Details

analyze336.0ms (10.3%)

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

sample38.0ms (1.2%)

Algorithm

1×

intervals

Results

8.0ms	182×	body	80	valid
6.0ms	24×	body	2560	valid
4.0ms	19×	body	1280	valid
4.0ms	13×	body	5120	valid
3.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

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: 39.6b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
30.0b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(+ (* re re) (* im im))
4.0ms	(sqrt (+ (* re re) (* im im)))

series47.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
10.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(+ (* re re) (* im im))

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4962	739
1	4962	739

prune136.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Merged error: 11.6b

Counts

66 → 8

localize8.0ms (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:

5.0ms

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

series15.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5758	162

prune56.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	13	11	24

Merged error: 11.6b

Counts

24 → 11

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt (- im re))
0.3b	(* (sqrt 2.0) (sqrt (- im re)))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`sqrt-prod`
11×	`*-un-lft-identity`
8×	`associate-r`
7×	`pow1` `add-cube-cbrt`
6×	`associate-l`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 51

Calls

2 calls:

8.0ms	(* (sqrt 2.0) (sqrt (- im re)))
3.0ms	(sqrt (- im re))

series24.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

15.0ms	(* (sqrt 2.0) (sqrt (- im re)))
9.0ms	(sqrt (- im re))

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4936	522
1	4936	522

prune115.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	57	11	68

Merged error: 11.6b

Counts

68 → 11

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (- im re)))
0.0b	(sqrt (- im re))
0.3b	(* (sqrt 2.0) (exp (log (sqrt (- im re)))))
3.3b	(exp (log (sqrt (- im re))))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`log-prod` `sqrt-prod`
23×	`*-un-lft-identity`
20×	`exp-sum`
15×	`add-cube-cbrt`
11×	`pow1` `associate-r`
8×	`sqrt-div`
6×	`add-exp-log` `log-div` `exp-prod` `associate-l` `log-pow` `add-cbrt-cube` `unswap-sqr`
4×	`flip3--` `exp-diff` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-*r/`
1×	`rem-sqrt-square` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

12.0ms	(* (sqrt 2.0) (exp (log (sqrt (- im re)))))
8.0ms	(exp (log (sqrt (- im re))))
6.0ms	(log (sqrt (- im re)))
3.0ms	(sqrt (- im re))

series46.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sqrt 2.0) (exp (log (sqrt (- im re)))))
12.0ms	(log (sqrt (- im re)))
9.0ms	(exp (log (sqrt (- im re))))
9.0ms	(sqrt (- im re))

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4955	997
1	4955	997

prune173.0ms (5.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	110	11	121

Merged error: 11.6b

Counts

121 → 11

regimes799.0ms (24.6%)

Accuracy

Total 10.1b remaining (50.4%)

Threshold costs 0b (0%)

bsearch50.0ms (1.5%)

Steps

Iters	Range		Point
7	1.0250922956797423e-98	3.9960023839108e-97	1.040253303888319e-98
9	-4.18142418170851e-60	-2.756128105475179e-68	-2.8053796276591436e-68
7	-4.285299441618348e+123	-2.2129268921572134e+122	-3.0912337318531483e+123

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	63
1	59	63

end0.0ms (0%)

sample1.1s (32.9%)

Algorithm

1×

intervals

Results

290.0ms	5958×	body	80	valid
196.0ms	687×	body	2560	valid
114.0ms	499×	body	1280	valid
108.0ms	8000×	pre	80	true
104.0ms	305×	body	5120	valid
54.0ms	291×	body	640	valid
24.0ms	174×	body	320	valid
10.0ms	86×	body	160	valid

Details

analyze336.0ms (10.3%)

sample38.0ms (1.2%)

simplify16.0ms (0.5%)

prune6.0ms (0.2%)

localize10.0ms (0.3%)

rewrite25.0ms (0.8%)

series47.0ms (1.4%)

simplify56.0ms (1.7%)

prune136.0ms (4.2%)

localize8.0ms (0.2%)

rewrite5.0ms (0.2%)

series15.0ms (0.5%)

simplify39.0ms (1.2%)

prune56.0ms (1.7%)

localize7.0ms (0.2%)

rewrite13.0ms (0.4%)

series24.0ms (0.7%)

simplify47.0ms (1.4%)

prune115.0ms (3.5%)

localize18.0ms (0.6%)

rewrite32.0ms (1%)

series46.0ms (1.4%)

simplify66.0ms (2%)

prune173.0ms (5.3%)

regimes799.0ms (24.6%)

bsearch50.0ms (1.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (32.9%)

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