Details

sample1.0s

Algorithm

intervals

Results

558.0ms	293×	body	80	valid
315.0ms	459×	body	80	nan

simplify673.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
3	693
2	157
1	50
0	21

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize63.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (* n (pow (/ l Om) 2)) (- U U*))
7.4b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
7.6b	(/ (* l l) Om)
21.6b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

46.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
140.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
18.0ms	(/ (* l l) Om)
142.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
672.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
25.0ms	(/ (* l l) Om)
1.7s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify878.0ms

Counts

157 → 157

Iterations

Iter	Nodes
done	2002
1	1161
0	376

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.7b

localize50.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2))
7.2b	(* (* n (pow (/ l Om) 2)) (- U U*))
7.4b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
21.6b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
26×	`associate-r`
25×	`pow1`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `unpow2` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

18.0ms	(* n (pow (/ l Om) 2))
33.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
171.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
130.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

63.0ms	(* n (pow (/ l Om) 2))
135.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
497.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify860.0ms

Counts

175 → 175

Iterations

Iter	Nodes
done	2001
1	1216
0	407

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.2b

localize41.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (/ l Om))
7.2b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
7.4b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
21.6b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite531.0ms

Algorithm

rewrite-expression-head

Rules

104×	`associate-*r/`
47×	`add-cbrt-cube` `add-exp-log`
45×	`frac-times`
44×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
34×	`pow1`
32×	`*-un-lft-identity`
30×	`prod-diff` `associate-*l/` `add-cube-cbrt`
25×	`prod-exp` `cbrt-unprod`
24×	`sqrt-div`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
19×	`pow-prod-down`
10×	`times-frac` `associate--l+`
6×	`cbrt-undiv` `sub-neg` `div-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

10.0ms	(* n (/ l Om))
122.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
236.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
155.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* n (/ l Om))
130.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
579.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify1.1s

Counts

222 → 222

Iterations

Iter	Nodes
done	2001
1	1642
0	531

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.5b

localize61.0ms

Local error

Found 4 expressions with local error:

4.6b	(* n (/ l Om))
5.9b	(* (/ l Om) (- U U*))
7.4b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
21.6b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

111×	`associate-*r/`
49×	`add-sqr-sqrt`
44×	`frac-sub`
42×	`flip3--` `flip--`
39×	`*-un-lft-identity`
38×	`frac-times`
37×	`add-cube-cbrt`
30×	`prod-diff`
27×	`pow1`
24×	`sqrt-div`
23×	`add-cbrt-cube` `add-exp-log`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
20×	`times-frac`
17×	`associate-l`
14×	`pow-prod-down`
13×	`associate-*l/`
10×	`prod-exp` `associate--l+` `cbrt-unprod`
6×	`sub-neg`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`cbrt-undiv` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

12.0ms	(* n (/ l Om))
31.0ms	(* (/ l Om) (- U U*))
165.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
169.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

21.0ms	(* n (/ l Om))
77.0ms	(* (/ l Om) (- U U*))
536.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

simplify1.2s

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
1	1594
0	527

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.1b

regimes1.6s

Accuracy

13.2% (8.4b remaining)

Error of 28.2b against oracle of 19.8b and baseline of 29.4b

bsearch1.1s

Steps

Iters	Range		Point
6	1.8917628008510762e+199	2.1076778306646135e+200	3.750417619434724e+199
10	1.8520156648733406e-21	6.927539149538789e-07	3.780023435277137e-09
9	1.327246488227529e-157	1.2812697067031588e-149	4.9836541702388693e-157
10	7.769412597450992e-263	5.455613985372002e-251	3.2328584205801053e-251

simplify13.0ms

Iterations

Iter	Nodes
done	59
1	59
0	46

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.6s	14841×	body	80	nan
2.6s	9156×	body	80	valid