Details

sample161.0ms

Algorithm

intervals

Results

51.0ms	521×	body	80	nan
42.0ms	299×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	152	28
3	627	28
4	2978	28
done	5000	28

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize47.0ms

Local error

Found 4 expressions with local error:

7.3b	(/ (* l l) Om)
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

10.0ms	(/ (* l l) Om)
54.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
149.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
121.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series8.1s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* l l) Om)
488.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.5s

Counts

115 → 115

Iterations

Useful iterations: 2 (892.0ms)

Iter	Nodes	Cost
0	318	3217
1	918	3026
2	4043	2706
done	5000	2706

prune683.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize44.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

43.0ms	(* n (pow (/ l Om) 2.0))
88.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
195.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
117.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.3s

Counts

4 → 12

Calls

4 calls:

230.0ms	(* n (pow (/ l Om) 2.0))
608.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.9s

Counts

131 → 131

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	350	3452
1	973	3239
2	4078	2945
done	5000	2945

prune789.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.8b

localize66.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b	(* n (pow (/ l Om) (/ 2.0 2)))
12.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite719.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

213.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
37.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
268.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
187.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.8s

Counts

4 → 12

Calls

4 calls:

579.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
287.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
8.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify3.1s

Counts

148 → 148

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	386	5057
1	1066	4054
2	4466	3650
done	5000	3650

prune800.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 25.7b

localize41.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.3b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.8b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 129

Calls

4 calls:

33.0ms	(* n (pow (/ l Om) 2.0))
197.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
55.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
164.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series10.3s

Counts

4 → 12

Calls

4 calls:

210.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
551.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.6s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify2.7s

Counts

141 → 141

Iterations

Useful iterations: 2 (995.0ms)

Iter	Nodes	Cost
0	368	3780
1	1035	3565
2	4034	3217
done	5000	3217

prune757.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.4b

regimes928.0ms

Accuracy

25.7% (9.3b remaining)

Error of 27.8b against oracle of 18.5b and baseline of 31.0b

bsearch213.0ms

Steps

Iters	Range		Point
10	-5.10070569146941e-304	1.0382457741670337e-301	3.2675070946382715e-308

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	71
1	46	71
done	46	71

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.1s	14816×	body	80	nan
2.2s	9208×	body	80	valid