Details

analyze1.6s (19.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

sample75.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	117×	body	160	valid
17.0ms	178×	body	80	nan
13.0ms	139×	body	80	valid

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	19

prune9.0ms (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: 10.5b

Counts

2 → 1

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `clear-num` `flip--`

Counts

4 → 130

Calls

4 calls:

13.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(pow (/ t l) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series270.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
98.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(pow (/ t l) 2.0)

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4953	3362
1	4953	3362

prune495.0ms (5.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Merged error: 10.5b

Counts

143 → 8

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(pow (/ t l) 2.0)
0.6b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `div-exp` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 79

Calls

4 calls:

4.0ms	(pow (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series91.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(pow (/ t l) 2.0)
13.0ms	(pow (/ Om Omc) 2.0)

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5111	1118

prune281.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 10.5b

Counts

99 → 7

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.7b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.7b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series234.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
51.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5060	1262

prune361.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Merged error: 10.5b

Counts

91 → 7

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(asin (* (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.3b	(sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
18.1b	(sqrt (pow (/ Om Omc) 2.0))
18.1b	(sqrt (pow (/ Om Omc) 2.0))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`sqrt-prod`
110×	`add-sqr-sqrt`
72×	`times-frac`
51×	`*-un-lft-identity`
42×	`unpow-prod-down`
39×	`add-cube-cbrt`
30×	`difference-of-squares`
10×	`rem-sqrt-square` `sqr-pow`
6×	`distribute-lft-out--`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `div-inv`
2×	`associate-/r/`
1×	`asin-acos` `flip3-+` `sqrt-div` `flip-+`

Counts

4 → 131

Calls

4 calls:

18.0ms	(sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(sqrt (pow (/ Om Omc) 2.0))
4.0ms	(sqrt (pow (/ Om Omc) 2.0))
1.0ms	(asin (* (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series350.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
51.0ms	(sqrt (pow (/ Om Omc) 2.0))
48.0ms	(sqrt (pow (/ Om Omc) 2.0))
22.0ms	(asin (* (sqrt (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))) (sqrt (/ (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5005	3603

prune697.0ms (8.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	142	8	150

Merged error: 10.5b

Counts

150 → 8

regimes1.4s (17.2%)

Accuracy

Total 0.1b remaining (0.7%)

Threshold costs 0.1b (0.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms (0%)

sample2.0s (23.6%)

Algorithm

1×

intervals

Results

726.0ms	3823×	body	160	valid
466.0ms	4831×	body	80	nan
391.0ms	4177×	body	80	valid

Details

analyze1.6s (19.6%)

sample75.0ms (0.9%)

simplify50.0ms (0.6%)

prune9.0ms (0.1%)

localize15.0ms (0.2%)

rewrite37.0ms (0.4%)

series270.0ms (3.2%)

simplify71.0ms (0.9%)

prune495.0ms (5.9%)

localize16.0ms (0.2%)

rewrite15.0ms (0.2%)

series91.0ms (1.1%)

simplify42.0ms (0.5%)

prune281.0ms (3.4%)

localize20.0ms (0.2%)

rewrite18.0ms (0.2%)

series234.0ms (2.8%)

simplify34.0ms (0.4%)

prune361.0ms (4.3%)

localize22.0ms (0.3%)

rewrite37.0ms (0.4%)

series350.0ms (4.2%)

simplify71.0ms (0.8%)

prune697.0ms (8.3%)

regimes1.4s (17.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.0s (23.6%)

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