Details

sample614.0ms

Algorithm

intervals

Results

187.0ms	290×	body	80	valid
109.0ms	500×	body	80	nan

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	154	27
3	642	27
4	3239	27
done	5000	27

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize35.0ms

Local error

Found 4 expressions with local error:

6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b	(/ (* l l) Om)
9.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite535.0ms

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` `log1p-expm1-u` `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 → 141

Calls

4 calls:

68.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
252.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
182.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.4s

Counts

4 → 12

Calls

4 calls:

580.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
47.0ms	(/ (* l l) Om)
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.3s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	411	4799
1	1142	4430
2	4689	3850
done	5000	3850

prune927.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.9b

localize25.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(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

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
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`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 157

Calls

4 calls:

27.0ms	(* n (pow (/ l Om) 2.0))
67.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
218.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
131.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts

4 → 12

Calls

4 calls:

184.0ms	(* n (pow (/ l Om) 2.0))
612.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

simplify3.1s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	443	5038
1	1197	4647
2	4702	4089
done	5000	4089

prune997.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.7b

localize54.0ms

Local error

Found 4 expressions with local error:

3.5b	(* n (pow (/ l Om) (/ 2.0 2)))
6.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.8b	(* (* (* 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*))))
19.3b	(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*)))))

rewrite752.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 174

Calls

4 calls:

27.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
264.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
249.0ms	(* (* (* 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*))))
195.0ms	(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*)))))

series10.2s

Counts

4 → 12

Calls

4 calls:

216.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
573.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.0s	(* (* (* 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*))))
7.4s	(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*)))))

simplify829.0ms

Counts

186 → 186

Iterations

Useful iterations: done (820.0ms)

Iter	Nodes	Cost
0	479	7307
1	1290	5730
done	5000	5038

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 19.7b

localize27.0ms

Local error

Found 4 expressions with local error:

3.5b	(* n (pow (/ l Om) (/ 2.0 2)))
5.6b	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
9.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

rewrite499.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
37×	`associate-r`
30×	`unpow-prod-down`
29×	`add-exp-log` `*-un-lft-identity`
27×	`add-cube-cbrt`
23×	`pow1`
20×	`times-frac` `associate-*r/`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`prod-diff` `pow-prod-down`
11×	`flip3--` `flip--`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `associate--l+`
9×	`associate-l`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 152

Calls

4 calls:

34.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
48.0ms	(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
233.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
178.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

series9.4s

Counts

4 → 12

Calls

4 calls:

222.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
678.0ms	(* (- U U*) (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))) (* (- U U*) (pow (/ l Om) (/ 2.0 2))))))
6.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))))

simplify2.9s

Counts

164 → 164

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	420	5540
1	1138	5261
2	4745	4273
done	5000	4273

prune738.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 19.0b

regimes802.0ms

Accuracy

22.1% (8.0b remaining)

Error of 28.2b against oracle of 20.3b and baseline of 30.5b

bsearch300.0ms

Steps

Iters	Range		Point
6	1.1516509461714753e+25	1.8367945092606406e+26	1.242234733160926e+25
9	-0.1328015100076685	-9.644267267126015e-10	-5.147845724912202e-05

simplify12.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	45	154
1	69	117
2	77	117
done	77	117

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	15066×	body	80	nan
1.3s	9216×	body	80	valid