Details

sample340.0ms

Algorithm

intervals

Results

32.0ms	475×	body	80	nan
19.0ms	297×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	149	28
3	569	28
4	2823	28
done	5000	28

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize23.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) 2.0))
8.9b	(/ (* l l) Om)
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2.0))
4.0ms	(/ (* l l) Om)
52.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
33.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* n (pow (/ l Om) 2.0))
20.0ms	(/ (* l l) Om)
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.3s

Counts

124 → 124

Iterations

Useful iterations: 2 (451.0ms)

Iter	Nodes	Cost
0	344	3129
1	958	2953
2	4248	2649
done	5000	2649

prune582.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 22.0b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.1b	(* n (pow (/ l Om) 2.0))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite125.0ms

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:

25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms	(* n (pow (/ l Om) 2.0))
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
147.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify1.6s

Counts

131 → 131

Iterations

Useful iterations: 2 (499.0ms)

Iter	Nodes	Cost
0	349	3452
1	987	3239
2	4487	2945
done	5000	2945

prune530.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.7b

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
5.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite205.0ms

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:

15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
82.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
62.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
39.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
372.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.5s

Counts

148 → 148

Iterations

Useful iterations: 2 (524.0ms)

Iter	Nodes	Cost
0	385	5057
1	1114	4054
2	4897	3650
done	5000	3650

prune570.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
20.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 136

Calls

4 calls:

24.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
59.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
36.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.7s

Counts

4 → 12

Calls

4 calls:

344.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
169.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify1.7s

Counts

148 → 148

Iterations

Useful iterations: 2 (689.0ms)

Iter	Nodes	Cost
0	397	4455
1	1080	4209
2	4705	3507
done	5000	3507

prune625.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 20.0b

regimes777.0ms

Accuracy

17.3% (8.0b remaining)

Error of 28.9b against oracle of 20.9b and baseline of 30.6b

bsearch354.0ms

Steps

Iters	Range		Point
8	6.666268870843101e+37	2.980559139220902e+41	2.856592318713015e+41
7	-1.1470207047355208e+50	-5.137084903285435e+48	-4.482863757784701e+49
9	-1.4524365819500653e+216	-8.163952542228318e+208	-7.718602062440974e+211

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	133
1	62	131
done	62	131

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	15049×	body	80	nan
625.0ms	9215×	body	80	valid