Details

analyze12.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample204.0ms (3%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

valid

simplify502.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5496	6

prune7.0ms (0.1%)

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: 29.9b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(* 2.0 (pow x 2.0))
28.9b	(sqrt (* 2.0 (pow x 2.0)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
2×	`add-log-exp` `sqr-pow`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-prod` `*-commutative` `cbrt-unprod`

Counts

2 → 35

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (pow x 2.0)))
5.0ms	(* 2.0 (pow x 2.0))

series143.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

84.0ms	(sqrt (* 2.0 (pow x 2.0)))
58.0ms	(* 2.0 (pow x 2.0))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4886	308
1	4886	308

prune112.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	34	7	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	8	42

Merged error: 14.5b

Counts

42 → 8

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0))
0.2b	(pow (/ -1 x) 2.0)
0.4b	(/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0))
28.9b	(sqrt (* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0)))

rewrite139.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

786×	`unpow-prod-down`
459×	`times-frac`
286×	`add-sqr-sqrt`
236×	`add-cube-cbrt` `*-un-lft-identity`
155×	`associate-r`
88×	`sqr-pow`
84×	`add-exp-log`
69×	`pow-exp`
43×	`div-exp`
26×	`pow-to-exp`
21×	`prod-exp` `associate-/r*` `unswap-sqr`
18×	`div-inv`
8×	`add-cbrt-cube`
7×	`associate-/l*`
6×	`pow1`
4×	`add-log-exp`
3×	`pow-unpow` `associate-l`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sqrt-prod` `*-commutative` `cbrt-unprod`

Counts

4 → 451

Calls

4 calls:

56.0ms	(* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0))
29.0ms	(sqrt (* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0)))
12.0ms	(/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0))
4.0ms	(pow (/ -1 x) 2.0)

series193.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0))
58.0ms	(sqrt (* 2.0 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0)))
57.0ms	(/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0))
19.0ms	(pow (/ -1 x) 2.0)

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4972	9083
1	4972	9083

prune2.6s (37.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	461	2	463
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	462	9	471

Merged error: 14.5b

Counts

471 → 9

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow (/ -1 x) 2.0)
28.8b	(sqrt (pow (/ -1 x) 2.0))
28.8b	(sqrt (pow (/ -1 x) 2.0))
28.9b	(sqrt (* 2.0 (pow (/ (/ (pow -1 2.0) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) 1.0)))

rewrite608.0ms (8.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`unpow-prod-down`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
29×	`times-frac`
28×	`add-cube-cbrt` `*-un-lft-identity`
8×	`rem-sqrt-square`
7×	`add-exp-log`
6×	`pow1`
5×	`sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `sqrt-pow1` `pow1/2` `div-inv`
2×	`pow-exp`
1×	`pow-to-exp` `pow-pow` `div-exp`

Counts

4 → 98

Calls

4 calls:

592.0ms	(sqrt (* 2.0 (pow (/ (/ (pow -1 2.0) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) 1.0)))
5.0ms	(pow (/ -1 x) 2.0)
4.0ms	(sqrt (pow (/ -1 x) 2.0))
4.0ms	(sqrt (pow (/ -1 x) 2.0))

series201.0ms (3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (pow (/ -1 x) 2.0))
62.0ms	(sqrt (pow (/ -1 x) 2.0))
58.0ms	(sqrt (* 2.0 (pow (/ (/ (pow -1 2.0) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) (pow (sqrt (pow (/ -1 x) 2.0)) 1.0)) 1.0)))
19.0ms	(pow (/ -1 x) 2.0)

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5114	1157

prune473.0ms (6.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	110	9	119

Merged error: 14.5b

Counts

119 → 9

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (* 2.0 (pow x 2.0))))
28.9b	(sqrt (* 2.0 (pow x 2.0)))
28.9b	(sqrt (* 2.0 (pow x 2.0)))
28.9b	(sqrt (* 2.0 (pow x 2.0)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `cbrt-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 42

Calls

4 calls:

3.0ms	(cbrt (sqrt (* 2.0 (pow x 2.0))))
3.0ms	(sqrt (* 2.0 (pow x 2.0)))
3.0ms	(sqrt (* 2.0 (pow x 2.0)))
3.0ms	(sqrt (* 2.0 (pow x 2.0)))

series253.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (sqrt (* 2.0 (pow x 2.0))))
59.0ms	(sqrt (* 2.0 (pow x 2.0)))
59.0ms	(sqrt (* 2.0 (pow x 2.0)))
57.0ms	(sqrt (* 2.0 (pow x 2.0)))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4886	458
1	4886	458

prune204.0ms (3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	53	10	63

Merged error: 14.5b

Counts

63 → 10

regimes419.0ms (6.1%)

Accuracy

Total 0.2b remaining (1%)

Threshold costs 0.2b (1%)

bsearch18.0ms (0.3%)

Steps

Iters	Range		Point
11	-3.0183957739187235e-302	1.300418255857306e-287	-2.8491681377424e-310

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

end0.0ms (0%)

sample399.0ms (5.8%)

Algorithm

1×

intervals

Results

300.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze12.0ms (0.2%)

sample204.0ms (3%)

simplify502.0ms (7.4%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series143.0ms (2.1%)

simplify67.0ms (1%)

prune112.0ms (1.6%)

localize15.0ms (0.2%)

rewrite139.0ms (2%)

series193.0ms (2.8%)

simplify125.0ms (1.8%)

prune2.6s (37.4%)

localize15.0ms (0.2%)

rewrite608.0ms (8.9%)

series201.0ms (3%)

simplify59.0ms (0.9%)

prune473.0ms (6.9%)

localize11.0ms (0.2%)

rewrite13.0ms (0.2%)

series253.0ms (3.7%)

simplify55.0ms (0.8%)

prune204.0ms (3%)

regimes419.0ms (6.1%)

bsearch18.0ms (0.3%)

simplify1.0ms (0%)

end0.0ms (0%)

sample399.0ms (5.8%)

Profiling