Details

sample245.0ms

Algorithm

intervals

Results

109.0ms	491×	body	80	nan
44.0ms	296×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize55.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
5.4b	(* (* n (pow (/ l Om) 2.0)) (- U* U))
6.0b	(* n (pow (/ l Om) 2.0))
22.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.0s

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:

478.0ms	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
54.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
34.0ms	(* n (pow (/ l Om) 2.0))
465.0ms	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series17.8s

Counts

4 → 12

Calls

4 calls:

1.8s	(* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
566.0ms	(* (* n (pow (/ l Om) 2.0)) (- U* U))
217.0ms	(* n (pow (/ l Om) 2.0))
15.2s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	4120
1	713
0	260

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.1b

localize61.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
5.4b	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.3b	(* (pow (/ l Om) (/ 2.0 2)) n)
22.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`add-sqr-sqrt` `pow1`
24×	`add-cbrt-cube`
20×	`pow-exp`
19×	`associate-l`
17×	`*-un-lft-identity`
15×	`unpow-prod-down` `add-cube-cbrt`
13×	`pow-prod-down` `cbrt-unprod`
11×	`associate-r`
10×	`pow-to-exp` `times-frac` `div-exp`
6×	`associate-*r/`
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:

1.8s	(* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
209.0ms	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U))
43.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
1.9s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series18.4s

Counts

4 → 12

Calls

4 calls:

1.7s	(* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
688.0ms	(* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U))
421.0ms	(* (pow (/ l Om) (/ 2.0 2)) n)
15.6s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* (pow (/ l Om) (/ 2.0 2)) n) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify2.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	4623
1	795
0	288

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.4b

localize61.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
5.4b	(* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
6.3b	(* n (* l (pow (/ 1 (pow Om 1.0)) 1.0)))
22.2b	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite17.2s

Algorithm

rewrite-expression-head

Rules

316×	`add-exp-log`
244×	`prod-exp`
93×	`pow-exp`
44×	`div-exp`
34×	`pow-to-exp`
32×	`add-cbrt-cube`
27×	`pow1`
19×	`cbrt-unprod`
15×	`rec-exp` `1-exp`
14×	`pow-prod-down`
9×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
7×	`add-cube-cbrt`
6×	`associate-*r/`
5×	`associate-l`
4×	`sqrt-pow1` `associate-*l/` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `flip-+`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 148

Calls

4 calls:

8.3s	(* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
740.0ms	(* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
62.0ms	(* n (* l (pow (/ 1 (pow Om 1.0)) 1.0)))
8.1s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

series24.4s

Counts

4 → 12

Calls

4 calls:

2.4s	(* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U)
783.0ms	(* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U))
264.0ms	(* n (* l (pow (/ 1 (pow Om 1.0)) 1.0)))
21.0s	(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (* l (pow (/ 1 (pow Om 1.0)) 1.0))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

simplify525.0ms

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
1	946
0	323

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 23.2b

localize81.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
7.1b	(* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U))))
8.4b	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
22.2b	(sqrt (* (* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U)))) (cbrt U)))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log`
53×	`prod-exp`
49×	`unpow-prod-down`
48×	`pow1`
39×	`add-sqr-sqrt`
35×	`associate-r`
33×	`*-un-lft-identity`
32×	`pow-prod-down`
31×	`times-frac`
29×	`add-cube-cbrt`
28×	`pow-exp`
25×	`add-cbrt-cube`
22×	`associate-l`
17×	`cbrt-unprod`
13×	`div-exp`
9×	`pow-to-exp`
7×	`sqrt-pow1`
6×	`rec-exp` `1-exp` `associate-*l/` `sqr-pow`
4×	`add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `div-inv`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

55.0ms	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
1.5s	(* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U))))
39.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
1.6s	(sqrt (* (* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U)))) (cbrt U)))

series12.5s

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0))
4.3s	(* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U))))
488.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U* U))
7.4s	(sqrt (* (* (+ t (- (* (* (* n l) (pow (/ 1 (pow Om 1.0)) 1.0)) (* (pow (/ l Om) (/ 2.0 2)) (- U* U))) (* (* (/ l Om) 2.0) l))) (* (* 2.0 n) (* (cbrt U) (cbrt U)))) (cbrt U)))

simplify709.0ms

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
1	1112
0	414

prune1.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 23.1b

regimes1.3s

Accuracy

35.5% (6.4b remaining)

Error of 28.0b against oracle of 21.6b and baseline of 31.5b

bsearch239.0ms

Steps

Iters	Range		Point
8	-3.4521554473820974e-305	4.410426703043699e-308	1.1147771080838e-310

simplify23.0ms

Iterations

Iter	Nodes
done	83
2	83
1	82
0	60

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.1s	15067×	body	80	nan
1.9s	9223×	body	80	valid