Details

sample67.0ms

Algorithm

intervals

Results

18.0ms	291×	body	80	nan
14.0ms	125×	body	160	valid
8.0ms	131×	body	80	valid

simplify128.0ms

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

localize19.0ms

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)))))

rewrite114.0ms

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))))))
39.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ t l) 2.0)
232.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
349.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (45.0ms)

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

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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:

6.0ms	(pow (/ t l) 2.0)
59.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ t l) 2.0)
347.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
20.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
193.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify61.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	623	2507
1	1987	2333
2	5001	2323
done	5001	2323

prune773.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.4b

localize19.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (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))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

6.0ms	(sqrt (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))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
250.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify83.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	201	720
1	658	700
2	2858	696
3	5002	688
done	5002	688

prune429.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.4b

localize23.0ms

Local error

Found 4 expressions with local error:

11.5b	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
17.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
21×	`add-sqr-sqrt`
18×	`cbrt-div`
14×	`times-frac`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`cbrt-prod` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `pow1/3`
2×	`unpow-prod-down` `associate-r/` `associate-l/`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

50.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

486.0ms	(sqrt (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
258.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
261.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
259.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify89.0ms

Counts

87 → 87

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	367	1353
1	817	1301
2	2924	1289
3	5002	1286
done	5002	1286

prune514.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 11.4b

regimes789.0ms

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

488.0ms	7915×	body	80	nan
446.0ms	3757×	body	160	valid
270.0ms	4243×	body	80	valid