Details

sample285.0ms

Algorithm

intervals

Results

63.0ms	291×	body	80	valid
56.0ms	464×	body	80	nan

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (42.0ms)

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: 35.6b

localize33.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.4b	(/ (* l l) Om)
21.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite453.0ms

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:

64.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
193.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.0ms	(/ (* l l) Om)
167.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.6s

Counts

4 → 12

Calls

4 calls:

594.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
25.0ms	(/ (* l l) Om)
8.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.1s

Counts

153 → 153

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	411	4799
1	1142	4430
2	4686	3850
done	5000	3850

prune923.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 23.4b

localize38.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite470.0ms

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:

49.0ms	(* n (pow (/ l Om) 2.0))
72.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
186.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
152.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts

4 → 12

Calls

4 calls:

263.0ms	(* n (pow (/ l Om) 2.0))
570.0ms	(* (* 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*))))
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.0s

Counts

169 → 169

Iterations

Useful iterations: 2 (1.4s)

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

prune969.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.0b

localize31.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
7.8b	(* (* (* 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*))))
21.0b	(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*)))))

rewrite653.0ms

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:

50.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
175.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
239.0ms	(* (* (* 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*))))
172.0ms	(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*)))))

series10.6s

Counts

4 → 12

Calls

4 calls:

293.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
602.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.1s	(* (* (* 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*))))
7.6s	(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*)))))

simplify952.0ms

Counts

186 → 186

Iterations

Useful iterations: done (942.0ms)

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

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.6b

localize45.0ms

Local error

Found 4 expressions with local error:

12.9b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
12.9b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
12.9b	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
21.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite865.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
10×	`associate-*r/`
6×	`sqrt-div` `pow-prod-down`
5×	`flip3--` `flip--`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1` `frac-sub` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 54

Calls

4 calls:

8.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
10.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
10.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
835.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series8.2s

Counts

4 → 12

Calls

4 calls:

315.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
325.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
336.0ms	(cbrt (* n (pow (/ l Om) (/ 2.0 2))))
7.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* (cbrt (* n (pow (/ l Om) (/ 2.0 2)))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (cbrt (* n (pow (/ l Om) (/ 2.0 2))))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify1.1s

Counts

66 → 66

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	186	2430
1	551	2244
2	2357	1679
done	5000	1598

prune402.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 20.6b

regimes571.0ms

Accuracy

14.7% (8.1b remaining)

Error of 29.8b against oracle of 21.7b and baseline of 31.2b

bsearch153.0ms

Steps

Iters	Range		Point
9	6.813752349909848e+88	1.387866107452373e+94	8.120471958061494e+92

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	97
1	51	97
done	51	97

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.0s	15327×	body	80	nan
1.2s	9227×	body	80	valid