Details

sample72.0ms

Algorithm

intervals

Results

18.0ms	120×	body	160	valid
18.0ms	233×	body	80	nan
11.0ms	136×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	16	811
1	29	811
2	51	786
3	108	786
4	292	786
5	1583	786
done	5001	786

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
9.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
28×	`sqrt-prod` `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` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `div-exp` `pow-exp` `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 → 134

Calls

4 calls:

5.0ms	(pow (/ t l) 2.0)
64.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
46.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(pow (/ t l) 2.0)
227.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
13.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
415.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify2.1s

Counts

146 → 146

Iterations

Useful iterations: 2 (783.0ms)

Iter	Nodes	Cost
0	285	125154
1	628	120641
2	1798	115601
done	5001	115601

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
9.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

701×	`times-frac`
654×	`sqrt-prod`
637×	`add-sqr-sqrt`
360×	`*-un-lft-identity`
274×	`add-cube-cbrt`
172×	`difference-of-squares`
86×	`unpow-prod-down`
43×	`distribute-lft-out--` `sqr-pow`
9×	`rem-sqrt-square`
8×	`div-inv` `associate-/l*`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

4 → 444

Calls

4 calls:

115.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
125.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

363.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
750.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
153.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
142.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.3s

Counts

456 → 456

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	829	655148
1	1546	631444
done	5001	624524

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.7b

localize62.0ms

Local error

Found 4 expressions with local error:

9.8b	(sqrt (/ (* (/ 1 (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `times-frac`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`
1×	`sqrt-div` `div-inv`

Counts

4 → 64

Calls

4 calls:

28.0ms	(sqrt (/ (* (/ 1 (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

543.0ms	(sqrt (/ (* (/ 1 (fabs (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0)))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
125.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
197.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))
197.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.1s

Counts

76 → 76

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	131	55250
1	246	52696
2	598	51562
3	1950	51242
done	5000	50112

prune616.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.7b

localize72.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
9.9b	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
13.9b	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
3.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
2.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series647.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
180.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
151.0ms	(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
167.0ms	(cbrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	67	30323
1	119	29063
2	225	28743
3	581	28583
4	2230	28103
done	5002	27740

prune658.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 10.7b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.2b and baseline of 10.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	786
done	15	786

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	3806×	body	160	valid
1.2s	8095×	body	80	nan
541.0ms	4194×	body	80	valid