Details

sample90.0ms

Algorithm

intervals

Results

29.0ms	436×	body	80	nan
18.0ms	303×	body	80	valid

simplify123.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14
done	5001	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0b	(/ (* l l) Om)
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite289.0ms

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:

128.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
47.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(/ (* l l) Om)
99.0ms	(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:

1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
379.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
5.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify46.0ms

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011
done	5001	2011

prune557.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.4b

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ l Om) 2.0))
5.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite302.0ms

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:

24.0ms	(* n (pow (/ l Om) 2.0))
127.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
98.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.1s

Counts

4 → 12

Calls

4 calls:

156.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
390.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify48.0ms

Counts

169 → 169

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1227	2457
1	5002	2136
done	5002	2136

prune632.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.6b

localize18.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ l Om) 2.0))
5.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.0b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite308.0ms

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:

23.0ms	(* n (pow (/ l Om) 2.0))
129.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
47.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
101.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.4s

Counts

4 → 12

Calls

4 calls:

151.0ms	(* n (pow (/ l Om) 2.0))
1.6s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
396.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Counts

169 → 169

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1229	2461
1	5001	2136
done	5001	2136

prune582.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.6b

localize29.0ms

Local error

Found 4 expressions with local error:

19.2b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
27.0b	(cbrt (* n (pow (/ l Om) 2.0)))
27.0b	(cbrt (* n (pow (/ l Om) 2.0)))
27.0b	(cbrt (* n (pow (/ l Om) 2.0)))

rewrite267.0ms

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:

243.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
7.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
8.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
8.0ms	(cbrt (* n (pow (/ l Om) 2.0)))

series5.8s

Counts

4 → 12

Calls

4 calls:

5.2s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
215.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
214.0ms	(cbrt (* n (pow (/ l Om) 2.0)))
214.0ms	(cbrt (* n (pow (/ l Om) 2.0)))

simplify68.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	544	1040
1	2318	983
2	5003	977
done	5003	977

prune331.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 18.6b

regimes444.0ms

Accuracy

15% (8.3b remaining)

Error of 29.8b against oracle of 21.5b and baseline of 31.3b

bsearch128.0ms

Steps

Iters	Range		Point
9	488209512.097372	1496987500799626.0	761464961700.1481

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	40
1	46	40
done	46	40

end0.0ms

sample2.6s

Algorithm

intervals

Results

911.0ms	15130×	body	80	nan
547.0ms	9212×	body	80	valid