Details

sample112.0ms

Algorithm

intervals

Results

47.0ms	270×	body	80	nan
24.0ms	126×	body	160	valid
12.0ms	130×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1551
4	277
3	101
2	49
1	29
0	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite145.0ms

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×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 130

Calls

4 calls:

65.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
69.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series942.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
109.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
478.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	2395
1	733
0	308

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite129.0ms

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` `associate-/r*` `add-cbrt-cube` `sqrt-div`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 151

Calls

4 calls:

102.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (fabs (/ (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))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

445.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
79.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
251.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.6s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	2253
1	703
0	329

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.8b

localize87.0ms

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)))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

9.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

364.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
367.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
267.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
304.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	3602
2	672
1	208
0	94

prune901.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.8b

localize63.0ms

Local error

Found 4 expressions with local error:

8.1b	(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.1b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-l/` `associate-r/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

84.0ms	(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

452.0ms	(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)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
404.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
388.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
426.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.8s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
2	3175
1	962
0	506

prune1.8s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 8.8b

regimes1.9s

Accuracy

0% (0.1b remaining)

Error of 9.8b against oracle of 9.7b and baseline of 9.8b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	16

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	7907×	body	80	nan
1.2s	3791×	body	160	valid
578.0ms	4209×	body	80	valid