Details

sample165.0ms

Algorithm

intervals

Results

65.0ms	277×	body	80	nan
49.0ms	130×	body	160	valid
23.0ms	126×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	3286
5	888
4	311
3	124
2	59
1	30
0	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite46.0ms

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:

17.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
13.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ Om Omc) (/ Om Omc))
10.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
94.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
139.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify6.2s

Counts

168 → 168

Iterations

Iter	Nodes
3	6686
2	1859
1	643
0	257

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
12.4b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite32.0ms

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:

18.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
10.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series283.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
145.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
79.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.3s

Counts

189 → 189

Iterations

Iter	Nodes
3	5569
2	1739
1	634
0	271

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite70.0ms

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:

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ Om Omc) (/ Om Omc))
9.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
76.0ms	(/ (- 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)))

simplify8.0s

Counts

168 → 168

Iterations

Iter	Nodes
3	6686
2	1859
1	643
0	257

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize72.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
6.5b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
12.2b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

124×	`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`
6×	`pow1/2` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 148

Calls

4 calls:

12.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
12.0ms	(sqrt (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)))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
265.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
184.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
209.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify3.1s

Counts

160 → 160

Iterations

Iter	Nodes
4	4808
3	1456
2	589
1	313
0	188

prune3.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

regimes701.0ms

Accuracy

98.4% (0.1b remaining)

Error of 5.3b against oracle of 5.3b and baseline of 9.5b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	25
1	25
0	24

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	3859×	body	160	valid
1.9s	8015×	body	80	nan
971.0ms	4141×	body	80	valid