Details

analyze4.1s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 24.317919%

Guaranteed chance to sample good point: 46.36188%

sample73.0ms

Algorithm

intervals

Results

22.0ms	116×	body	160	valid
13.0ms	140×	body	80	valid
13.0ms	136×	body	80	nan

simplify127.0ms

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: 10.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

8.0ms	(pow (/ t l) 2.0)
4.0ms	(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))))))
12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ t l) 2.0)
13.0ms	(pow (/ Om Omc) 2.0)
14.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
135.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	724	1249
1	2152	1176
2	5001	1152

prune310.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 10.5b

Counts

119 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.4b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.4b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

4.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
14.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
136.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	689	2519
1	2333	2350
2	5001	2330

prune397.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	163	9	172

Merged error: 10.5b

Counts

172 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.4b	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`asin-acos` `pow1/2`

Counts

4 → 54

Calls

4 calls:

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

series219.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (/ (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (fabs (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
63.0ms	(sqrt (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	397	894
1	1227	828
2	5001	815

prune300.0ms

Filtered

62 candidates to 66 candidates (-6.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 10.5b

Counts

75 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

10.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
18.3b	(cbrt (/ t l))
18.3b	(cbrt (/ t l))
18.3b	(cbrt (/ t l))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
55×	`times-frac`
43×	`*-un-lft-identity`
39×	`cbrt-prod`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`difference-of-squares`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `distribute-lft-out--` `sqr-pow`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 108

Calls

4 calls:

12.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
2.0ms	(cbrt (/ t l))
2.0ms	(cbrt (/ t l))
3.0ms	(cbrt (/ t l))

series173.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (pow (* (cbrt (/ t l)) (cbrt (/ t l))) 2.0) (pow (cbrt (/ t l)) 2.0))))))
12.0ms	(cbrt (/ t l))
13.0ms	(cbrt (/ t l))
15.0ms	(cbrt (/ t l))

simplify147.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	414	1767
1	994	1697
2	4516	1682
3	5001	1624

prune298.0ms

Filtered

97 candidates to 120 candidates (-23.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	3	5
Picked	0	1	1
Done	0	3	3
Total	120	9	129

Merged error: 10.5b

Counts

129 → 9

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

analyze4.1s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 24.317919%

Guaranteed chance to sample good point: 46.36188%

sample2.0s

Algorithm

intervals

Results

747.0ms	3766×	body	160	valid
413.0ms	4120×	body	80	nan
411.0ms	4234×	body	80	valid

Details

analyze4.1s

sample73.0ms

simplify127.0ms

prune5.0ms

localize15.0ms

rewrite29.0ms

series174.0ms

simplify58.0ms

prune310.0ms

localize16.0ms

rewrite31.0ms

series208.0ms

simplify69.0ms

prune397.0ms

localize20.0ms

rewrite9.0ms

series219.0ms

simplify39.0ms

prune300.0ms

localize20.0ms

rewrite23.0ms

series173.0ms

simplify147.0ms

prune298.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.1s

sample2.0s

Profiling