diff --git a/addchain_5inv.py b/addchain_5inv.py
new file mode 100755
index 0000000..369e366
--- /dev/null
+++ b/addchain_5inv.py
@@ -0,0 +1,123 @@
+#!/usr/bin/env python3
+
+class Chain(object):
+    SQR_COST = 0.8
+    MUL_COST = 1
+
+    def __init__(self):
+        self.muls = 0
+        self.sqrs = 0
+        self.computed = set((1,))
+
+    def sqr(self, x, n=1):
+        for i in range(n):
+            assert(x in self.computed)
+            self.sqrs += 1
+            x = 2*x
+            self.computed.add(x)
+
+        return x
+
+    def mul(self, x, y):
+        assert(x in self.computed)
+        assert(y in self.computed)
+        assert(x != y)
+        self.muls += 1
+        r = x+y
+        self.computed.add(r)
+        return r
+
+    def sqrmul(self, x, n, y):
+        return self.mul(self.sqr(x, n), y)
+
+    def cost(self):
+        return self.sqrs*self.SQR_COST + self.muls*self.MUL_COST
+
+    def __repr__(self):
+        return "%dS + %dM (%.1f)" % (self.sqrs, self.muls, self.cost())
+
+
+x_p = 0b11001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001101001110100111101110000011001001101000010000101001100000111000101110000011110000111100111111000011001100110011001100110011001101
+#                                                                                                                                         a       b   c d      e     f  g    h      i   j       k   l   m        n       o     p q                                 r s
+#                                                                                                                                          11001100110011
+#                                                                                                                                               111   1
+
+pc = Chain()
+p1    = 1
+p10   = pc.sqr(p1)
+p11   = pc.mul(p10, p1)
+p101  = pc.mul(p10, p11)
+p110  = pc.sqr(p11)
+p111  = pc.mul(p110, p1)
+p1001 = pc.mul(p111, p10)
+p1111 = pc.mul(p1001, p110)
+pr2   = pc.sqrmul(p110, 3, p11)
+pr4   = pc.sqrmul(pr2, 8, pr2)
+pr8   = pc.sqrmul(pr4, 16, pr4)
+pr16  = pc.sqrmul(pr8, 32, pr8)
+pr32  = pc.sqrmul(pr16, 64, pr16)
+pr32a = pc.sqrmul(pr32, 5, p1001)
+pr32b = pc.sqrmul(pr32a, 8, p111)
+pr32c = pc.sqrmul(pr32b, 4, p1)
+pr32d = pc.sqrmul(pr32c, 2, pr4)
+pr32e = pc.sqrmul(pr32d, 7, p11)
+pr32f = pc.sqrmul(pr32e, 6, p1001)
+pr32g = pc.sqrmul(pr32f, 3, p101)
+pr32h = pc.sqrmul(pr32g, 5, p1)
+pr32i = pc.sqrmul(pr32h, 7, p101)
+pr32j = pc.sqrmul(pr32i, 4, p11)
+pr32k = pc.sqrmul(pr32j, 8, p111)
+pr32l = pc.sqrmul(pr32k, 4, p1)
+pr32m = pc.sqrmul(pr32l, 4, p111)
+pr32n = pc.sqrmul(pr32m, 9, p1111)
+pr32o = pc.sqrmul(pr32n, 8, p1111)
+pr32p = pc.sqrmul(pr32o, 6, p1111)
+pr32q = pc.sqrmul(pr32p, 2, p11)
+pr32r = pc.sqrmul(pr32q, 34, pr8)
+pr32s = pc.sqrmul(pr32r, 2, p1)
+assert pr32s == x_p
+print(pc)
+
+x_q = 0b11001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001101001110100111101110000011001001101000010100001110111010010010101101011010011111001000101000000011001100110011001100110011001101
+#                                                                                                                                         a       b   c d      e     f  g      h      i   j    k    l  m   n  o     p   q     r                                    s t
+#                                                                                                                                          11001100110011
+#                                                                                                                                               111   1
+
+qc = Chain()
+q1    = 1
+q10   = qc.sqr(q1)
+q11   = qc.mul(q10, q1)
+q101  = qc.mul(q10, q11)
+q110  = qc.sqr(q11)
+q111  = qc.mul(q110, q1)
+q1001 = qc.mul(q111, q10)
+q1111 = qc.mul(q1001, q110)
+qr2   = qc.sqrmul(q110, 3, q11)
+qr4   = qc.sqrmul(qr2, 8, qr2)
+qr8   = qc.sqrmul(qr4, 16, qr4)
+qr16  = qc.sqrmul(qr8, 32, qr8)
+qr32  = qc.sqrmul(qr16, 64, qr16)
+qr32a = qc.sqrmul(qr32, 5, q1001)
+qr32b = qc.sqrmul(qr32a, 8, q111)
+qr32c = qc.sqrmul(qr32b, 4, q1)
+qr32d = qc.sqrmul(qr32c, 2, qr4)
+qr32e = qc.sqrmul(qr32d, 7, q11)
+qr32f = qc.sqrmul(qr32e, 6, q1001)
+qr32g = qc.sqrmul(qr32f, 3, q101)
+# diverges here
+qr32h = qc.sqrmul(qr32g, 7, q101)
+qr32i = qc.sqrmul(qr32h, 7, q111)
+qr32j = qc.sqrmul(qr32i, 4, q111)
+qr32k = qc.sqrmul(qr32j, 5, q1001)
+qr32l = qc.sqrmul(qr32k, 5, q101)
+qr32m = qc.sqrmul(qr32l, 3, q11)
+qr32n = qc.sqrmul(qr32m, 4, q101)
+qr32o = qc.sqrmul(qr32n, 3, q101)
+qr32p = qc.sqrmul(qr32o, 6, q1111)
+qr32q = qc.sqrmul(qr32p, 4, q1001)
+qr32r = qc.sqrmul(qr32q, 6, q101)
+qr32s = qc.sqrmul(qr32r, 37, qr8)
+qr32t = qc.sqrmul(qr32s, 2, q1)
+assert qr32t == x_q
+print(qc)
+
diff --git a/addchain.py b/addchain_sqrt.py
similarity index 94%
rename from addchain.py
rename to addchain_sqrt.py
index 9f5d52e..72eca4f 100755
--- a/addchain.py
+++ b/addchain_sqrt.py
@@ -36,7 +36,10 @@ class Chain(object):
         return self.mul(self.sqr(x, n), y)
 
