Details

sample4.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.169922%

Guaranteed chance to sample good point: 46.36188%

Results

24.0ms	123×	body	160	valid
17.0ms	133×	body	80	valid
12.0ms	126×	body	80	nan

simplify135.0ms

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: 13.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
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))))))
13.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite25.0ms

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:

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

series178.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
12.0ms	(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))))))
140.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (42.0ms)

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

prune342.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	9	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 13.6b

Counts

119 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite31.0ms

Algorithm

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:

6.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.0ms	(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))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
133.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
47.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
51.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	605	2292
1	1651	2239
2	5001	2188

prune531.0ms

Filtered

101 candidates to 152 candidates (-50.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	151	11	162

Merged error: 13.5b

Counts

162 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.9b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
18.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite26.0ms

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

series288.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
130.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
67.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
65.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	618	2081
1	1575	1993
2	5001	1980

prune542.0ms

Filtered

100 candidates to 113 candidates (-13.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	113	11	124

Merged error: 13.5b

Counts

124 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
13.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite12.0ms

Algorithm

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:

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
46.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
48.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify113.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	262	736
1	822	719
2	3917	716
3	5002	710

prune447.0ms

Filtered

62 candidates to 78 candidates (-25.8%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	78	11	89

Merged error: 13.5b

Counts

89 → 11

regimes1.4s

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample6.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 24.169922%

Guaranteed chance to sample good point: 46.36188%

Results

743.0ms	3771×	body	160	valid
409.0ms	4095×	body	80	nan
405.0ms	4229×	body	80	valid

Details

sample4.1s

simplify135.0ms

prune5.0ms

localize14.0ms

rewrite25.0ms

series178.0ms

simplify56.0ms

prune342.0ms

localize21.0ms

rewrite31.0ms

series306.0ms

simplify63.0ms

prune531.0ms

localize18.0ms

rewrite26.0ms

series288.0ms

simplify53.0ms

prune542.0ms

localize28.0ms

rewrite12.0ms

series207.0ms

simplify113.0ms

prune447.0ms

regimes1.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling