Details

analyze339.0ms (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample33.0ms (1.1%)

Algorithm

1×

intervals

Results

9.0ms	193×	body	80	valid
7.0ms	26×	body	2560	valid
3.0ms	15×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.0b

Counts

2 → 1

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

7.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series35.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4936	551
1	4936	551

prune114.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 17.8b

Counts

50 → 7

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.4b	(sqrt (+ (* re re) (* im im)))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms (1.5%)

Algorithm

1×	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:

16.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
15.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series24.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune221.0ms (7.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 17.8b

Counts

143 → 7

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

8.2b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
29.4b	(sqrt (+ (* re re) (* im im)))
29.4b	(sqrt (+ (* re re) (* im im)))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

23.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series25.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (* (pow (sqrt (cbrt (sqrt (+ (* re re) (* im im))))) 4) (cbrt (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5058	634

prune154.0ms (5.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	68	7	75

Merged error: 17.8b

Counts

75 → 7

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
29.4b	(sqrt (* (* im im) 2.0))
29.4b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `sqrt-prod`
37×	`*-un-lft-identity`
36×	`times-frac`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`pow1`
9×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`sqrt-pow1` `sqrt-div` `associate-/l*`
3×	`pow-prod-down`
2×	`flip3--` `pow1/2` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

13.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (* (* im im) 2.0))
4.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (sqrt (* (* im im) 2.0)) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (* (* im im) 2.0))

simplify41.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4917	2308
1	4917	2308

prune191.0ms (6.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	1	3	4
Picked	1	0	1
Done	2	0	2
Total	116	8	124

Merged error: 10.2b

Counts

124 → 8

regimes283.0ms (9.6%)

Accuracy

Total 14.0b remaining (57.2%)

Threshold costs 0b (0%)

bsearch126.0ms (4.3%)

Steps

Iters	Range		Point
10	7.879054437551379e+57	1.2371522206970305e+70	8.99727301172237e+57
6	9.624781449627483e+56	7.879054437551379e+57	9.810431200447886e+56
7	1.2694555867180504e-78	2.4744285905050064e-77	1.4310037079643518e-78
6	1.6748916741442751e-118	1.4878500325911111e-117	4.000710555951358e-118
9	3.254534619998204e-188	7.142653857917004e-181	3.3363403467192465e-186
8	-3.0721949970216363e-267	-2.615506481311857e-271	-3.2410829879680627e-270
9	-1.8388342581148795e+169	-2.6092957248578346e+162	-2.649308197943826e+162

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	130
1	77	130

end0.0ms (0%)

sample928.0ms (31.7%)

Algorithm

1×

intervals

Results

297.0ms	6048×	body	80	valid
194.0ms	664×	body	2560	valid
122.0ms	523×	body	1280	valid
89.0ms	262×	body	5120	valid
50.0ms	274×	body	640	valid
22.0ms	147×	body	320	valid
7.0ms	82×	body	160	valid

Details

analyze339.0ms (11.6%)

sample33.0ms (1.1%)

simplify3.0ms (0.1%)

prune6.0ms (0.2%)

localize13.0ms (0.4%)

rewrite19.0ms (0.6%)

series35.0ms (1.2%)

simplify53.0ms (1.8%)

prune114.0ms (3.9%)

localize12.0ms (0.4%)

rewrite43.0ms (1.5%)

series24.0ms (0.8%)

simplify65.0ms (2.2%)

prune221.0ms (7.5%)

localize20.0ms (0.7%)

rewrite37.0ms (1.3%)

series25.0ms (0.8%)

simplify61.0ms (2.1%)

prune154.0ms (5.3%)

localize12.0ms (0.4%)

rewrite31.0ms (1.1%)

series40.0ms (1.4%)

simplify41.0ms (1.4%)

prune191.0ms (6.5%)

regimes283.0ms (9.6%)

bsearch126.0ms (4.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample928.0ms (31.7%)

Profiling