Details

analyze14.0ms (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

sample209.0ms (3.1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

valid

simplify504.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4811	6
1	4811	6

prune10.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 29.9b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(* (pow x 2.0) 2)
28.9b	(sqrt (* (pow x 2.0) 2))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`pow1` `associate-r` `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 (* (pow x 2.0) 2))
4.0ms	(* (pow x 2.0) 2)

series144.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

86.0ms	(sqrt (* (pow x 2.0) 2))
58.0ms	(* (pow x 2.0) 2)

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4905	307
1	4905	307

prune110.0ms (1.7%)

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

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* 2 (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 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0)))

rewrite137.0ms (2.1%)

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 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0))
28.0ms	(sqrt (* 2 (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)

series194.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (* 2 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0)))
57.0ms	(* 2 (pow (/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0)) 1.0))
53.0ms	(/ (pow -1 2.0) (pow (pow (/ -1 x) 2.0) 1.0))
19.0ms	(pow (/ -1 x) 2.0)

simplify125.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4984	9083
1	4984	9083

prune2.5s (37.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	462	1	463
Fresh	0	6	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 (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)))

rewrite606.0ms (9.1%)

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:

590.0ms	(sqrt (* 2 (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)))
4.0ms	(sqrt (pow (/ -1 x) 2.0))
4.0ms	(sqrt (pow (/ -1 x) 2.0))
4.0ms	(pow (/ -1 x) 2.0)

series201.0ms (3%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (pow (/ -1 x) 2.0))
61.0ms	(sqrt (* 2 (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)))
60.0ms	(sqrt (pow (/ -1 x) 2.0))
19.0ms	(pow (/ -1 x) 2.0)

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5095	1157

prune464.0ms (7%)

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

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (* (pow x 2.0) 2)))
28.9b	(sqrt (* (pow x 2.0) 2))
28.9b	(sqrt (* (pow x 2.0) 2))
28.9b	(sqrt (* (pow x 2.0) 2))

rewrite14.0ms (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 (* (pow x 2.0) 2)))
3.0ms	(sqrt (* (pow x 2.0) 2))
3.0ms	(sqrt (* (pow x 2.0) 2))
3.0ms	(sqrt (* (pow x 2.0) 2))

series253.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (sqrt (* (pow x 2.0) 2)))
59.0ms	(sqrt (* (pow x 2.0) 2))
59.0ms	(sqrt (* (pow x 2.0) 2))
58.0ms	(sqrt (* (pow x 2.0) 2))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4886	458
1	4886	458

prune200.0ms (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

regimes190.0ms (2.9%)

Accuracy

Total 0.2b remaining (1%)

Threshold costs 0.2b (1%)

bsearch21.0ms (0.3%)

Steps

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

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms (0%)

sample536.0ms (8.1%)

Algorithm

1×

intervals

Results

430.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze14.0ms (0.2%)

sample209.0ms (3.1%)

simplify504.0ms (7.6%)

prune10.0ms (0.1%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series144.0ms (2.2%)

simplify56.0ms (0.8%)

prune110.0ms (1.7%)

localize12.0ms (0.2%)

rewrite137.0ms (2.1%)

series194.0ms (2.9%)

simplify125.0ms (1.9%)

prune2.5s (37.5%)

localize15.0ms (0.2%)

rewrite606.0ms (9.1%)

series201.0ms (3%)

simplify59.0ms (0.9%)

prune464.0ms (7%)

localize9.0ms (0.1%)

rewrite14.0ms (0.2%)

series253.0ms (3.8%)

simplify55.0ms (0.8%)

prune200.0ms (3%)

regimes190.0ms (2.9%)

bsearch21.0ms (0.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample536.0ms (8.1%)

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