Details

sample159.0ms

Algorithm

intervals

Results

65.0ms	403×	body	80	nan
40.0ms	295×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.0b

localize42.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
6.0b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
6.7b	(* n (pow (/ l Om) 2.0))
17.7b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite847.0ms

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))
392.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
36.0ms	(* n (pow (/ l Om) 2.0))
343.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series16.0s

Counts

4 → 12

Calls

4 calls:

580.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
1.4s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
200.0ms	(* n (pow (/ l Om) 2.0))
13.8s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify3.2s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	4130
1	715
0	260

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.7b

localize60.0ms

Local error

Found 4 expressions with local error:

4.0b	(* n (pow (/ l Om) (/ 2.0 2)))
5.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.0b	(* (* (* 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)
17.7b	(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:

38.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
185.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
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))

series17.6s

Counts

4 → 12

Calls

4 calls:

248.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
533.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
1.6s	(* (* (* 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)
15.2s	(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))

simplify3.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	4571
1	828
0	295

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.0b

localize103.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* (* 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)
6.0b	(* (* (* 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)
17.7b	(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))
17.7b	(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))

rewrite6.9s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.8s	(* (* (* 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)
1.8s	(* (* (* 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)
1.7s	(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))
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))

series32.6s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (* (* 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	(* (* (* 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)
14.6s	(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))
14.9s	(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))

simplify2.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
2	2366
1	380
0	130

prune994.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 20.0b

localize84.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) (* (cbrt U) (cbrt U)))
4.0b	(* n (pow (/ l Om) (/ 2.0 2)))
5.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
17.7b	(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))))) (* (cbrt U) (cbrt U))) (cbrt U)))

rewrite8.2s

Algorithm

rewrite-expression-head

Rules

111×	`add-exp-log`
76×	`prod-exp`
57×	`pow1`
38×	`pow-prod-down`
30×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-r`
22×	`cbrt-unprod`
20×	`pow-exp`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`sqrt-pow1`
6×	`associate-l/` `associate-r/`
5×	`associate-l`
4×	`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 → 131

Calls

4 calls:

1.6s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) (* (cbrt U) (cbrt U)))
35.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
167.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.4s	(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))))) (* (cbrt U) (cbrt U))) (cbrt U)))

series21.3s

Counts

4 → 12

Calls

4 calls:

2.8s	(* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) (* (cbrt U) (cbrt U)))
240.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
493.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
17.8s	(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))))) (* (cbrt U) (cbrt U))) (cbrt U)))

simplify3.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	4839
1	934
0	323

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 20.0b

regimes2.3s

Accuracy

36.2% (6.1b remaining)

Error of 27.2b against oracle of 21.1b and baseline of 30.6b

bsearch342.0ms

Steps

Iters	Range		Point
4	9.972512795869245e-208	1.552997766212762e-207	1.188289134364556e-207
8	-8.847328721651057e-54	-2.558814542246615e-56	-8.761276549602834e-54

simplify28.0ms

Iterations

Iter	Nodes
done	74
1	74
0	51

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.0s	14786×	body	80	nan
1.9s	9202×	body	80	valid