Details

sample724.0ms

Algorithm

intervals

Results

415.0ms	533×	body	80	nan
47.0ms	305×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize93.0ms

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*)))))

rewrite268.0ms

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:

19.0ms	(* n (pow (/ l Om) 2.0))
43.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
117.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
84.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.8s

Counts

4 → 12

Calls

4 calls:

232.0ms	(* n (pow (/ l Om) 2.0))
630.0ms	(* (* 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*))))
7.1s	(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

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.0b

localize81.0ms

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*))))))

rewrite220.0ms

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:

15.0ms	(/ (* l l) Om)
36.0ms	(* n (pow (/ l Om) 2.0))
48.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
114.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.9s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* l l) Om)
196.0ms	(* n (pow (/ l Om) 2.0))
515.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.2s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify2.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
2	3622
1	913
0	322

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.3b

localize81.0ms

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*))))))

rewrite408.0ms

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:

154.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
22.0ms	(* n (pow (/ l Om) 2.0))
74.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
149.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series10.4s

Counts

4 → 12

Calls

4 calls:

2.4s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
197.0ms	(* n (pow (/ l Om) 2.0))
521.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.2s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify2.8s

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
2	4075
1	1063
0	368

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.1b

localize53.0ms

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*)))))))

rewrite387.0ms

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*)))))
131.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
33.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
110.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

series8.4s

Counts

4 → 12

Calls

4 calls:

872.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
374.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
5.8s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

simplify1.8s

Counts

138 → 138

Iterations

Iter	Nodes
done	5006
2	4109
1	1005
0	329

prune688.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 19.9b

regimes1.5s

Accuracy

34.3% (9.1b remaining)

Error of 27.6b against oracle of 18.5b and baseline of 32.4b

bsearch5.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	64
1	64
0	49

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	14706×	body	80	nan
1.3s	9181×	body	80	valid