Details

sample152.0ms

Algorithm

intervals

Results

62.0ms	124×	body	160	valid
39.0ms	236×	body	80	nan
22.0ms	132×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	3385
5	909
4	313
3	127
2	61
1	32
0	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
9.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
19×	`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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `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 → 156

Calls

4 calls:

27.0ms	(* (/ Om Omc) (/ Om Omc))
26.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ Om Omc) (/ Om Omc))
127.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
10.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
150.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify3.1s

Counts

168 → 168

Iterations

Iter	Nodes
3	6115
2	1838
1	641
0	257

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.7b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
9.2b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

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*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`sqrt-div` `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 → 177

Calls

4 calls:

25.0ms	(* (/ Om Omc) (/ Om Omc))
20.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
2.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series289.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ Om Omc) (/ Om Omc))
152.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
14.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
93.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify2.3s

Counts

189 → 189

Iterations

Iter	Nodes
3	5509
2	1731
1	634
0	271

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
9.0b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
71×	`times-frac`
58×	`*-un-lft-identity`
51×	`add-cube-cbrt`
19×	`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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`rem-sqrt-square` `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 → 156

Calls

4 calls:

22.0ms	(* (/ Om Omc) (/ Om Omc))
21.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ Om Omc) (/ Om Omc))
78.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
9.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
189.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify2.6s

Counts

168 → 168

Iterations

Iter	Nodes
3	6115
2	1838
1	641
0	257

prune2.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
7.8b	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
9.2b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.2b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

4.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series1.0s

Counts

4 → 12

Calls

4 calls:

206.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
196.0ms	(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
530.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
97.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
4	2115
3	702
2	247
1	118
0	68

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes797.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.2b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	27
1	27
0	24

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	3805×	body	160	valid
1.7s	7937×	body	80	nan
984.0ms	4195×	body	80	valid