Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	291×	body	80	nan
14.0ms	125×	body	160	valid
7.0ms	131×	body	80	valid

simplify127.0ms

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
done	5002	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite117.0ms

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:

6.0ms	(pow (/ t l) 2.0)
60.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (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))))))
44.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ t l) 2.0)
236.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
23.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
350.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify68.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	648	1882
1	2047	1787
2	5001	1774
done	5001	1774

prune568.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
10.5b	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
38.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series816.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
416.0ms	(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
189.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
191.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify99.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	265	790
1	811	728
2	3959	726
3	5002	726
done	5002	726

prune341.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.4b

localize23.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

95×	`sqrt-prod`
88×	`add-sqr-sqrt`
56×	`times-frac`
43×	`*-un-lft-identity`
31×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`unpow-prod-down`
11×	`sqrt-div`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`associate-/r/`
1×	`div-inv`

Counts

4 → 118

Calls

4 calls:

48.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

386.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
252.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
191.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
192.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify128.0ms

Counts

130 → 130

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	480	1931
1	1265	1885
2	4838	1857
3	5002	1843
done	5002	1843

prune728.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.4b

localize22.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite23.0ms

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:

6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series821.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
187.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
195.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify86.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	201	660
1	658	642
2	2858	640
3	5002	634
done	5002	634

prune416.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.4b

regimes725.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10
done	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

475.0ms	7915×	body	80	nan
438.0ms	3757×	body	160	valid
252.0ms	4243×	body	80	valid