Details

Time bar (total: 1.5s)

sample12.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
068
193
2113
done113

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize2.0ms

Local error

Found 1 expressions with local error:

0.0b
(hypot re im)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt hypot-udef *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(hypot re im)

series52.0ms

Counts
1 → 3
Calls
1 calls:
52.0ms
(hypot re im)

simplify991.0ms

Counts
13 → 13
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01760
12258
22552
33052
43652
54652
66952
713452
835052
9129452
done500152

prune32.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot re im))
0.0b
(hypot re im)
0.0b
(hypot re im)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
13×add-cube-cbrt *-un-lft-identity
9×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×hypot-udef
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 86
Calls
4 calls:
1.0ms
(sqrt (hypot re im))
0.0ms
(hypot re im)
0.0ms
(hypot re im)
6.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (hypot re im))
51.0ms
(hypot re im)
47.0ms
(hypot re im)
51.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))

simplify136.0ms

Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
086890
1163565
2445505