     def cost(self):
-        return (self.sqrs, self.muls, self.sqrs*self.SQR_COST + self.muls*self.MUL_COST)
+        return self.sqrs*self.SQR_COST + self.muls*self.MUL_COST
+
+    def __repr__(self):
+        return "%dS + %dM (%.1f)" % (self.sqrs, self.muls, self.cost())
 
 
 p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
@@ -80,7 +83,7 @@ rr    = rch.sqrmul(rq,  7, r111)
 rs    = rch.sqrmul(rr,  3, r11)
 rt    = rch.sqr(rs)
 assert rt == r, format(rt, 'b')
-print(rch.cost())
+print(rch)
 
 
 # print(format(q >> (n+1), 'b'))
@@ -120,4 +123,4 @@ sr    = sch.sqrmul(sq,  5, s1011)
 ss    = sch.sqrmul(sr,  3, s1)
 st    = sch.sqr(ss, 4)
 assert st == s, format(st, 'b')
-print(sch.cost())
+print(sch)
diff --git a/squareroottab.sage b/squareroottab.sage
index 969683c..144e82d 100755
--- a/squareroottab.sage
+++ b/squareroottab.sage
@@ -165,7 +165,7 @@ class SqrtField:
 p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
 q = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
 
-# see addchain.py for base costs of u^{(m-1)/2}
+# see addchain_sqrt.py for base costs of u^{(m-1)/2}
 F_p = SqrtField(p, 5, Cost(223, 23), hash_xor=0x11BE,   hash_mod=1098)
 F_q = SqrtField(q, 5, Cost(223, 24), hash_xor=0x116A9E, hash_mod=1206)