcasted(x, reverse=reverse)
+    # start with b ** e = exp(e * log(b))
     ret = base.abs().log().mul(exponent).exp()
     # correct sign of negative base with odd exponent (cos has a period of 2pi so we use it here to get the oddness of the exponent)
-    sign = (exponent * math.pi).cos()
     negative_base = (base < 0).detach().where(1, 0)
     # 1 for non-negative base or negative even exponent, -1 for negative odd exponent, don't care about non-integer exponent
-    correct_sign = sign * negative_base + (1 - negative_base)
-    # inject nan for negative base is negative and non-integer exponent
-    to_nan = negative_base * (exponent != exponent.trunc()).detach()
-    # 0 -> 1; 1 -> nan
-    inject_nan = (-to_nan * 2 + 1).log().add(1)
-    ret = ret.mul(correct_sign).mul(inject_nan)
-    # fix 0 ** 0 = 1
-    return ((base == 0) * (exponent == 0)).detach().where(1, ret)
+    correct_sign = 1 + negative_base * ((exponent * math.pi).cos() - 1)
+    # inject nan for negative base and non-integer exponent
+    inject_nan = (negative_base * (exponent != exponent.trunc())).detach().where(math.nan, 1)
+    # apply correct_sign inject_nan, and fix 0 ** 0 = 1
+    return ((base == 0) * (exponent == 0)).detach().where(1, ret * correct_sign * inject_nan)
 
   def maximum(self, x:Union[Tensor, ConstType]) -> Tensor:
     """