Details

sample119.0ms

Algorithm

intervals

Results

38.0ms	242×	body	80	nan
33.0ms	128×	body	160	valid
17.0ms	128×	body	80	valid

simplify2.9s

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: 8.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ Om Omc) (/ Om Omc))
0.3b	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.9b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite37.0ms

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:

13.0ms	(* (/ Om Omc) (/ Om Omc))
13.0ms	(/ (- 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))))
5.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ Om Omc) (/ Om Omc))
75.0ms	(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))
9.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
121.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify2.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1951
1	655
0	257

prune961.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (- 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))))
7.9b	(sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (- 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))))
8.0b	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))
8.0b	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-div`
2×	`rem-sqrt-square`
1×	`frac-times` `asin-acos` `pow-prod-down` `associate-l/` `associate-r/`

Counts

4 → 60

Calls

4 calls:

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

series367.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(asin (sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (- 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))))
191.0ms	(sqrt (* (/ (+ 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))) (/ (- 1 (/ Om Omc)) (sqrt (fma 2 (* (/ t l) (/ t l)) 1)))))
93.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))
66.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5036
4	2968
3	777
2	246
1	124
0	79

prune484.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.6b

localize56.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))))
12.2b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
12.2b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
12.2b	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

31.0ms	(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (sqrt (- 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))

series657.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (* (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma 2 (* (/ t l) (/ t l)) 1)) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma 2 (* (/ t l) (/ t l)) 1)))))
184.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
151.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))
179.0ms	(cbrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify2.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
5	4591
4	1571
3	665
2	306
1	138
0	77

prune507.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (* (fabs (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))) (sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))))
0.8b	(sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
11.9b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
11.9b	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

59×	`cbrt-prod`
46×	`times-frac`
45×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
32×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-pow1`
1×	`asin-acos` `pow1/2` `sqrt-div`

Counts

4 → 112

Calls

4 calls:

1.0ms	(asin (* (fabs (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))) (sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))))
6.0ms	(sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
3.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin (* (fabs (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))) (sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))))
291.0ms	(sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
283.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
273.0ms	(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5014
3	2203
2	751
1	379
0	220

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 8.6b

regimes441.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.3b and baseline of 10.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	7763×	body	80	nan
1.1s	3818×	body	160	valid
645.0ms	4182×	body	80	valid