Details

sample59.0ms

Algorithm

intervals

Results

14.0ms	130×	body	160	valid
13.0ms	237×	body	80	nan
7.0ms	126×	body	80	valid

simplify2.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.4b	(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)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
38×	`*-un-lft-identity`
32×	`add-cube-cbrt` `unpow-prod-down`
30×	`sqrt-prod`
12×	`difference-of-squares`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow`
5×	`sqr-pow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`div-inv` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `div-exp` `associate-/r/`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 106

Calls

4 calls:

6.0ms	(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))))))
41.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ t l) 2.0)
68.0ms	(pow (/ Om Omc) 2.0)
21.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
356.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.7s

Counts

118 → 118

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	352	2388
1	693	2272
2	1438	2160
3	3922	2150
done	5000	2144

prune450.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.4b	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
9.0b	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`times-frac`
28×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`unpow-prod-down`
15×	`sqrt-prod`
10×	`add-exp-log`
8×	`pow1`
6×	`pow-unpow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `div-inv`
2×	`pow-to-exp` `pow-pow` `div-exp` `associate-/r/` `sqr-pow`
1×	`asin-acos` `pow-flip` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `inv-pow`

Counts

4 → 94

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.0ms	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ t l) 2.0)
61.0ms	(pow (/ Om Omc) 2.0)
20.0ms	(asin (* (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
210.0ms	(sqrt (/ 1 (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.8s

Counts

106 → 106

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	302	1624
1	598	1501
2	1330	1388
3	4218	1374
done	5001	1368

prune408.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (/ (/ -1 l) -1) t) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.4b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))))
9.0b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
37×	`times-frac`
31×	`*-un-lft-identity`
30×	`sqrt-prod`
25×	`add-cube-cbrt`
20×	`unpow-prod-down`
17×	`add-exp-log`
12×	`difference-of-squares`
9×	`pow1`
6×	`pow-unpow` `pow-exp`
5×	`sqr-pow`
4×	`div-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `prod-exp` `distribute-lft-out--`
2×	`pow-to-exp` `rem-sqrt-square` `associate-/r/` `div-inv`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `pow-prod-down` `flip-+`

Counts

4 → 97

Calls

4 calls:

14.0ms	(pow (* (/ (/ -1 l) -1) t) 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 (* (/ (/ -1 l) -1) t) 2.0))))))
44.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (* (/ (/ -1 l) -1) t) 2.0)
66.0ms	(pow (/ Om Omc) 2.0)
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))))
341.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))

simplify1.7s

Counts

109 → 109

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	321	2657
1	624	2524
2	1330	2195
3	3831	2189
done	5000	1998

prune422.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.5b

localize20.0ms

Local error

Found 4 expressions with local error:

10.6b	(sqrt (/ 1 (* (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)) (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
15.9b	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
15.9b	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
15.9b	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
15×	`sqrt-prod`
13×	`pow1`
11×	`add-sqr-sqrt` `sqrt-pow1`
10×	`*-un-lft-identity`
9×	`cbrt-prod` `add-cube-cbrt` `pow-flip` `flip3-+` `pow1/3` `flip-+`
8×	`associate-/r/`
5×	`times-frac`
4×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `pow1/2` `sqrt-div` `div-inv` `inv-pow`

Counts

4 → 77

Calls

4 calls:

62.0ms	(sqrt (/ 1 (* (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)) (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
12.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
9.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
9.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (/ 1 (* (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)) (cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))))
254.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
256.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
252.0ms	(cbrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify1.0s

Counts

89 → 89

Iterations

Useful iterations: 3 (318.0ms)

Iter	Nodes	Cost
0	141	2121
1	275	1923
2	562	1770
3	2062	1739
done	5000	1739

prune428.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.5b

regimes817.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	23
1	22	23
done	22	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

442.0ms	7914×	body	80	nan
435.0ms	3840×	body	160	valid
236.0ms	4160×	body	80	valid