Details

analyze93.0ms (4%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

sample15.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

prune9.0ms (0.4%)

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: 32.1b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite8.0ms (0.3%)

Algorithm

1×	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:

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

series15.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (* re re) (* im im))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4909	295
1	4909	295

prune56.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 5.2b

Counts

33 → 6

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* re re) (* im im))))
0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite30.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`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`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series41.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (sqrt (+ (* re re) (* im im))))
7.0ms	(* (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)))

simplify96.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5201	1559

prune180.0ms (7.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Merged error: 5.2b

Counts

152 → 7

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3)))
20.7b	(cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`sqrt-prod`
77×	`add-sqr-sqrt`
72×	`cbrt-prod`
32×	`sqrt-div`
27×	`unpow-prod-down` `cube-prod` `associate-r` `unswap-sqr`
24×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `associate-l` `flip-+`
8×	`pow1` `cube-div` `cbrt-div`
6×	`add-exp-log`
5×	`add-cbrt-cube` `sqr-pow`
4×	`frac-times` `add-log-exp`
2×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-r/` `associate-l/`
1×	`pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 147

Calls

4 calls:

19.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3)))
6.0ms	(cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3))
6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (cbrt (pow (sqrt (sqrt (+ (* re re) (* im im)))) 3)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4903	2306
1	4903	2306

prune234.0ms (10.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	158	8	166

Merged error: 5.2b

Counts

166 → 8

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

20.7b	(cbrt (pow (sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (sqrt (+ (* re re) (* im im)))))) 3))
30.1b	(sqrt (+ (* re re) (* im im)))
30.1b	(sqrt (+ (* re re) (* im im)))
31.1b	(cbrt (+ (* re re) (* im im)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-div`
18×	`sqrt-div`
17×	`cbrt-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `flip-+`
8×	`cube-div` `sqrt-prod`
6×	`pow1`
4×	`add-exp-log` `frac-times` `unpow-prod-down` `cube-prod` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-r/` `associate-l/`
1×	`cube-mult` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

5.0ms	(cbrt (pow (sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (sqrt (+ (* re re) (* im im)))))) 3))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series53.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (pow (sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (sqrt (+ (* re re) (* im im)))))) 3))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4879	1435
1	4879	1435

prune154.0ms (6.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	86	8	94

Merged error: 5.2b

Counts

94 → 8

regimes561.0ms (24.2%)

Accuracy

Total 10.7b remaining (56.7%)

Threshold costs 0b (0%)

bsearch43.0ms (1.9%)

Steps

Iters	Range		Point
7	6.395471245595238e+116	6.569570556200689e+118	5.63142386051803e+118
9	-5.1104012668249873e-113	-2.112445118291879e-120	-5.047961066574088e-113
7	-7.472276120275499e-54	-4.459269101237006e-56	-4.576170092116779e-56
9	-1.838124499293251e+119	-1.1182452024942966e+113	-2.7569446232380357e+114

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	36
1	27	36

end0.0ms (0%)

sample417.0ms (18%)

Algorithm

1×

intervals

Results

274.0ms

8000×

body

valid

Details

analyze93.0ms (4%)

sample15.0ms (0.6%)

simplify3.0ms (0.1%)

prune9.0ms (0.4%)

localize5.0ms (0.2%)

rewrite8.0ms (0.3%)

series15.0ms (0.7%)

simplify62.0ms (2.7%)

prune56.0ms (2.4%)

localize8.0ms (0.3%)

rewrite30.0ms (1.3%)

series41.0ms (1.8%)

simplify96.0ms (4.1%)

prune180.0ms (7.8%)

localize11.0ms (0.5%)

rewrite39.0ms (1.7%)

series40.0ms (1.7%)

simplify63.0ms (2.7%)

prune234.0ms (10.1%)

localize17.0ms (0.7%)

rewrite19.0ms (0.8%)

series53.0ms (2.3%)

simplify45.0ms (1.9%)

prune154.0ms (6.6%)

regimes561.0ms (24.2%)

bsearch43.0ms (1.9%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample417.0ms (18%)

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