Details

sample79.0ms

Algorithm

intervals

Results

25.0ms	278×	body	80	nan
20.0ms	115×	body	160	valid
12.0ms	141×	body	80	valid

simplify128.0ms

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

prune8.0ms

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: 10.0b

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)
0.6b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite26.0ms

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)))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ Om Omc) 2.0)
65.0ms	(pow (/ t l) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
320.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	695	1235
1	2043	1164
2	5002	1152

prune597.0ms

Filtered

118 candidates to 92 candidates (78.0%)

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: 9.9b

Counts

119 → 10

localize20.0ms

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))))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite38.0ms

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:

7.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
19.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (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))))

series962.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
338.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
178.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
179.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	544	2235
1	1451	2182
2	5001	2134

prune558.0ms

Filtered

152 candidates to 101 candidates (66.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 9.9b

Counts

162 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.7b	(sqrt (pow (/ Om Omc) 2.0))
21.7b	(sqrt (pow (/ Om Omc) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series998.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
237.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
255.0ms	(sqrt (pow (/ Om Omc) 2.0))
262.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	371	842
1	977	808
2	4022	800
3	5001	798

prune565.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	6	7
Picked	0	1	1
Done	1	1	2
Total	99	9	108

Merged error: 9.9b

Counts

108 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
21.7b	(sqrt (pow (/ Om Omc) 2.0))
21.7b	(sqrt (pow (/ Om Omc) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
7.0ms	(sqrt (pow (/ Om Omc) 2.0))
5.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

249.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
242.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
267.0ms	(sqrt (pow (/ Om Omc) 2.0))
268.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	371	842
1	977	808
2	4022	800
3	5001	798

prune618.0ms

Filtered

98 candidates to 82 candidates (83.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	98	9	107

Merged error: 9.9b

Counts

107 → 9

regimes760.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

721.0ms	8002×	body	80	nan
681.0ms	3789×	body	160	valid
383.0ms	4211×	body	80	valid

Details

sample79.0ms

simplify128.0ms

prune8.0ms

localize14.0ms

rewrite26.0ms

series470.0ms

simplify57.0ms

prune597.0ms

localize20.0ms

rewrite38.0ms

series962.0ms

simplify65.0ms

prune558.0ms

localize28.0ms

rewrite18.0ms

series998.0ms

simplify103.0ms

prune565.0ms

localize29.0ms

rewrite19.0ms

series1.0s

simplify103.0ms

prune618.0ms

regimes760.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling