Details

sample65.0ms

Algorithm

intervals

Results

16.0ms	285×	body	80	nan
14.0ms	116×	body	160	valid
8.0ms	140×	body	80	valid

simplify129.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10
done	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 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))))))
11.3b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite130.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 138

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
72.0ms	(/ (- 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))))))
45.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ Om Omc) 2.0)
235.0ms	(/ (- 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))))))
356.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	650	1948
1	2076	1846
2	5001	1827
done	5001	1827

prune755.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.3b	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.5b	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
11.3b	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `times-frac`
16×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `associate-/r/`
13×	`unpow-prod-down`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `div-exp` `div-inv` `difference-of-squares`
2×	`cbrt-undiv` `pow-exp` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
45.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
1.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
35.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ Om Omc) 2.0)
647.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
35.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
821.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify90.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	810	1964
1	3553	1783
2	5002	1779
done	5002	1779

prune528.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.3b	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
99×	`sqrt-prod`
73×	`times-frac`
58×	`*-un-lft-identity`
44×	`add-cube-cbrt`
28×	`difference-of-squares`
14×	`pow1` `unpow-prod-down`
11×	`sqrt-div` `associate-/l*`
8×	`sqrt-pow1`
7×	`distribute-lft-out--` `sqr-pow`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `pow1/2` `flip-+`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-times` `sqrt-undiv` `flip3--` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 157

Calls

4 calls:

60.0ms	(/ (sqrt (- 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))))
7.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
56.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

352.0ms	(/ (sqrt (- 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))))
192.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
353.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify55.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	428	2667
1	1227	2536
2	5001	2493
done	5001	2493

prune675.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize21.0ms

Local error

Found 4 expressions with local error:

11.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.3b	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt` `sqrt-prod`
9×	`sqrt-div`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 67

Calls

4 calls:

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))))
111.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

series909.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
193.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
348.0ms	(sqrt (* (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

simplify77.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	209	900
1	622	850
2	2717	827
3	5002	824
done	5002	824

prune404.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

regimes619.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18
done	24	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

466.0ms	7983×	body	80	nan
422.0ms	3781×	body	160	valid
246.0ms	4219×	body	80	valid