Details

analyze1.5s (16.2%)

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

sample72.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	119×	body	160	valid
15.0ms	149×	body	80	nan
13.0ms	137×	body	80	valid

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4745	19
1	4745	19

prune11.0ms (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: 9.7b

Counts

2 → 1

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite39.0ms (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))))
7.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series258.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
95.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(pow (/ Om Omc) 2.0)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5030	3354

prune506.0ms (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 9.6b

Counts

143 → 9

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.7b	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`sqrt-prod`
104×	`add-sqr-sqrt`
78×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
10×	`pow1` `rem-sqrt-square` `sqrt-div`
9×	`sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-flip`
2×	`div-inv`
1×	`inv-pow`

Counts

4 → 140

Calls

4 calls:

16.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series306.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
78.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
50.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4968	3674
1	4968	3674

prune810.0ms (8.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Merged error: 9.6b

Counts

161 → 9

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.1b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`sqrt-prod`
14×	`add-sqr-sqrt`
10×	`sqrt-div`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
7×	`sqrt-pow1`
5×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 66

Calls

4 calls:

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

series208.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
49.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5060	1183

prune483.0ms (5.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	78	9	87

Merged error: 9.6b

Counts

87 → 9

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.4b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
92×	`cbrt-prod`
82×	`times-frac`
59×	`*-un-lft-identity`
41×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`sqrt-prod`
18×	`unpow-prod-down`
9×	`distribute-lft-out--` `sqr-pow`
6×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 133

Calls

4 calls:

14.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
12.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))

series470.0ms (5%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
148.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
146.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
27.0ms	(asin (* (fabs (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4965	4796
1	4965	4796

prune841.0ms (8.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	145	9	154

Merged error: 9.6b

Counts

154 → 9

regimes1.4s (15.3%)

Accuracy

Total 0.1b remaining (0.6%)

Threshold costs 0.1b (0.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms (0%)

sample2.0s (21.3%)

Algorithm

1×

intervals

Results

754.0ms	3788×	body	160	valid
467.0ms	4752×	body	80	nan
411.0ms	4212×	body	80	valid

Details

analyze1.5s (16.2%)

sample72.0ms (0.8%)

simplify41.0ms (0.4%)

prune11.0ms (0.1%)

localize16.0ms (0.2%)

rewrite39.0ms (0.4%)

series258.0ms (2.7%)

simplify58.0ms (0.6%)

prune506.0ms (5.4%)

localize22.0ms (0.2%)

rewrite34.0ms (0.4%)

series306.0ms (3.3%)

simplify53.0ms (0.6%)

prune810.0ms (8.6%)

localize31.0ms (0.3%)

rewrite15.0ms (0.2%)

series208.0ms (2.2%)

simplify36.0ms (0.4%)

prune483.0ms (5.1%)

localize20.0ms (0.2%)

rewrite45.0ms (0.5%)

series470.0ms (5%)

simplify58.0ms (0.6%)

prune841.0ms (8.9%)

regimes1.4s (15.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.0s (21.3%)

Profiling