Details

sample169.0ms

Algorithm

intervals

Results

50.0ms	126×	body	160	valid
47.0ms	260×	body	80	nan
42.0ms	130×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite61.0ms

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:

26.0ms	(* (/ Om Omc) (/ Om Omc))
23.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
6.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ Om Omc) (/ Om Omc))
36.0ms	(* (/ t l) (/ t l))
18.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
182.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts

197 → 197

Iterations

Iter	Nodes
done	5001
2	2841
1	919
0	324

prune974.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

rewrite46.0ms

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:

12.0ms	(* (/ Om Omc) (/ Om Omc))
25.0ms	(* (/ t l) (/ t l))
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)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ Om Omc) (/ Om Omc))
32.0ms	(* (/ t l) (/ t l))
18.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1))))
136.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))

simplify1.9s

Counts

197 → 197

Iterations

Iter	Nodes
done	5001
2	2841
1	919
0	324

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ Om Omc) (/ Om Omc))
0.3b	(* (/ t l) (/ t l))
0.4b	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
7.7b	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `asin-acos` `sqrt-pow1` `pow1/2`

Counts

4 → 167

Calls

4 calls:

15.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(* (/ t l) (/ t l))
1.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
2.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

series163.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ Om Omc) (/ Om Omc))
32.0ms	(* (/ t l) (/ t l))
9.0ms	(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma 2 (* (/ t l) (/ t l)) 1))))
77.0ms	(sqrt (fma 2 (* (/ t l) (/ t l)) 1))

simplify1.7s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2616
1	805
0	260

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

localize57.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
7.6b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
7.8b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))
7.8b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

44×	`sqrt-prod`
38×	`add-sqr-sqrt`
32×	`times-frac`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`pow1`
6×	`rem-sqrt-square`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div` `div-inv`

Counts

4 → 100

Calls

4 calls:

13.0ms	(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)))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))
2.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
154.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))
31.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))
32.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma 2 (* (/ t l) (/ t l)) 1)))))

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
4	1989
3	747
2	346
1	205
0	127

prune651.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

regimes626.0ms

Accuracy

97.7% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.1b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	28

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.6s	8044×	body	80	nan
1.5s	3826×	body	160	valid
1.2s	4174×	body	80	valid