Golfed square root

# More efficient, 58 bytes (+ function name)

def square_root(x,i):
 v=x
 while(v*v-x)*i:v=v/2+x/v/2;i-=1
 return v

# Inefficient, 51 bytes (+ function name)

def square_root_b(x,i):
 v=x
 while i:v=v/2+x/v/2;i-=1
 return v

# Benchmark

import time, math
size = 10000
r = range(1, size + 1)
a = [0] * (size + 1)
b = [0] * (size + 1)
# Processor warmup
print("Warming up...", end = "")
for i in r:
    square_root(i, 1000)
    square_root_b(i, 1000)
print("Done")
# Efficient method
print("Benchmarking efficient method...", end = "")
time_a = time.perf_counter()
for i in r:
    a[i] = square_root(i, 1000)
time_b = time.perf_counter()
print("Done")
# Inefficient method
print("Benchmarking inefficient method...", end = "")
time_c = time.perf_counter()
for i in r:
    b[i] = square_root_b(i, 1000)
time_d = time.perf_counter()
print("Done")
# Result
err_a = 0
err_b = 0
for i in r:
    err_a += abs(a[i] - math.sqrt(i))
    err_b += abs(b[i] - math.sqrt(i))
print("Efficient method:   %d roots in %.3fms, total error %.8f" % (size, (time_b - time_a) * 1000, err_a))
print("Inefficient method: %d roots in %.3fms, total error %.8f" % (size, (time_d - time_c) * 1000, err_b))