Details

analyze333.0ms (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample34.0ms (1.3%)

Algorithm

1×

intervals

Results

9.0ms	194×	body	80	valid
6.0ms	23×	body	2560	valid
3.0ms	15×	body	1280	valid
3.0ms	256×	pre	80	true
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify18.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	265	15
1	265	15

prune6.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 38.6b

Counts

2 → 1

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
31.4b	(sqrt (+ (* re re) (* im im)))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series50.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
14.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5010	608

prune117.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Merged error: 10.3b

Counts

52 → 8

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

(sqrt (* 2.0 (- im re)))

series14.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

14.0ms

(sqrt (* 2.0 (- im re)))

simplify43.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5758	162

prune49.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	15	9	24

Merged error: 10.3b

Counts

24 → 9

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (- im re)))
3.6b	(exp (log (sqrt (* 2.0 (- im re)))))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1`
7×	`exp-prod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `-un-lft-identity` `sqrt-pow1` `sqrt-div` `associate-r/` `exp-sum` `log-pow`
2×	`add-exp-log` `log-div` `flip3--` `pow1/2` `exp-diff` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`
1×	`rem-exp-log`

Counts

2 → 34

Calls

2 calls:

6.0ms	(exp (log (sqrt (* 2.0 (- im re)))))
4.0ms	(sqrt (* 2.0 (- im re)))

series31.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(sqrt (* 2.0 (- im re)))
14.0ms	(exp (log (sqrt (* 2.0 (- im re)))))

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4952	382
1	4952	382

prune96.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	39	10	49

Merged error: 10.3b

Counts

49 → 10

localize15.0ms (0.5%)

Local error

Found 1 expressions with local error:

3.9b	(pow (exp 1/2) (log (* 2.0 (- im re))))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1` `pow-unpow`
4×	`add-sqr-sqrt` `add-cube-cbrt` `pow-pow` `*-un-lft-identity`
3×	`unpow-prod-down` `exp-prod`
2×	`log-div` `associate-*r/` `log-pow` `pow-sub`
1×	`unpow-prod-up` `add-exp-log` `pow-to-exp` `log-prod` `flip3--` `pow-prod-down` `pow-exp` `add-cbrt-cube` `flip--` `add-log-exp` `sqr-pow`

Counts

1 → 25

Calls

1 calls:

7.0ms

(pow (exp 1/2) (log (* 2.0 (- im re))))

series39.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

39.0ms

(pow (exp 1/2) (log (* 2.0 (- im re))))

simplify62.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5076	321

prune62.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	3	4	7
Picked	1	0	1
Done	1	1	2
Total	30	8	38

Merged error: 10.1b

Counts

38 → 8

regimes532.0ms (19.6%)

Accuracy

Total 10.2b remaining (50.5%)

Threshold costs 0b (0%)

bsearch55.0ms (2%)

Steps

Iters	Range	Point
8	1.5910882628693757e+50	1.997077409729872e+54	1.6159376490511677e+50
6	-2.26008391369202e-57	-2.7796175438424402e-58	-2.8173110054179868e-58
8	-7.908073286170721e+124	-6.8454521643222085e+121	-2.314214383594253e+124

Iters

Range

Point

1.5910882628693757e+50

1.997077409729872e+54

1.6159376490511677e+50

-2.26008391369202e-57

-2.7796175438424402e-58

-2.8173110054179868e-58

-7.908073286170721e+124

-6.8454521643222085e+121

-2.314214383594253e+124

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	61
1	56	61

end0.0ms (0%)

sample993.0ms (36.6%)

Algorithm

1×

intervals

Results

273.0ms	6004×	body	80	valid
204.0ms	739×	body	2560	valid
109.0ms	489×	body	1280	valid
96.0ms	8000×	pre	80	true
82.0ms	249×	body	5120	valid
48.0ms	282×	body	640	valid
20.0ms	158×	body	320	valid
7.0ms	79×	body	160	valid

Details

analyze333.0ms (12.3%)

sample34.0ms (1.3%)

simplify18.0ms (0.7%)

prune6.0ms (0.2%)

localize10.0ms (0.4%)

rewrite22.0ms (0.8%)

series50.0ms (1.8%)

simplify29.0ms (1.1%)

prune117.0ms (4.3%)

localize6.0ms (0.2%)

rewrite5.0ms (0.2%)

series14.0ms (0.5%)

simplify43.0ms (1.6%)

prune49.0ms (1.8%)

localize9.0ms (0.3%)

rewrite12.0ms (0.4%)

series31.0ms (1.1%)

simplify65.0ms (2.4%)

prune96.0ms (3.5%)

localize15.0ms (0.5%)

rewrite7.0ms (0.3%)

series39.0ms (1.4%)

simplify62.0ms (2.3%)

prune62.0ms (2.3%)

regimes532.0ms (19.6%)

bsearch55.0ms (2%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample993.0ms (36.6%)

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