Details

sample70.0ms

Algorithm

intervals

Results

19.0ms	290×	body	80	nan
15.0ms	110×	body	160	valid
13.0ms	146×	body	80	valid

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 11.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
65×	`times-frac`
46×	`sqrt-prod`
38×	`unpow-prod-down`
36×	`add-cube-cbrt`
24×	`difference-of-squares`
18×	`sqrt-div` `distribute-lft-out`
10×	`add-exp-log`
9×	`associate-l`
8×	`associate-/l*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `distribute-lft-out--`
5×	`associate-/r*`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/` `associate-/l/`
1×	`asin-acos` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `flip--` `flip-+`

Counts

4 → 139

Calls

4 calls:

8.0ms	(pow (/ t l) 2.0)
5.0ms	(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))))))
26.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
63.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	776	1707
1	2297	1638
2	5001	1626

prune503.0ms

Filtered

151 candidates to 104 candidates (68.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	7	152

Merged error: 11.3b

Counts

152 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

9.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

140×	`sqrt-prod`
117×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
75×	`times-frac`
36×	`add-cube-cbrt` `difference-of-squares`
31×	`sqrt-div`
24×	`distribute-lft-out`
18×	`unpow-prod-down`
12×	`associate-l`
9×	`pow1` `distribute-lft-out--` `sqr-pow`
8×	`associate-/r` `associate-/l`
7×	`rem-sqrt-square` `sqrt-pow1`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

4 → 160

Calls

4 calls:

29.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series982.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
249.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	572	2577
1	1578	2542
2	5001	2446

prune650.0ms

Filtered

172 candidates to 104 candidates (60.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	170	9	179

Merged error: 11.3b

Counts

179 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))))
10.2b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

180×	`sqrt-prod`
136×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
101×	`times-frac`
74×	`cbrt-prod`
51×	`add-cube-cbrt`
36×	`difference-of-squares`
34×	`sqrt-div`
30×	`distribute-lft-out`
18×	`unpow-prod-down`
15×	`associate-l`
11×	`associate-/r*`
9×	`pow1` `rem-sqrt-square` `distribute-lft-out--` `sqr-pow`
8×	`associate-/l*`
7×	`sqrt-pow1`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`cbrt-div` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`

Counts

4 → 189

Calls

4 calls:

36.0ms	(sqrt (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))))
14.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series928.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(sqrt (/ (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))))
243.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify67.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	614	3414
1	1589	3377
2	5001	3310

prune880.0ms

Filtered

201 candidates to 121 candidates (60.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	201	9	210

Merged error: 11.3b

Counts

210 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.5b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.5b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`cbrt-prod`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
8×	`sqrt-div` `distribute-lft-out`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `associate-l` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 71

Calls

4 calls:

13.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series947.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
247.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
254.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
255.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	195	886
1	632	839
2	2748	827
3	5002	815

prune418.0ms

Filtered

83 candidates to 63 candidates (75.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	83	9	92

Merged error: 11.3b

Counts

92 → 9

regimes722.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

569.0ms	8139×	body	80	nan
523.0ms	3793×	body	160	valid
293.0ms	4207×	body	80	valid