Details

sample160.0ms

Algorithm

intervals

Results

54.0ms	249×	body	80	nan
35.0ms	121×	body	160	valid
18.0ms	135×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.2b	(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))))))
7.6b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite84.0ms

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:

8.0ms	(pow (/ Om Omc) 2.0)
8.0ms	(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))))))
58.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (/ Om Omc) 2.0)
84.0ms	(pow (/ t l) 2.0)
38.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
482.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.7s

Counts

118 → 118

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	352	2388
1	693	2272
2	1438	2160
3	3929	2150
done	5001	2144

prune610.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite134.0ms

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

Counts

4 → 151

Calls

4 calls:

13.0ms	(pow (/ t l) 2.0)
93.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
11.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(pow (/ t l) 2.0)
456.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
35.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
290.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.5s

Counts

163 → 163

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	334	4597
1	617	4246
2	1335	4128
3	3945	4120
done	5001	4117

prune911.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (/ (/ -1 l) -1) t) 2.0)
0.2b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))
0.5b	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))))
7.5b	(sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
95×	`sqrt-prod`
73×	`times-frac`
58×	`*-un-lft-identity`
44×	`add-cube-cbrt`
28×	`difference-of-squares`
16×	`add-exp-log`
15×	`unpow-prod-down`
11×	`associate-/l*`
8×	`pow1` `sqr-pow`
7×	`distribute-lft-out--`
6×	`sqrt-div` `associate-/r*` `add-cbrt-cube`
4×	`div-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`pow-pow` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `flip--` `div-inv`

Counts

4 → 142

Calls

4 calls:

24.0ms	(pow (* (/ (/ -1 l) -1) t) 2.0)
84.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))
2.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))))
10.0ms	(sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(pow (* (/ (/ -1 l) -1) t) 2.0)
499.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0)))))
21.0ms	(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))))
197.0ms	(sqrt (+ 1.0 (* 2.0 (pow (* (/ (/ -1 l) -1) t) 2.0))))

simplify2.4s

Counts

154 → 154

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	301	5354
1	544	4930
2	1233	4375
3	3834	4375
done	5000	3975

prune845.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.1b

localize74.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.3b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`add-sqr-sqrt` `sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 63

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

316.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
382.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
338.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
396.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.5s

Counts

75 → 75

Iterations

Useful iterations: 3 (446.0ms)

Iter	Nodes	Cost
0	90	1532
1	198	1432
2	572	1336
3	2317	1315
done	5001	1315

prune746.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 8.1b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	18	19
done	18	19

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.8s	3785×	body	160	valid
1.2s	7828×	body	80	nan
683.0ms	4215×	body	80	valid