Details

sample201.0ms

Algorithm

intervals

Results

80.0ms	297×	body	80	nan
52.0ms	115×	body	160	valid
32.0ms	141×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize49.0ms

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

rewrite60.0ms

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`
19×	`pow1` `sqrt-prod`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 185

Calls

4 calls:

22.0ms	(* (/ t l) (/ t l))
22.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
9.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ t l) (/ t l))
50.0ms	(* (/ Om Omc) (/ Om Omc))
12.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
175.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify739.0ms

Counts

197 → 197

Iterations

Iter	Nodes
2	2669
1	900
0	324

prune2.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

18.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
7.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series898.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
289.0ms	(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)))
160.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify2.7s

Counts

160 → 160

Iterations

Iter	Nodes
4	4832
3	1462
2	592
1	314
0	188

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize82.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
12.2b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
12.2b	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
40×	`add-sqr-sqrt`
32×	`times-frac`
31×	`*-un-lft-identity`
25×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`pow1`
7×	`rem-sqrt-square` `sqrt-pow1`
5×	`pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-div`
2×	`div-inv`

Counts

4 → 106

Calls

4 calls:

10.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (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))
6.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
70.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
87.0ms	(sqrt (fma (* (/ t l) (/ t l)) 2 1))
145.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify4.7s

Counts

118 → 118

Iterations

Iter	Nodes
4	5090
3	1535
2	630
1	334
0	202

prune3.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.1b

localize57.0ms

Local error

Found 4 expressions with local error:

12.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)))
32.3b	(cbrt (* (/ t l) (/ t l)))
32.3b	(cbrt (* (/ t l) (/ t l)))
32.3b	(cbrt (* (/ t l) (/ t l)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `sqrt-prod`
16×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt`
9×	`cbrt-div`
6×	`difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-l/` `associate-r/`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div` `div-inv`

Counts

4 → 79

Calls

4 calls:

5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)))
5.0ms	(cbrt (* (/ t l) (/ t l)))
5.0ms	(cbrt (* (/ t l) (/ t l)))
5.0ms	(cbrt (* (/ t l) (/ t l)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (cbrt (* (/ t l) (/ t l))) (cbrt (* (/ t l) (/ t l)))) (cbrt (* (/ t l) (/ t l)))) 2 1)))
123.0ms	(cbrt (* (/ t l) (/ t l)))
131.0ms	(cbrt (* (/ t l) (/ t l)))
148.0ms	(cbrt (* (/ t l) (/ t l)))

simplify762.0ms

Counts

91 → 91

Iterations

Iter	Nodes
4	2300
3	860
2	409
1	238
0	147

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.1b

regimes591.0ms

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.4b and baseline of 10.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.1s	7835×	body	80	nan
1.8s	3788×	body	160	valid
952.0ms	4212×	body	80	valid