Details

sample107.0ms

Algorithm

intervals

Results

39.0ms	120×	body	160	valid
30.0ms	235×	body	80	nan
17.0ms	136×	body	80	valid

simplify781.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
5	1100
4	363
3	142
2	61
1	32
0	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
0.5b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
8.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
21×	`sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `asin-acos` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `sqrt-div` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 152

Calls

4 calls:

32.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
29.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
15.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ Om Omc) (/ Om Omc))
20.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
134.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
180.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify681.0ms

Counts

164 → 164

Iterations

Iter	Nodes
done	2001
1	723
0	267

prune900.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
0.6b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
8.5b	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
85×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
65×	`add-cube-cbrt` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
8×	`associate-/l*`
6×	`associate-/r*` `sqrt-div`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `frac-times` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 173

Calls

4 calls:

20.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
21.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
6.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
132.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
92.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

simplify1.5s

Counts

185 → 185

Iterations

Iter	Nodes
done	2006
2	1836
1	687
0	281

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize63.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
7.7b	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
8.5b	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
8.5b	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

230×	`sqrt-prod`
104×	`times-frac`
96×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
64×	`add-cube-cbrt`
24×	`difference-of-squares`
12×	`rem-sqrt-square`
10×	`sqrt-div`
8×	`pow1`
4×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate-/r/` `flip-+` `insert-posit16` `add-log-exp`
2×	`div-inv`

Counts

4 → 172

Calls

4 calls:

9.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
14.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
11.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
6.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
213.0ms	(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))))
93.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))
87.0ms	(sqrt (+ 1 (* (+ (/ t l) (/ t l)) (/ t l))))

simplify613.0ms

Counts

184 → 184

Iterations

Iter	Nodes
done	2001
2	771
1	381
0	238

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.2b

localize57.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
8.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
8.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
8.5b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
50×	`add-sqr-sqrt`
48×	`times-frac`
41×	`*-un-lft-identity`
32×	`add-cube-cbrt`
18×	`difference-of-squares`
7×	`pow1`
6×	`rem-sqrt-square` `associate-/r/`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
17.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))))
139.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
129.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))
120.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (+ (/ t l) (/ t l)) (/ t l)))))

simplify580.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
2	573
1	266
0	143

prune928.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.1b

regimes560.0ms

Accuracy

98.8% (0.1b remaining)

Error of 5.4b against oracle of 5.4b and baseline of 10.2b

bsearch3.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	7893×	body	80	nan
1.4s	3744×	body	160	valid
1.2s	4256×	body	80	valid