Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	116×	body	160	valid
15.0ms	265×	body	80	nan
8.0ms	140×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	29	19
2	49	19
3	100	19
4	249	19
5	799	19
6	2700	19
done	5000	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize15.0ms

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))))))
0.6b	(/ (- 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)))))

rewrite78.0ms

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:

3.0ms	(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))))))
38.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
30.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ Om Omc) 2.0)
17.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
220.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
336.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.7s

Counts

142 → 142

Iterations

Useful iterations: 3 (807.0ms)

Iter	Nodes	Cost
0	308	3657
1	636	3542
2	1501	3367
3	4850	3355
done	5000	3355

prune563.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.8b

localize19.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
126×	`sqrt-prod`
117×	`add-sqr-sqrt`
80×	`cbrt-div`
72×	`*-un-lft-identity`
71×	`cbrt-prod`
60×	`add-cube-cbrt`
50×	`associate-/r/`
40×	`flip3-+` `flip-+`
24×	`frac-times` `difference-of-squares`
12×	`unpow-prod-down` `associate-r/` `associate-l/`
7×	`div-inv`
6×	`distribute-lft-out--` `sqr-pow`
5×	`pow1` `rem-sqrt-square`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 180

Calls

4 calls:

51.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
1.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

339.0ms	(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
252.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
251.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify855.0ms

Counts

192 → 192

Iterations

Useful iterations: 2 (395.0ms)

Iter	Nodes	Cost
0	505	11496
1	904	11006
2	2293	10258
done	5000	10258

prune931.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.8b

localize26.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

436×	`add-sqr-sqrt`
336×	`times-frac`
300×	`sqrt-prod`
196×	`*-un-lft-identity`
172×	`unpow-prod-down`
144×	`difference-of-squares`
124×	`add-cube-cbrt`
106×	`cbrt-prod`
100×	`cube-prod`
54×	`sqr-pow`
36×	`distribute-lft-out--`
16×	`cube-mult` `unpow3`
14×	`rem-sqrt-square`
8×	`cbrt-div`
6×	`pow1`
4×	`add-exp-log` `cube-div` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `div-inv`

Counts

4 → 360

Calls

4 calls:

48.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
45.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
1.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

334.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
336.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
253.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
450.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify797.0ms

Counts

372 → 372

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	411	15364
1	750	13564
2	2368	12344
done	5000	12344

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.8b

localize32.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
15.7b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
15.7b	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0b	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

292×	`add-sqr-sqrt`
222×	`times-frac`
150×	`sqrt-prod`
136×	`*-un-lft-identity`
113×	`cbrt-prod`
98×	`unpow-prod-down`
96×	`difference-of-squares`
88×	`add-cube-cbrt`
50×	`cube-prod`
33×	`sqr-pow`
24×	`distribute-lft-out--`
8×	`cube-mult` `unpow3`
7×	`rem-sqrt-square`
6×	`cbrt-div` `associate-/r/`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`cube-div`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 258

Calls

4 calls:

50.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
14.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
14.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
2.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

327.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (pow (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) 3)))
348.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
353.0ms	(cbrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
259.0ms	(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify844.0ms

Counts

270 → 270

Iterations

Useful iterations: 2 (371.0ms)

Iter	Nodes	Cost
0	509	10596
1	911	9636
2	2604	8810
done	5001	8810

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.8b

regimes620.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	18	19
done	18	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

475.0ms	8146×	body	80	nan
441.0ms	3778×	body	160	valid
244.0ms	4222×	body	80	valid