Details

sample338.0ms

Algorithm

intervals

Results

127.0ms	500×	body	80	nan
47.0ms	290×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize38.0ms

Local error

Found 4 expressions with local error:

6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b	(/ (* l l) Om)
9.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite454.0ms

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:

60.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms	(/ (* l l) Om)
190.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
182.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series10.2s

Counts

4 → 12

Calls

4 calls:

584.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
30.0ms	(/ (* l l) Om)
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.7s

Counts

115 → 115

Iterations

Useful iterations: 2 (900.0ms)

Iter	Nodes	Cost
0	318	3217
1	919	3026
2	4051	2706
done	5001	2706

prune703.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.7b

localize39.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
6.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite413.0ms

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:

25.0ms	(* n (pow (/ l Om) 2.0))
90.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
167.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
124.0ms	(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:

225.0ms	(* n (pow (/ l Om) 2.0))
619.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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*)))))

simplify2.9s

Counts

131 → 131

Iterations

Useful iterations: 2 (1.1s)

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

prune811.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.7b

localize46.0ms

Local error

Found 4 expressions with local error:

3.5b	(* n (pow (/ l Om) (/ 2.0 2)))
6.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.8b	(* (* (* 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*))))
19.3b	(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*)))))

rewrite726.0ms

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:

37.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
203.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
287.0ms	(* (* (* 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*))))
192.0ms	(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:

223.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
529.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
2.1s	(* (* (* 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*))))
7.5s	(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*)))))

simplify2.5s

Counts

148 → 148

Iterations

Useful iterations: 2 (1.0s)

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

prune729.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 19.8b

localize39.0ms

Local error

Found 4 expressions with local error:

3.5b	(* n (pow (/ l Om) (/ 2.0 2)))
5.6b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.8b	(* (* (* 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*)))))
19.3b	(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*))))))

rewrite449.0ms

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:

27.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
52.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
192.0ms	(* (* (* 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*)))))
169.0ms	(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*))))))

series8.2s

Counts

4 → 12

Calls

4 calls:

175.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
358.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.7s	(* (* (* 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*)))))
5.9s	(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*))))))

simplify1.8s

Counts

148 → 148

Iterations

Useful iterations: 2 (731.0ms)

Iter	Nodes	Cost
0	398	4455
1	1066	4209
2	4366	3507
done	5000	3507

prune656.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 19.8b

regimes694.0ms

Accuracy

20.8% (7.7b remaining)

Error of 28.5b against oracle of 20.8b and baseline of 30.5b

bsearch266.0ms

Steps

Iters	Range		Point
7	2.1887456472240332e-103	1.0963330928825291e-101	7.697060986820553e-102
9	-32544877.961439718	-1.7004310701068142	-68.72400249619959

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	38	116
1	53	79
done	53	79

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.2s	15066×	body	80	nan
964.0ms	9216×	body	80	valid