Details

sample196.0ms

Algorithm

intervals

Results

101.0ms	459×	body	80	nan
56.0ms	306×	body	80	valid

simplify791.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2837
3	602
2	155
1	50
0	21

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.5b

localize40.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (/ n (/ Om l)) (- U* U))
6.9b	(/ n (/ Om l))
10.6b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
21.3b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
93×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
82×	`add-cube-cbrt`
45×	`associate-l`
31×	`pow1`
30×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
13×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
9×	`div-inv`
6×	`cbrt-undiv` `sub-neg` `div-exp` `associate-r`
5×	`sqrt-pow1`
4×	`flip3--` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`frac-times` `sqrt-div` `associate-/r/` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 198

Calls

4 calls:

22.0ms	(* (/ n (/ Om l)) (- U* U))
6.0ms	(/ n (/ Om l))
35.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
21.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (/ n (/ Om l)) (- U* U))
37.0ms	(/ n (/ Om l))
527.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
1.9s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

simplify980.0ms

Counts

210 → 210

Iterations

Iter	Nodes
2	3989
1	1053
0	377

prune3.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.7b

localize52.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (/ 1 (/ (/ Om l) n)) (- U* U))
6.7b	(/ (/ Om l) n)
10.6b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U)))))))
21.3b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U))))))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

414×	`times-frac`
221×	`add-sqr-sqrt`
201×	`*-un-lft-identity`
196×	`add-cube-cbrt`
135×	`associate-l`
53×	`add-exp-log`
35×	`add-cbrt-cube`
31×	`pow1`
18×	`div-exp` `prod-exp` `div-inv`
17×	`pow-prod-down`
13×	`associate-/l*`
12×	`cbrt-unprod`
10×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
9×	`cbrt-undiv`
7×	`unswap-sqr`
6×	`sub-neg` `associate-r`
5×	`sqrt-pow1`
4×	`flip3--` `insert-posit16` `flip--` `add-log-exp`
3×	`rec-exp` `associate-/r*` `1-exp`
2×	`frac-times` `sqrt-div` `*-commutative`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*l/` `associate-/r/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 300

Calls

4 calls:

36.0ms	(* (/ 1 (/ (/ Om l) n)) (- U* U))
7.0ms	(/ (/ Om l) n)
39.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U)))))))
33.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ 1 (/ (/ Om l) n)) (- U* U))
20.0ms	(/ (/ Om l) n)
422.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U)))))))
2.1s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ 1 (/ (/ Om l) n)) (- U* U))))))))

simplify1.6s

Counts

312 → 312

Iterations

Iter	Nodes
2	4648
1	1731
0	609

prune4.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 22.3b

localize54.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (/ Om l))
14.1b	(cbrt (/ Om l))
14.1b	(cbrt (/ Om l))
21.3b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ (/ n (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (cbrt (/ Om l))) (- U* U))))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`pow1`
8×	`pow-prod-down`
5×	`sqrt-pow1`
4×	`add-cbrt-cube` `associate-*r/` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-div`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--`

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt (/ Om l))
1.0ms	(cbrt (/ Om l))
1.0ms	(cbrt (/ Om l))
21.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ (/ n (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (cbrt (/ Om l))) (- U* U))))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (/ Om l))
76.0ms	(cbrt (/ Om l))
94.0ms	(cbrt (/ Om l))
1.8s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ (/ n (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (cbrt (/ Om l))) (- U* U))))))))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
3	3974
2	901
1	297
0	146

prune1.8s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 22.3b

localize49.0ms

Local error

Found 4 expressions with local error:

10.6b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
10.6b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
21.3b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
21.3b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

54×	`pow1`
32×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate-*r/` `cbrt-unprod`
10×	`sqrt-pow1`
8×	`sub-neg`
4×	`add-sqr-sqrt` `*-un-lft-identity` `flip3--` `sqrt-div` `add-cube-cbrt` `insert-posit16` `flip--` `add-log-exp`
2×	`pow1/2` `associate-r` `associate-l` `*-commutative` `sqrt-prod`

Counts

4 → 100

Calls

4 calls:

43.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
40.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
32.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
27.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

series5.4s

Counts

4 → 12

Calls

4 calls:

583.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
567.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U)))))))
2.2s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))
2.1s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (/ n (/ Om l)) (- U* U))))))))

simplify5.0s

Counts

112 → 112

Iterations

Iter	Nodes
3	10389
2	1662
1	408
0	142

prune2.9s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.3b

regimes1.8s

Accuracy

13% (7.9b remaining)

Error of 27.9b against oracle of 20.0b and baseline of 29.1b

bsearch147.0ms

Steps

Iters	Range		Point
5	5.0357833129844e+45	1.1642262788994253e+46	1.141827696680125e+46

simplify7.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample8.8s

Algorithm

intervals

Results

4.9s	15504×	body	80	nan
2.4s	9237×	body	80	valid