Details

sample574.0ms

Algorithm

intervals

Results

255.0ms	290×	body	80	valid
86.0ms	490×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	28
1	49	28
2	152	28
3	627	28
4	2978	28
done	5000	28

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize52.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.7b	(/ (* l l) Om)
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite456.0ms

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:

87.0ms	(* (* 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)
153.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.6s

Counts

4 → 12

Calls

4 calls:

547.0ms	(* (* 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*))))
24.0ms	(/ (* l l) Om)
7.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.9s

Counts

115 → 115

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	318	3217
1	919	3026
2	4052	2706
done	5000	2706

prune692.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.5b

localize39.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite424.0ms

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:

43.0ms	(* n (pow (/ l Om) 2.0))
72.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
188.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

series9.6s

Counts

4 → 12

Calls

4 calls:

232.0ms	(* n (pow (/ l Om) 2.0))
561.0ms	(* (* 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*))))
7.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.2s

Counts

131 → 131

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	350	3452
1	973	3239
2	4078	2945
done	5000	2945

prune853.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.8b

localize31.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.3b	(* (* (* 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*))))
20.3b	(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*)))))

rewrite784.0ms

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:

39.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
257.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
276.0ms	(* (* (* 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*))))
204.0ms	(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*)))))

series9.6s

Counts

4 → 12

Calls

4 calls:

276.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
502.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(* (* (* 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*))))
6.9s	(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*)))))

simplify2.7s

Counts

148 → 148

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	386	5057
1	1066	4054
2	4467	3650
done	5000	3650

prune708.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.5b

localize37.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
40×	`associate-*r/`
24×	`pow-prod-down`
22×	`add-exp-log` `add-cbrt-cube`
20×	`flip3--` `flip--`
16×	`frac-sub`
12×	`sqrt-div` `prod-exp` `cbrt-unprod`
8×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate--l+`
6×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`add-log-exp`
2×	`pow1/2` `associate-l` `sqrt-prod` `*-commutative`

Counts

4 → 108

Calls

4 calls:

203.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
170.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
100.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
87.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series13.3s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* (* 2.0 n) 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*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	228	5044
1	701	4780
2	3211	4304
done	5000	4288

prune575.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.5b

regimes511.0ms

Accuracy

19.3% (8.8b remaining)

Error of 29.9b against oracle of 21.1b and baseline of 32.0b

bsearch77.0ms

Steps

Iters	Range		Point
5	6.6284886086586095e+128	2.0010442062530377e+129	8.480782664814814e+128

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	69
1	40	69
done	40	69

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	14522×	body	80	nan
1.0s	9173×	body	80	valid