Details

sample158.0ms

Algorithm

intervals

Results

49.0ms	126×	body	160	valid
47.0ms	260×	body	80	nan
34.0ms	130×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4967
5	1097
4	396
3	153
2	63
1	32
0	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

384×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
198×	`times-frac`
169×	`add-cube-cbrt`
162×	`frac-times`
145×	`associate-/l*`
123×	`associate-/r*`
73×	`sqrt-prod`
72×	`difference-of-squares`
43×	`clear-num`
42×	`swap-sqr`
41×	`frac-2neg`
40×	`unswap-sqr`
31×	`sqrt-div`
30×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r`
19×	`pow1`
18×	`associate-l/` `associate-r/`
10×	`*-commutative`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `rem-sqrt-square` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`asin-acos` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 465

Calls

4 calls:

37.0ms	(* (/ Om Omc) (/ Om Omc))
53.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
284.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (/ Om Omc) (/ Om Omc))
30.0ms	(* (/ t l) (/ t l))
18.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
176.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.7s

Counts

477 → 477

Iterations

Iter	Nodes
done	5000
1	2217
0	787

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ l t) (/ l t))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

384×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
198×	`times-frac`
169×	`add-cube-cbrt`
162×	`frac-times`
145×	`associate-/l*`
123×	`associate-/r*`
73×	`sqrt-prod`
72×	`difference-of-squares`
43×	`clear-num`
42×	`swap-sqr`
41×	`frac-2neg`
40×	`unswap-sqr`
31×	`sqrt-div`
30×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r`
19×	`pow1`
18×	`associate-l/` `associate-r/`
10×	`*-commutative`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `rem-sqrt-square` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`asin-acos` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 465

Calls

4 calls:

33.0ms	(* (/ l t) (/ l t))
31.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
204.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ l t) (/ l t))
30.0ms	(* (/ Om Omc) (/ Om Omc))
12.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
157.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))

simplify1.6s

Counts

477 → 477

Iterations

Iter	Nodes
done	5000
1	2211
0	789

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

384×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
198×	`times-frac`
169×	`add-cube-cbrt`
162×	`frac-times`
145×	`associate-/l*`
123×	`associate-/r*`
73×	`sqrt-prod`
72×	`difference-of-squares`
43×	`clear-num`
42×	`swap-sqr`
41×	`frac-2neg`
40×	`unswap-sqr`
31×	`sqrt-div`
30×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
26×	`associate-r`
19×	`pow1`
18×	`associate-l/` `associate-r/`
10×	`*-commutative`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `un-div-inv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `rem-sqrt-square` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`asin-acos` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 465

Calls

4 calls:

31.0ms	(* (/ Om Omc) (/ Om Omc))
37.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
294.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ Om Omc) (/ Om Omc))
31.0ms	(* (/ t l) (/ t l))
12.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
182.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts

477 → 477

Iterations

Iter	Nodes
done	5000
1	2217
0	787

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.1b

localize69.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))
7.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
7.7b	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))
7.7b	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

402×	`add-sqr-sqrt`
231×	`sqrt-prod`
224×	`times-frac`
155×	`*-un-lft-identity`
126×	`difference-of-squares`
64×	`add-cube-cbrt`
56×	`unswap-sqr`
34×	`sqrt-div`
28×	`swap-sqr`
23×	`associate-/l*`
14×	`*-commutative` `distribute-lft-out--`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1` `associate-l`
6×	`associate-/r*`
5×	`pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--`

Counts

4 → 245

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))
278.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
1.0ms	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))
2.0ms	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))

series681.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1)))
347.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))))
65.0ms	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))
94.0ms	(sqrt (fma 2 (/ 1 (* (/ l t) (/ l t))) 1))

simplify3.2s

Counts

257 → 257

Iterations

Iter	Nodes
done	5003
3	3674
2	1417
1	765
0	463

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.1b

regimes537.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	8044×	body	80	nan
1.7s	3826×	body	160	valid
819.0ms	4174×	body	80	valid