Details

sample60.0ms

Algorithm

intervals

Results

16.0ms	284×	body	80	nan
15.0ms	128×	body	160	valid
7.0ms	128×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	242	19
5	729	19
6	2640	19
done	5000	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite48.0ms

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 (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
36.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
61.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
326.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: 3 (621.0ms)

Iter	Nodes	Cost
0	352	2388
1	697	2272
2	1496	2160
3	4364	2150
done	5000	2150

prune464.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite61.0ms

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)
47.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(asin (fabs (/ (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))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ Om Omc) 2.0)
316.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
17.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
183.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.4s

Counts

163 → 163

Iterations

Useful iterations: 3 (596.0ms)

Iter	Nodes	Cost
0	329	4611
1	611	4268
2	1379	4140
3	4486	4134
done	5000	4134

prune603.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

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:

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

series879.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
253.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify900.0ms

Counts

84 → 84

Iterations

Useful iterations: 3 (221.0ms)

Iter	Nodes	Cost
0	93	1458
1	204	1280
2	629	1226
3	3153	1218
done	5000	1218

prune426.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite55.0ms

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))))))
35.0ms	(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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

279.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
361.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
191.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
189.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts

152 → 152

Iterations

Useful iterations: 3 (447.0ms)

Iter	Nodes	Cost
0	310	4138
1	548	3735
2	1207	3576
3	4473	3575
done	5000	3575

prune574.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.3b

regimes649.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	20	21
done	20	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

466.0ms	7987×	body	80	nan
454.0ms	3799×	body	160	valid
241.0ms	4201×	body	80	valid