Details

sample207.0ms

Algorithm

intervals

Results

106.0ms	533×	body	80	nan
37.0ms	305×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
4	2710
3	599
2	148
1	49
0	21

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize61.0ms

Local error

Found 4 expressions with local error:

6.5b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.2b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
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:

39.0ms	(* n (pow (/ l Om) 2.0))
64.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
166.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
92.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.2s

Counts

4 → 12

Calls

4 calls:

162.0ms	(* n (pow (/ l Om) 2.0))
549.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.7s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	3945
1	1015
0	350

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.0b

localize41.0ms

Local error

Found 4 expressions with local error:

6.1b	(/ (* l l) Om)
6.5b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.1b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
26×	`add-sqr-sqrt`
22×	`associate-r`
19×	`pow1`
18×	`-un-lft-identity` `associate-r/`
16×	`add-cbrt-cube` `add-cube-cbrt`
15×	`unpow-prod-down`
14×	`prod-exp`
13×	`times-frac`
9×	`pow-prod-down`
6×	`flip3--` `sqrt-div` `flip--`
5×	`sqrt-pow1` `cbrt-unprod`
4×	`div-exp` `associate-l` `pow-exp` `frac-sub` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `sub-neg` `distribute-lft-in` `*-commutative` `div-inv` `sqr-pow`
1×	`clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

9.0ms	(/ (* l l) Om)
31.0ms	(* n (pow (/ l Om) 2.0))
53.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
100.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.6s

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (* l l) Om)
225.0ms	(* n (pow (/ l Om) 2.0))
500.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify2.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
2	3622
1	913
0	322

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.3b

localize60.0ms

Local error

Found 4 expressions with local error:

5.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.5b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.1b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`add-cbrt-cube` `associate-r`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `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 → 129

Calls

4 calls:

170.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
39.0ms	(* n (pow (/ l Om) 2.0))
44.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
92.0ms	(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:

1.9s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
193.0ms	(* n (pow (/ l Om) 2.0))
573.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.5s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify3.4s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
2	4075
1	1063
0	368

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.1b

localize73.0ms

Local error

Found 4 expressions with local error:

4.5b	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
5.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
7.4b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
20.1b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

58×	`associate-*r/`
33×	`pow1`
32×	`add-exp-log`
28×	`distribute-rgt-in` `distribute-lft-in`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
16×	`sub-neg` `flip3--` `flip--`
12×	`associate--l+` `frac-sub` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-r`
4×	`add-log-exp`
3×	`*-commutative`
2×	`pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

108.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
181.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
55.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
138.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

series11.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
1.9s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
543.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
7.8s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

simplify3.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	5006
2	4109
1	1005
0	329

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 19.9b

regimes2.3s

Accuracy

34.2% (9.2b remaining)

Error of 27.6b against oracle of 18.4b and baseline of 32.4b

bsearch7.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	64
1	64
0	49

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	14706×	body	80	nan
2.4s	9181×	body	80	valid