Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	254×	body	80	nan
13.0ms	116×	body	160	valid
8.0ms	140×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.4b	(/ (- 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))))))
10.4b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite114.0ms

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:

6.0ms	(pow (/ t l) 2.0)
60.0ms	(/ (- 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))))))
43.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series670.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ t l) 2.0)
237.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
23.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
349.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.1s

Counts

142 → 142

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	317	3657
1	647	3534
2	1507	3367
3	4695	3363
done	5000	3360

prune562.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ t l) 2.0)
0.3b	(/ (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)))))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite82.0ms

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:

6.0ms	(pow (/ t l) 2.0)
63.0ms	(/ (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)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (/ t l) 2.0)
347.0ms	(/ (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)))))))
190.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.7s

Counts

163 → 163

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	338	4611
1	621	4260
2	1337	4140
3	3951	4132
done	5000	4129

prune611.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize20.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
7.9b	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite23.0ms

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:

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

series921.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
290.0ms	(sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
193.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
192.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 3 (540.0ms)

Iter	Nodes	Cost
0	93	1458
1	204	1280
2	590	1226
3	2374	1218
done	5000	1218

prune427.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.5b

localize27.0ms

Local error

Found 4 expressions with local error:

8.1b	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
10.9b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (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))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
188.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
182.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
181.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.0s

Counts

73 → 73

Iterations

Useful iterations: 3 (341.0ms)

Iter	Nodes	Cost
0	90	1340
1	198	1216
2	572	1152
3	2316	1145
done	5000	1145

prune451.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.5b

regimes601.0ms

Accuracy

0% (0.2b remaining)

Error of 10.6b against oracle of 10.4b and baseline of 10.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	48
1	28	48
done	28	48

end0.0ms

sample1.8s

Algorithm

intervals

Results

479.0ms	8153×	body	80	nan
439.0ms	3789×	body	160	valid
246.0ms	4211×	body	80	valid