Details

sample71.0ms

Algorithm

intervals

Results

21.0ms	291×	body	80	nan
14.0ms	125×	body	160	valid
7.0ms	131×	body	80	valid

simplify129.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	51	10
2	107	10
3	290	10
4	1054	10
5	4445	10
6	5001	10
done	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 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))))))
10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite275.0ms

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×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `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 → 138

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
72.0ms	(/ (- 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))))))
190.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
229.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
19.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
348.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	664	1948
1	2106	1846
2	5001	1828
done	5001	1828

prune584.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.4b

localize17.0ms

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 (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite79.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 159

Calls

4 calls:

6.0ms	(pow (/ t l) 2.0)
60.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
6.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ t l) 2.0)
346.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
20.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify65.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	642	2571
1	2047	2395
2	5002	2384
done	5002	2384

prune631.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series861.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
244.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
185.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify86.0ms

Counts

92 → 92

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	213	762
1	703	740
2	3026	738
3	5002	730
done	5002	730

prune469.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.8b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.5b	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
24×	`cbrt-prod`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
9×	`unpow-prod-down` `cube-prod`
8×	`pow1`
6×	`sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`cube-div` `cbrt-div`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
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	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

series868.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
184.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
250.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) 3))

simplify40.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	334	956
1	1155	933
2	5001	923
done	5001	923

prune495.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 11.4b

regimes774.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10
done	18	10

end0.0ms

sample1.8s

Algorithm

intervals

Results

465.0ms	7915×	body	80	nan
437.0ms	3757×	body	160	valid
253.0ms	4243×	body	80	valid