Details

sample167.0ms

Algorithm

intervals

Results

63.0ms	309×	body	80	valid
44.0ms	449×	body	80	nan

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3869
3	632
2	152
1	49
0	21

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.1b

localize75.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
5.8b	(* n (pow (/ l Om) 2.0))
7.1b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite949.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-sqr-sqrt` `pow1` `associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down`
10×	`times-frac` `cbrt-unprod`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

69.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
29.0ms	(* n (pow (/ l Om) 2.0))
422.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
421.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series15.2s

Counts

4 → 12

Calls

4 calls:

409.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
173.0ms	(* n (pow (/ l Om) 2.0))
1.8s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
12.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify1.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5002
2	4127
1	716
0	260

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.2b

localize47.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
7.1b	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`add-sqr-sqrt` `pow1` `associate-r`
24×	`add-cbrt-cube`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down` `cbrt-unprod`
10×	`pow-to-exp` `times-frac` `div-exp`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `flip-+` `sqr-pow`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

145.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
36.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.7s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
1.6s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.3s

Counts

4 → 12

Calls

4 calls:

642.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
235.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.7s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
14.7s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.6s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	4565
1	833
0	295

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.7b

localize122.0ms

Local error

Found 4 expressions with local error:

4.3b	(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
5.8b	(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
7.1b	(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
17.6b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite17.5s

Algorithm

rewrite-expression-head

Rules

1007×	`add-exp-log`
775×	`prod-exp`
322×	`pow-exp`
171×	`div-exp`
111×	`pow-to-exp`
40×	`rec-exp` `1-exp`
34×	`associate-r`
32×	`add-cbrt-cube`
25×	`pow1`
22×	`add-sqr-sqrt` `unpow-prod-down` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`cbrt-unprod`
18×	`times-frac`
13×	`pow-prod-down`
9×	`cbrt-prod`
6×	`associate-*r/`
4×	`sqrt-pow1` `associate-*l/` `add-log-exp`
3×	`associate-l` `*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `flip-+`
1×	`flip3--` `pow1/2` `sqrt-prod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 305

Calls

4 calls:

59.0ms	(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
760.0ms	(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
8.8s	(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
7.9s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series24.7s

Counts

4 → 12

Calls

4 calls:

535.0ms	(* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2)))
1.3s	(* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
2.7s	(* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
20.2s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (* (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) n) (pow (/ l (cbrt Om)) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify666.0ms

Counts

317 → 317

Iterations

Iter	Nodes
done	5000
1	1668
0	551

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 20.7b

localize156.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U))
7.4b	(* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))))
7.4b	(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
17.6b	(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

1630×	`add-exp-log`
1247×	`prod-exp`
558×	`pow-exp`
296×	`div-exp`
194×	`pow-to-exp`
68×	`rec-exp` `1-exp`
46×	`add-cbrt-cube`
36×	`pow1`
29×	`cbrt-unprod`
22×	`associate-*r/`
20×	`pow-prod-down`
12×	`associate-*l/`
11×	`flip3--` `flip--`
8×	`frac-sub`
7×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
6×	`sqrt-div`
5×	`sqrt-pow1` `add-cube-cbrt`
4×	`add-log-exp`
3×	`associate-l` `*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 431

Calls

4 calls:

368.0ms	(* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U))
116.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))))
1.4s	(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
1.4s	(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))

series37.5s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U))
672.0ms	(* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2))))
2.5s	(* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U))
33.2s	(sqrt (* (* 2.0 n) (* (- (* (* (* (pow (/ l Om) (/ 2.0 2)) (pow (/ l (cbrt Om)) (/ 2.0 2))) (* n (pow (/ 1 (* (cbrt Om) (cbrt Om))) (/ 2.0 2)))) (- U* U)) (- (* (/ l Om) (* l 2.0)) t)) U)))

simplify1.0s

Counts

443 → 443

Iterations

Iter	Nodes
done	5001
1	1736
0	504

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 19.0b

regimes1.6s

Accuracy

30.6% (8.6b remaining)

Error of 27.0b against oracle of 18.5b and baseline of 30.8b

bsearch479.0ms

Steps

Iters	Range		Point
9	2.4256268370447587e-303	5.292323950905223e-294	2.469810196486197e-303
7	-5.769464553509918e-44	-4.636171290286106e-46	-7.411448247083684e-46

simplify11.0ms

Iterations

Iter	Nodes
done	75
2	75
1	74
0	54

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.7s	14813×	body	80	nan
2.4s	9174×	body	80	valid