Details

sample149.0ms

Algorithm

intervals

Results

55.0ms	273×	body	80	nan
31.0ms	124×	body	160	valid
17.0ms	132×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	265	19
5	798	19
6	3016	19
done	5001	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(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))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite182.0ms

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×	`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 → 130

Calls

4 calls:

13.0ms	(pow (/ Om Omc) 2.0)
97.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
62.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series996.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow (/ Om Omc) 2.0)
322.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
22.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
567.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.9s

Counts

142 → 142

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	308	3657
1	633	3542
2	1483	3367
3	4467	3355
done	5001	3352

prune960.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.8b

localize32.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.5b	(sqrt (pow (/ Om Omc) 2.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

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))))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

202.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
195.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
305.0ms	(sqrt (pow (/ Om Omc) 2.0))
392.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	175	1610
1	366	1486
2	840	1454
3	2375	1454
done	5001	1454

prune708.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.8b

localize67.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.4b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.5b	(sqrt (pow (/ Om Omc) 2.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
32×	`add-sqr-sqrt`
30×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
10×	`rem-sqrt-square`
6×	`pow1`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`flip3-+` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms	(sqrt (pow (/ Om Omc) 2.0))
16.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

240.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
255.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
375.0ms	(sqrt (pow (/ Om Omc) 2.0))
426.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: 2 (186.0ms)

Iter	Nodes	Cost
0	175	1610
1	366	1486
2	840	1454
3	2375	1454
done	5001	1454

prune962.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

localize37.0ms

Local error

Found 4 expressions with local error:

13.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.9b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.5b	(sqrt (pow (/ Om Omc) 2.0))
18.5b	(sqrt (pow (/ Om Omc) 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
8×	`rem-sqrt-square`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+` `div-inv`

Counts

4 → 86

Calls

4 calls:

5.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))
9.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

345.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
326.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
368.0ms	(sqrt (pow (/ Om Omc) 2.0))
347.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.7s

Counts

98 → 98

Iterations

Useful iterations: 3 (683.0ms)

Iter	Nodes	Cost
0	176	1616
1	371	1530
2	858	1472
3	2590	1462
done	5001	1462

prune875.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 10.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	26	43
done	26	43

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	8083×	body	80	nan
936.0ms	4305×	body	80	valid
883.0ms	3695×	body	160	valid