Details

sample134.0ms

Algorithm

intervals

Results

33.0ms	275×	body	80	nan
30.0ms	135×	body	80	valid
29.0ms	121×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1551
4	277
3	101
2	49
1	29
0	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.8b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite138.0ms

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×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 130

Calls

4 calls:

10.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
80.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
41.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

112.0ms	(pow (/ Om Omc) 2.0)
28.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
331.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
556.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2401
1	733
0	308

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
647×	`sqrt-prod`
560×	`add-sqr-sqrt`
325×	`*-un-lft-identity`
253×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
19×	`sqrt-div`
14×	`associate-/r/`
9×	`rem-sqrt-square` `flip3-+` `flip-+`
7×	`pow1` `div-inv`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos`

Counts

4 → 385

Calls

4 calls:

0.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
118.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
4.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series942.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
465.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
229.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
222.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.2s

Counts

397 → 397

Iterations

Iter	Nodes
done	5001
1	1595
0	873

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
11.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
647×	`sqrt-prod`
560×	`add-sqr-sqrt`
325×	`*-un-lft-identity`
253×	`add-cube-cbrt`
144×	`difference-of-squares`
72×	`unpow-prod-down`
36×	`distribute-lft-out--` `sqr-pow`
19×	`sqrt-div`
14×	`associate-/r/`
9×	`rem-sqrt-square` `flip3-+` `flip-+`
7×	`pow1` `div-inv`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
1×	`asin-acos`

Counts

4 → 385

Calls

4 calls:

0.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
100.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
9.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

36.0ms	(asin (sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
487.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
304.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
304.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.4s

Counts

397 → 397

Iterations

Iter	Nodes
done	5001
1	1595
0	873

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.9b

localize76.0ms

Local error

Found 4 expressions with local error:

11.8b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
12.1b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

197×	`sqrt-prod`
180×	`times-frac`
153×	`sqrt-div`
120×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-l/` `associate-r/`
8×	`pow1` `rem-sqrt-square`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `add-log-exp`

Counts

4 → 186

Calls

4 calls:

95.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

450.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (sqrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
193.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
208.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
229.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.4s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	3348
1	900
0	470

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.9b

regimes1.5s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	28
2	28
1	27
0	22

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	3756×	body	160	valid
1.1s	8012×	body	80	nan
473.0ms	4244×	body	80	valid