Details

Time bar (total: 11.9s)

sample27.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
178
done78

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
8.0ms
(+ (* re re) (* im im))
8.0ms
(sqrt (+ (* re re) (* im im)))

series117.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(+ (* re re) (* im im))
66.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts
32 → 32
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
048379
1124347
2343295
3968295
42668295
done5000295

prune84.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
29.1b
(sqrt (+ (* re re) (* im im)))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
14.0ms
(+ (* re re) (* im im))
67.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series185.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (* re re) (* im im))
56.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
42.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.9s

Counts
136 → 136
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01212803
12331759
26381533
321871496
done50001457

prune295.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.9b

localize38.0ms

Local error

Found 4 expressions with local error:

29.1b
(sqrt (+ (* re re) (* im im)))
29.1b
(sqrt (+ (* re re) (* im im)))
29.1b
(sqrt (+ (* re re) (* im im)))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
9.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
9.0ms
(sqrt (+ (* re re) (* im im)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ (* re re) (* im im)))
52.0ms
(sqrt (+ (* re re) (* im im)))
61.0ms
(sqrt (+ (* re re) (* im im)))
74.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
038852
191744
2205680
3444656
41114656
53182656
done5001656

prune357.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.9b
(exp (log (sqrt (+ (* re re) (* im im)))))
29.1b
(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×add-exp-log flip3-+ log-pow add-cbrt-cube 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:
12.0ms
(+ (* re re) (* im im))
15.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
9.0ms
(sqrt (+ (* re re) (* im im)))

series139.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* re re) (* im im))
55.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
48.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.5s

Counts
57 → 57
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
087739
1169626
2398534
31056534
42807528
done5001528

prune167.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.9b

regimes1.0ms