Details

sample176.0ms

Algorithm

intervals

Results

60.0ms	124×	body	160	valid
42.0ms	273×	body	80	nan
21.0ms	132×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize18.0ms

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)))))

rewrite174.0ms

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:

7.0ms	(pow (/ Om Omc) 2.0)
86.0ms	(/ (- 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))))))
74.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series890.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ Om Omc) 2.0)
303.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
34.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
465.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.6s

Counts

142 → 142

Iterations

Useful iterations: done (2.5s)

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

prune850.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.8b

localize33.0ms

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))

rewrite31.0ms

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:

229.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
206.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
291.0ms	(sqrt (pow (/ Om Omc) 2.0))
329.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: 2 (184.0ms)

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

prune832.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.8b

localize48.0ms

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))

rewrite39.0ms

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:

9.0ms	(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))

series1.4s

Counts

4 → 12

Calls

4 calls:

258.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
277.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
385.0ms	(sqrt (pow (/ Om Omc) 2.0))
441.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: 2 (238.0ms)

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

prune843.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

localize65.0ms

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))

rewrite32.0ms

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:

4.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.0ms	(sqrt (pow (/ Om Omc) 2.0))
10.0ms	(sqrt (pow (/ Om Omc) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

398.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
358.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
455.0ms	(sqrt (pow (/ Om Omc) 2.0))
434.0ms	(sqrt (pow (/ Om Omc) 2.0))

simplify1.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (589.0ms)

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

prune996.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.8b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3695×	body	160	valid
1.2s	8083×	body	80	nan
697.0ms	4305×	body	80	valid