Details

sample151.0ms

Algorithm

intervals

Results

37.0ms	270×	body	80	nan
34.0ms	126×	body	160	valid
18.0ms	130×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2725
5	723
4	243
3	97
2	49
1	29
0	16

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.1b	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
65×	`times-frac`
51×	`*-un-lft-identity`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
28×	`difference-of-squares`
27×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*` `sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`rem-sqrt-square` `flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `asin-acos` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `flip--`

Counts

4 → 130

Calls

4 calls:

87.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
51.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series967.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
93.0ms	(pow (/ Om Omc) 2.0)
23.0ms	(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
499.0ms	(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify2.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	1736
1	722
0	308

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.3b	(pow (/ Om Omc) 2.0)
0.5b	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.2b	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
95×	`sqrt-prod`
82×	`times-frac`
65×	`*-un-lft-identity`
51×	`add-cube-cbrt`
28×	`difference-of-squares`
27×	`unpow-prod-down`
11×	`associate-/l*`
9×	`add-exp-log`
8×	`sqr-pow`
7×	`distribute-lft-out--`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `div-exp` `pow-exp` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `asin-acos` `sqrt-undiv` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 151

Calls

4 calls:

87.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
6.0ms	(pow (/ Om Omc) 2.0)
1.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
5.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series860.0ms

Counts

4 → 12

Calls

4 calls:

459.0ms	(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
80.0ms	(pow (/ Om Omc) 2.0)
25.0ms	(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
297.0ms	(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify3.5s

Counts

163 → 163

Iterations

Iter	Nodes
done	5012
3	4881
2	1543
1	693
0	329

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ Om Omc) (/ Om Omc))
0.5b	(/ 2.0 (* (/ l t) (/ l t)))
0.5b	(asin (fabs (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
8.1b	(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
60×	`times-frac`
51×	`*-un-lft-identity`
43×	`add-cube-cbrt`
34×	`add-cbrt-cube` `add-exp-log`
22×	`sqrt-prod`
13×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l`
12×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`div-inv`
5×	`associate-/r/`
4×	`distribute-lft-out` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`associate-/l*`
2×	`frac-times` `rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `asin-acos` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `sqrt-div` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `flip-+`

Counts

4 → 139

Calls

4 calls:

36.0ms	(* (/ Om Omc) (/ Om Omc))
16.0ms	(/ 2.0 (* (/ l t) (/ l t)))
1.0ms	(asin (fabs (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
43.0ms	(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ Om Omc) (/ Om Omc))
42.0ms	(/ 2.0 (* (/ l t) (/ l t)))
19.0ms	(asin (fabs (sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
214.0ms	(sqrt (/ (- 1.0 (* (/ Om Omc) (/ Om Omc))) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

simplify2.2s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	2389
1	757
0	286

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* (/ l t) (/ l t)))
0.5b	(asin (fabs (sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
5.0b	(/ (* Om (/ Om Omc)) Omc)
8.1b	(sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
31×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
27×	`times-frac`
26×	`sqrt-prod`
18×	`add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `associate-/r/` `distribute-lft-out`
4×	`associate-/r` `associate-/l` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`div-inv`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `asin-acos` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+` `associate-/l/`

Counts

4 → 100

Calls

4 calls:

12.0ms	(/ 2.0 (* (/ l t) (/ l t)))
1.0ms	(asin (fabs (sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
20.0ms	(/ (* Om (/ Om Omc)) Omc)
43.0ms	(sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 2.0 (* (/ l t) (/ l t)))
31.0ms	(asin (fabs (sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))))
32.0ms	(/ (* Om (/ Om Omc)) Omc)
209.0ms	(sqrt (/ (- 1.0 (/ (* Om (/ Om Omc)) Omc)) (+ 1.0 (/ 2.0 (* (/ l t) (/ l t))))))

simplify1.8s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1800
1	555
0	236

prune795.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.8b

regimes1.6s

Accuracy

0% (0.1b remaining)

Error of 9.8b against oracle of 9.7b and baseline of 9.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	7907×	body	80	nan
1.0s	3791×	body	160	valid
554.0ms	4209×	body	80	valid