Details

sample119.0ms

Algorithm

intervals

Results

38.0ms	126×	body	160	valid
30.0ms	197×	body	80	nan
19.0ms	130×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5022
6	4794
5	1100
4	363
3	142
2	61
1	32
0	16

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
0.2b	(* (/ Om Omc) (/ Om Omc))
0.4b	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
11.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt` `times-frac`
84×	`*-un-lft-identity`
70×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
19×	`pow1`
9×	`div-inv`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
5×	`distribute-lft-out`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`

Counts

4 → 184

Calls

4 calls:

43.0ms	(* (/ t l) (/ t l))
43.0ms	(* (/ Om Omc) (/ Om Omc))
1.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
129.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ t l) (/ t l))
41.0ms	(* (/ Om Omc) (/ Om Omc))
20.0ms	(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
155.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify3.0s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
2	3244
1	980
0	334

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
0.6b	(cbrt l)
11.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (cbrt l) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
26×	`sqrt-prod`
24×	`add-sqr-sqrt`
21×	`times-frac`
17×	`add-cube-cbrt`
9×	`cbrt-prod`
8×	`difference-of-squares`
5×	`pow1` `distribute-lft-out`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
1.0ms	(cbrt l)
66.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (cbrt l) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt l)
191.0ms	(cbrt l)
215.0ms	(cbrt l)
141.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (cbrt l) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

simplify2.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	2530
2	678
1	274
0	144

prune614.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt l))
0.7b	(cbrt (cbrt l))
0.7b	(cbrt (cbrt l))
11.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`cbrt-prod` `add-sqr-sqrt`
26×	`sqrt-prod`
21×	`times-frac`
20×	`add-cube-cbrt`
8×	`difference-of-squares`
5×	`pow1` `distribute-lft-out`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`rem-sqrt-square` `associate-/r/`
1×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt (cbrt l))
1.0ms	(cbrt (cbrt l))
1.0ms	(cbrt (cbrt l))
69.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

341.0ms	(cbrt (cbrt l))
319.0ms	(cbrt (cbrt l))
291.0ms	(cbrt (cbrt l))
172.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ (/ t l) (* (/ (cbrt l) (cbrt t)) (/ (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))) (cbrt t)))) (/ (cbrt t) (cbrt l)))))))

simplify2.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5007
3	2567
2	696
1	289
0	155

prune840.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.9b

localize51.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
6.4b	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
11.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
11.4b	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

58×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
16×	`difference-of-squares`
10×	`distribute-lft-out`
8×	`pow1`
6×	`rem-sqrt-square`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `associate-/r/` `insert-posit16` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
1.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
95.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
95.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
33.0ms	(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))))
145.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
160.0ms	(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))

simplify2.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
3	2010
2	575
1	265
0	142

prune752.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.9b

regimes592.0ms

Accuracy

0% (0.1b remaining)

Error of 10.2b against oracle of 10.1b and baseline of 10.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	8067×	body	80	nan
1.1s	3824×	body	160	valid
496.0ms	4176×	body	80	valid