Details

sample175.0ms

Algorithm

intervals

Results

59.0ms	141×	body	160	valid
50.0ms	252×	body	80	nan
36.0ms	115×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4967
5	1097
4	396
3	153
2	63
1	32
0	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
8.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite57.0ms

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:

32.0ms	(* (/ t l) (/ t l))
12.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ t l) (/ t l))
102.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
11.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
149.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify2.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
2	1918
1	644
0	258

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.2b	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
0.7b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
8.4b	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite51.0ms

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:

26.0ms	(* (/ t l) (/ t l))
17.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
1.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

series271.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ t l) (/ t l))
125.0ms	(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))
9.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
102.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify1.7s

Counts

189 → 189

Iterations

Iter	Nodes
done	5002
2	1843
1	642
0	272

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize68.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (* (* (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))))
12.9b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
12.9b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
12.9b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
12×	`sqrt-pow1`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `associate-*r/`
2×	`pow2` `pow-sqr`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 73

Calls

4 calls:

73.0ms	(sqrt (* (* (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))))
1.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
1.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

series674.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(sqrt (* (* (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))))
179.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
155.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
177.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify2.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
4	2026
3	740
2	343
1	168
0	98

prune535.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.7b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1))))
1.2b	(* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l))
8.3b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log`
34×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`add-cube-cbrt`
22×	`add-cbrt-cube` `associate-r`
19×	`sqrt-prod`
18×	`prod-exp` `cbrt-unprod`
14×	`pow1`
12×	`cbrt-prod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `difference-of-squares`
5×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `div-inv`
1×	`frac-times` `asin-acos` `sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `associate-l` `associate-l/` `-commutative`

Counts

4 → 115

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1))))
80.0ms	(* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l))
11.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt t)
17.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1))))
52.0ms	(* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l))
168.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (* (cbrt t) (* (cbrt t) (/ t l))) (/ (cbrt t) l)) 1)))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2213
1	639
0	260

prune622.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 4.6b

regimes487.0ms

Accuracy

98.6% (0.1b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 10.3b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	8238×	body	80	nan
1.7s	3813×	body	160	valid
696.0ms	4187×	body	80	valid