Details

analyze1.5s

Algorithm: search

sample72.0ms

Algorithm

intervals

Results

27.0ms	120×	body	160	valid
15.0ms	154×	body	80	nan
13.0ms	136×	body	80	valid

simplify126.0ms

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

prune5.0ms

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

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b	(/ (- 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)))))

rewrite35.0ms

Algorithm

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:

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

series263.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(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))))))
96.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
140.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	662	1889
1	2099	1789
2	5002	1774

prune453.0ms

Filtered

114 candidates to 142 candidates (-24.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	133	9	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	10	143

Merged error: 10.4b

Counts

143 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-div` `flip-+`
2×	`sqrt-pow1`
1×	`frac-times` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod`

Counts

4 → 53

Calls

4 calls:

23.0ms	(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (* (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
64.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify112.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	271	870
1	841	814
2	4180	786
3	5001	777

prune315.0ms

Filtered

56 candidates to 65 candidates (-16.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	66	9	75

Merged error: 10.4b

Counts

75 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
0.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
56×	`times-frac`
54×	`sqrt-prod`
41×	`*-un-lft-identity`
31×	`cbrt-prod`
29×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
6×	`cbrt-div` `distribute-lft-out--` `sqr-pow`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
2×	`pow1/3` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 101

Calls

4 calls:

1.0ms	(asin (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (/ (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
142.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
69.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	626	2070
1	1633	1984
2	5001	1971

prune552.0ms

Filtered

100 candidates to 113 candidates (-13.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 10.4b

Counts

122 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.3b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.3b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
110×	`times-frac`
92×	`cbrt-prod`
80×	`*-un-lft-identity`
54×	`add-cube-cbrt`
52×	`difference-of-squares`
33×	`sqrt-prod`
26×	`unpow-prod-down`
13×	`distribute-lft-out--` `sqr-pow`
8×	`associate-/r/` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `pow1/3` `associate-/r*`
2×	`sqrt-pow1` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

4 → 177

Calls

4 calls:

12.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms	(sqrt (cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
150.0ms	(sqrt (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)))))
153.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	518	3286
1	1360	3205
2	5001	3187

prune1.0s

Filtered

161 candidates to 189 candidates (-17.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	189	9	198

Merged error: 10.4b

Counts

198 → 9

regimes1.3s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b 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

analyze1.4s

Algorithm: search

sample1.9s

Algorithm

intervals

Results

749.0ms	3850×	body	160	valid
450.0ms	4705×	body	80	nan
390.0ms	4150×	body	80	valid

Details

analyze1.5s

sample72.0ms

simplify126.0ms

prune5.0ms

localize15.0ms

rewrite35.0ms

series263.0ms

simplify63.0ms

prune453.0ms

localize21.0ms

rewrite31.0ms

series341.0ms

simplify112.0ms

prune315.0ms

localize19.0ms

rewrite28.0ms

series303.0ms

simplify54.0ms

prune552.0ms

localize19.0ms

rewrite59.0ms

series548.0ms

simplify65.0ms

prune1.0s

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.4s

sample1.9s

Profiling