Details

sample344.0ms

Algorithm

intervals

Results

33.0ms	475×	body	80	nan
20.0ms	297×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	151	27
3	603	27
4	3162	27
done	5000	27

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize22.0ms

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*)))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `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 → 132

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2.0))
4.0ms	(/ (* l l) Om)
56.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
45.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

142.0ms	(* n (pow (/ l Om) 2.0))
25.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify399.0ms

Counts

144 → 144

Iterations

Useful iterations: done (394.0ms)

Iter	Nodes	Cost
0	389	3995
1	1090	3803
done	5000	3705

prune670.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.9b

localize18.0ms

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*)))))

rewrite145.0ms

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:

25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms	(* n (pow (/ l Om) 2.0))
55.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts

4 → 12

Calls

4 calls:

374.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
149.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify558.0ms

Counts

169 → 169

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	442	5038
1	1244	4647
done	5000	4531

prune652.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.9b

localize21.0ms

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*)))))

rewrite232.0ms

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:

17.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
88.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
65.0ms	(* (* (* 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*))))
54.0ms	(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*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
388.0ms	(* (* (* 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*)))))

simplify436.0ms

Counts

186 → 186

Iterations

Useful iterations: done (428.0ms)

Iter	Nodes	Cost
0	478	7307
1	1370	5730
done	5000	5624

prune746.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.0b

localize21.0ms

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*))))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`unpow-prod-down` `associate-*r/` `prod-diff`
29×	`add-exp-log`
25×	`associate-r`
23×	`pow1`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `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 → 174

Calls

4 calls:

30.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
16.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
65.0ms	(* (* (* 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*)))))
49.0ms	(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*))))))

series6.8s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
173.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.3s	(* (* (* 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*)))))
5.0s	(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*))))))

simplify436.0ms

Counts

186 → 186

Iterations

Useful iterations: done (429.0ms)

Iter	Nodes	Cost
0	490	6325
1	1298	5900
done	5001	5332

prune812.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.0b

regimes937.0ms

Accuracy

17.3% (8.0b remaining)

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

bsearch381.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	55	156
1	74	156
done	74	156

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	15049×	body	80	nan
661.0ms	9215×	body	80	valid