Details

sample573.0ms

Algorithm

intervals

Results

244.0ms	433×	body	80	nan
120.0ms	293×	body	80	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	152	28
3	632	28
4	3919	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize47.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(/ (* l l) Om)
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `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 → 103

Calls

4 calls:

81.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
22.0ms	(/ (* l l) Om)
206.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
132.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.0s

Counts

4 → 12

Calls

4 calls:

545.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
40.0ms	(/ (* l l) Om)
2.1s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify640.0ms

Counts

115 → 115

Iterations

Useful iterations: done (625.0ms)

Iter	Nodes	Cost
0	318	3217
1	991	3034
done	5000	2742

prune862.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.4b

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b	(* n (pow (/ l Om) 2.0))
6.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

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

32.0ms	(* n (pow (/ l Om) 2.0))
54.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
190.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
127.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.6s

Counts

4 → 12

Calls

4 calls:

222.0ms	(* n (pow (/ l Om) 2.0))
530.0ms	(* (* 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*))))
8.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify618.0ms

Counts

131 → 131

Iterations

Useful iterations: done (612.0ms)

Iter	Nodes	Cost
0	350	3452
1	1024	3247
done	5001	2971

prune847.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.4b

localize49.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b	(* (* (* 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*))))
21.4b	(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*)))))

rewrite762.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `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 → 136

Calls

4 calls:

48.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
195.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
315.0ms	(* (* (* 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*))))
191.0ms	(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*)))))

series10.4s

Counts

4 → 12

Calls

4 calls:

285.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
584.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.2s	(* (* (* 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*))))
7.4s	(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*)))))

simplify734.0ms

Counts

148 → 148

Iterations

Useful iterations: done (726.0ms)

Iter	Nodes	Cost
0	386	5057
1	1136	4213
done	5000	3676

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.9b

localize42.0ms

Local error

Found 4 expressions with local error:

6.1b	(* n (pow (/ l Om) (/ 2.0 2)))
7.5b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.1b	(* (* (* 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*)))))
21.4b	(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*))))))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `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 → 136

Calls

4 calls:

40.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
53.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
263.0ms	(* (* (* 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*)))))
154.0ms	(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*))))))

series9.7s

Counts

4 → 12

Calls

4 calls:

188.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
372.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.5s	(* (* (* 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*))))))

simplify461.0ms

Counts

148 → 148

Iterations

Useful iterations: done (455.0ms)

Iter	Nodes	Cost
0	398	4455
1	1114	4251
done	5000	3831

prune718.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

regimes599.0ms

Accuracy

16.2% (7.5b remaining)

Error of 29.2b against oracle of 21.7b and baseline of 30.6b

bsearch1.0s

Steps

Iters	Range		Point
3	4.242956956210584e+125	5.419790816469547e+125	5.199134467670991e+125
10	1.713202050375768e-106	8.437061114098603e-88	1.6688577252728646e-95
8	1.110000930973235e-152	3.3367201306177223e-149	7.226024415244728e-151
9	4.863701395372121e-266	3.16795383277746e-259	8.818347807754774e-264
8	-2.980914418999091e-126	-8.342930497722065e-131	-6.798116842299236e-128

simplify15.0ms

Iterations

Useful iterations: done (14.0ms)

Iter	Nodes	Cost
0	47	291
1	60	253
2	63	216
3	66	216
done	66	215

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	14858×	body	80	nan
1.1s	9220×	body	80	valid