Details

sample214.0ms

Algorithm

intervals

Results

63.0ms	297×	body	80	nan
49.0ms	115×	body	160	valid
29.0ms	141×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	3345
5	901
4	307
3	122
2	59
1	32
0	16

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ Om Omc) (/ Om Omc))
0.6b	(/ 2 (* (/ l t) (/ l t)))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
63×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
44×	`add-cube-cbrt`
34×	`add-cbrt-cube` `add-exp-log`
26×	`sqrt-prod`
13×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l`
12×	`pow1`
8×	`prod-exp` `cbrt-unprod` `difference-of-squares`
6×	`div-inv`
5×	`associate-/r/` `distribute-lft-out`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`frac-times` `rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `asin-acos` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `flip-+`

Counts

4 → 147

Calls

4 calls:

13.0ms	(* (/ Om Omc) (/ Om Omc))
22.0ms	(/ 2 (* (/ l t) (/ l t)))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
13.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ Om Omc) (/ Om Omc))
59.0ms	(/ 2 (* (/ l t) (/ l t)))
12.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t)))))))
169.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (/ 2 (* (/ l t) (/ l t))))))

simplify829.0ms

Counts

159 → 159

Iterations

Iter	Nodes
2	2372
1	767
0	298

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.3b	(* (/ Om Omc) (/ Om Omc))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
96×	`times-frac`
72×	`*-un-lft-identity`
69×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
21×	`sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 179

Calls

4 calls:

29.0ms	(* (/ t l) (/ t l))
13.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
10.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ t l) (/ t l))
27.0ms	(* (/ Om Omc) (/ Om Omc))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
172.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify995.0ms

Counts

191 → 191

Iterations

Iter	Nodes
2	2845
1	949
0	334

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.1b

localize51.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
6.9b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

136×	`sqrt-prod`
68×	`add-sqr-sqrt`
64×	`times-frac`
54×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`difference-of-squares`
10×	`pow1` `rem-sqrt-square` `sqrt-pow1`
8×	`associate-/r/`
6×	`pow1/2` `sqrt-div`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

4 → 148

Calls

4 calls:

8.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
21.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
16.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series975.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
302.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
195.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
180.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify1.1s

Counts

160 → 160

Iterations

Iter	Nodes
3	2643
2	788
1	367
0	206

prune3.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.1b

localize60.0ms

Local error

Found 4 expressions with local error:

11.2b	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
18.0b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
18.0b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
18.0b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
45×	`times-frac`
40×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
18×	`difference-of-squares`
12×	`pow1`
9×	`sqrt-pow1` `pow1/3`
7×	`cbrt-div`
6×	`associate-/r/`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `sqrt-div` `flip-+` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `sqrt-prod`

Counts

4 → 116

Calls

4 calls:

10.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
5.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
8.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
310.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
318.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
257.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify801.0ms

Counts

128 → 128

Iterations

Iter	Nodes
3	2342
2	757
1	347
0	180

prune2.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 13.1b

regimes484.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.5s	7835×	body	80	nan
1.4s	3788×	body	160	valid
1.2s	4212×	body	80	valid