Details

sample185.0ms

Algorithm

intervals

Results

57.0ms	260×	body	80	nan
56.0ms	126×	body	160	valid
35.0ms	130×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5022
6	4794
5	1100
4	363
3	142
2	61
1	32
0	16

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ t l) (/ t l))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt` `times-frac`
84×	`*-un-lft-identity`
70×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
5×	`distribute-lft-out`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 184

Calls

4 calls:

14.0ms	(* (/ t l) (/ t l))
13.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
54.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ t l) (/ t l))
40.0ms	(* (/ t l) (/ t l))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
162.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify1.8s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
2	1706
1	627
0	238

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ t l) (/ t l))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
7.7b	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`sqrt-prod` `insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

4 → 162

Calls

4 calls:

25.0ms	(* (/ t l) (/ t l))
22.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
43.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ t l) (/ t l))
46.0ms	(* (/ t l) (/ t l))
22.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
91.0ms	(sqrt (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))

simplify1.8s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1540
1	516
0	172

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

19.0ms	(* (/ Om Omc) (/ Om Omc))
19.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
81.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (/ Om Omc) (/ Om Omc))
36.0ms	(* (/ t l) (/ t l))
13.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1))))
165.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (* (* (/ t l) (/ t l)) 2) 1)))

simplify2.1s

Counts

191 → 191

Iterations

Iter	Nodes
done	5004
2	3004
1	974
0	334

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.2b

localize60.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
7.8b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
7.8b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

58×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
16×	`difference-of-squares`
10×	`distribute-lft-out`
8×	`pow1`
6×	`rem-sqrt-square`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate-/r/` `insert-posit16` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

57.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
51.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
148.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
26.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
35.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))

simplify1.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	5005
3	2080
2	575
1	265
0	142

prune770.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

regimes544.0ms

Accuracy

97.8% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	25

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	8044×	body	80	nan
1.4s	3826×	body	160	valid
735.0ms	4174×	body	80	valid