Details

sample406.0ms

Algorithm

intervals

Results

175.0ms	491×	body	80	nan
82.0ms	301×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
4	2775
3	598
2	153
1	50
0	21

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize68.0ms

Local error

Found 4 expressions with local error:

6.3b	(* (- U* U) (/ l (/ Om n)))
7.8b	(/ l (/ Om n))
11.1b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
18.0b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 194

Calls

4 calls:

25.0ms	(* (- U* U) (/ l (/ Om n)))
11.0ms	(/ l (/ Om n))
67.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
34.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (- U* U) (/ l (/ Om n)))
27.0ms	(/ l (/ Om n))
585.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
2.3s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

simplify1.7s

Counts

206 → 206

Iterations

Iter	Nodes
2	4482
1	1059
0	373

prune4.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.7b

localize76.0ms

Local error

Found 4 expressions with local error:

5.0b	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
6.3b	(* (- U* U) (/ l (/ Om n)))
7.8b	(/ l (/ Om n))
18.0b	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 189

Calls

4 calls:

23.0ms	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
25.0ms	(* (- U* U) (/ l (/ Om n)))
9.0ms	(/ l (/ Om n))
55.0ms	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

486.0ms	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
120.0ms	(* (- U* U) (/ l (/ Om n)))
22.0ms	(/ l (/ Om n))
2.4s	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

simplify2.0s

Counts

201 → 201

Iterations

Iter	Nodes
2	4254
1	1001
0	362

prune3.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.1b

localize95.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om))))
4.8b	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n))))))))))
5.0b	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))
18.0b	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
41×	`add-cbrt-cube`
34×	`prod-exp` `cbrt-unprod`
33×	`pow1`
32×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-*r/`
18×	`pow-prod-down`
12×	`cbrt-undiv` `sub-neg` `div-exp`
11×	`associate-l`
10×	`add-sqr-sqrt`
9×	`frac-times` `*-un-lft-identity`
7×	`flip3--` `add-cube-cbrt` `flip--`
5×	`associate-*l/`
4×	`sqrt-pow1` `insert-posit16` `add-log-exp`
3×	`associate-r` `*-commutative`
2×	`sqrt-div`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

106.0ms	(* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om))))
76.0ms	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n))))))))))
29.0ms	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))
55.0ms	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))))

series4.2s

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om))))
652.0ms	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n))))))))))
1.0s	(* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))
2.2s	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))))

simplify2.6s

Counts

146 → 146

Iterations

Iter	Nodes
2	3610
1	909
0	337

prune3.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 16.3b

localize74.0ms

Local error

Found 4 expressions with local error:

7.8b	(/ l (/ Om n))
7.8b	(/ l (/ Om n))
18.0b	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
18.0b	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/r*`
24×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `associate-*r/`
10×	`div-inv`
8×	`sqrt-pow1`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3--` `pow1/2` `associate-/r/` `sqrt-prod` `flip--`

Counts

4 → 174

Calls

4 calls:

12.0ms	(/ l (/ Om n))
12.0ms	(/ l (/ Om n))
59.0ms	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
66.0ms	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

series4.4s

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ l (/ Om n))
30.0ms	(/ l (/ Om n))
2.1s	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
2.3s	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

simplify2.8s

Counts

186 → 186

Iterations

Iter	Nodes
3	6935
2	1731
1	540
0	218

prune4.5s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 16.3b

regimes1.3s

Accuracy

23.5% (8.6b remaining)

Error of 27.1b against oracle of 18.5b and baseline of 29.7b

bsearch193.0ms

Steps

Iters	Range		Point
7	8.292854244148947e-258	1.948321498797613e-255	8.515544881339301e-258

simplify44.0ms

Iterations

Iter	Nodes
2	55
1	55
0	43

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.0s	14839×	body	80	nan
2.8s	9128×	body	80	valid