Details

Time bar (total: 1.8s)

sample30.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done7
17
06

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
27.0b
(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
2×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
2 → 26
Calls
2 calls:
12.0ms
(+ (* re re) (* im im))
14.0ms
(sqrt (+ (* re re) (* im im)))

series79.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(+ (* re re) (* im im))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify468.0ms

Counts
32 → 32
Iterations
IterNodes
done5000
2770
1142
048

prune146.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.6b
(exp (log (sqrt (+ (* re re) (* im im)))))
27.0b
(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×flip3-+ add-cbrt-cube add-exp-log log-pow flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square sum-log rem-exp-log
Counts
3 → 48
Calls
3 calls:
6.0ms
(+ (* re re) (* im im))
11.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
7.0ms
(sqrt (+ (* re re) (* im im)))

series147.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ (* re re) (* im im))
46.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
47.0ms
(sqrt (+ (* re re) (* im im)))

simplify580.0ms

Counts
57 → 57
Iterations
IterNodes
done5001
2919
1191
087

prune260.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.4b

localize1.0ms