Details

sample63.0ms

Algorithm

intervals

Results

15.0ms	268×	body	80	nan
13.0ms	116×	body	160	valid
8.0ms	140×	body	80	valid

simplify124.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	10
1	49	10
2	101	10
3	279	10
4	1029	10
5	4384	10
6	5002	10
done	5002	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.2b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite115.0ms

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 (/ Om Omc) 2.0)
58.0ms	(/ (- 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))))))
45.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series684.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ Om Omc) 2.0)
243.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
25.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
355.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	634	1882
1	2017	1787
2	5001	1774
done	5001	1774

prune588.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.5b	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.8b	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
8.2b	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `times-frac`
16×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `associate-/r/`
13×	`unpow-prod-down`
12×	`add-exp-log` `flip3-+` `flip-+`
9×	`add-cbrt-cube`
8×	`frac-times`
6×	`pow1`
4×	`associate-r/` `associate-l/` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `div-exp` `div-inv` `difference-of-squares`
2×	`cbrt-undiv` `pow-exp` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `asin-acos` `flip3--` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

6.0ms	(pow (/ Om Omc) 2.0)
43.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
1.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
37.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ Om Omc) 2.0)
805.0ms	(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))
31.0ms	(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0))))))
846.0ms	(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify86.0ms

Counts

109 → 109

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	789	1849
1	3446	1677
2	5003	1677
done	5003	1677

prune520.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.7b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
111×	`times-frac`
80×	`*-un-lft-identity`
58×	`cbrt-prod`
54×	`add-cube-cbrt` `sqrt-prod`
52×	`difference-of-squares`
26×	`unpow-prod-down`
13×	`distribute-lft-out--` `sqr-pow`
8×	`cbrt-div` `associate-/l*`
6×	`add-exp-log` `associate-/r*`
5×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`rem-sqrt-square`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

4 → 172

Calls

4 calls:

61.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
46.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

362.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
381.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
256.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
283.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify65.0ms

Counts

184 → 184

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	544	3196
1	1453	3125
2	5001	3108
done	5001	3108

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.5b

localize25.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
257.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
261.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify66.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	144	652
1	451	604
2	1974	588
3	5001	588
done	5001	588

prune445.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.5b

regimes913.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18
done	24	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

453.0ms	7854×	body	80	nan
448.0ms	3857×	body	160	valid
252.0ms	4143×	body	80	valid