Details

sample60.0ms

Algorithm

intervals

Results

17.0ms	284×	body	80	nan
14.0ms	128×	body	160	valid
7.0ms	128×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	101	19
4	254	19
5	810	19
6	3062	19
done	5001	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.2b	(pow (/ Om Omc) 2.0)
0.7b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite44.0ms

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:

4.0ms	(pow (/ t l) 2.0)
4.0ms	(pow (/ Om Omc) 2.0)
0.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
32.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ t l) 2.0)
65.0ms	(pow (/ Om Omc) 2.0)
18.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
326.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify670.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	352	2388
1	701	2272
2	2009	2160
done	5000	2160

prune470.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ Om Omc) 2.0)
0.5b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite60.0ms

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:

4.0ms	(pow (/ Om Omc) 2.0)
46.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ Om Omc) 2.0)
335.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
18.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
189.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify668.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (187.0ms)

Iter	Nodes	Cost
0	329	4611
1	616	4288
2	1813	4140
done	5001	4140

prune622.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.8b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite18.0ms

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` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
251.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
186.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.3s

Counts

84 → 84

Iterations

Useful iterations: 3 (262.0ms)

Iter	Nodes	Cost
0	93	1458
1	204	1286
2	648	1226
3	3376	1218
done	5000	1218

prune427.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.3b

localize24.0ms

Local error

Found 4 expressions with local error:

11.3b	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
16.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.4b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite22.0ms

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:

14.0ms	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

269.0ms	(sqrt (/ 1 (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
249.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
246.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: 3 (479.0ms)

Iter	Nodes	Cost
0	141	2121
1	272	1885
2	801	1754
3	3750	1739
done	5000	1739

prune410.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.3b

regimes595.0ms

Accuracy

0% (0.1b remaining)

Error of 10.7b against oracle of 10.6b and baseline of 10.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	20	21
done	20	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

470.0ms	7987×	body	80	nan
439.0ms	3799×	body	160	valid
241.0ms	4201×	body	80	valid