Details

sample362.0ms

Algorithm

intervals

Results

127.0ms	304×	body	80	valid
114.0ms	428×	body	80	nan

simplify1.2s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize44.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (- U* U) (/ l (/ Om n)))
5.6b	(/ l (/ Om n))
9.8b	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
20.0b	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

rewrite123.0ms

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:

23.0ms	(* (- U* U) (/ l (/ Om n)))
6.0ms	(/ l (/ Om n))
45.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
43.0ms	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

series2.8s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- U* U) (/ l (/ Om n)))
38.0ms	(/ l (/ Om n))
554.0ms	(* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))
2.1s	(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

simplify1.8s

Counts

206 → 206

Iterations

Iter	Nodes
2	4482
1	1059
0	373

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.7b

localize69.0ms

Local error

Found 4 expressions with local error:

4.8b	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
5.1b	(* (- U* U) (/ l (/ Om n)))
5.6b	(/ l (/ Om n))
20.0b	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
94×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
83×	`add-cube-cbrt`
45×	`associate-r`
27×	`add-cbrt-cube` `add-exp-log`
25×	`pow1`
24×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/r` `pow-prod-down` `associate-r/`
9×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`sub-neg` `associate-l`
6×	`cbrt-undiv` `div-exp`
4×	`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 → 200

Calls

4 calls:

107.0ms	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
28.0ms	(* (- U* U) (/ l (/ Om n)))
6.0ms	(/ l (/ Om n))
39.0ms	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

506.0ms	(* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
96.0ms	(* (- U* U) (/ l (/ Om n)))
34.0ms	(/ l (/ Om n))
2.0s	(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

simplify3.5s

Counts

212 → 212

Iterations

Iter	Nodes
2	4813
1	1083
0	392

prune1.7s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.6b

localize86.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))
7.2b	(/ n (/ Om l))
7.2b	(/ n (/ Om l))
20.0b	(sqrt (+ (* U (* (* t 2) n)) (* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
90×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
46×	`add-cbrt-cube` `add-exp-log`
26×	`associate-/r*`
18×	`prod-exp` `cbrt-unprod`
17×	`pow1`
12×	`cbrt-undiv` `div-exp`
10×	`div-inv`
8×	`pow-prod-down`
6×	`associate-l/` `associate-/l`
4×	`insert-posit16` `distribute-neg-frac` `add-log-exp`
3×	`sqrt-prod`
2×	`frac-times` `clear-num` `frac-2neg` `flip3--` `sqrt-div` `associate-*r/` `associate-/r/` `flip--`
1×	`distribute-lft-neg-out` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `associate-l` `*-commutative` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 195

Calls

4 calls:

125.0ms	(* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))
7.0ms	(/ n (/ Om l))
6.0ms	(/ n (/ Om l))
85.0ms	(sqrt (+ (* U (* (* t 2) n)) (* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))))

series3.5s

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))
28.0ms	(/ n (/ Om l))
34.0ms	(/ n (/ Om l))
3.2s	(sqrt (+ (* U (* (* t 2) n)) (* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))))

simplify2.1s

Counts

207 → 207

Iterations

Iter	Nodes
2	3509
1	841
0	301

prune1.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.9b

localize68.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (- U* U) (/ n (/ Om l)))
7.2b	(/ n (/ Om l))
7.2b	(/ n (/ Om l))
20.0b	(sqrt (+ (* U (* (* t 2) n)) (* (/ n (/ Om l)) (* (- (- (* l 2) (* (- U* U) (/ n (/ Om l))))) (* 2 U)))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

219×	`times-frac`
137×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
125×	`add-cube-cbrt`
44×	`associate-r`
26×	`associate-/r*`
23×	`add-cbrt-cube` `add-exp-log`
14×	`div-inv`
9×	`cbrt-undiv` `div-exp`
7×	`pow1`
6×	`associate-/l*`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`prod-exp` `associate-/r/` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `clear-num` `frac-2neg` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 231

Calls

4 calls:

36.0ms	(* (- U* U) (/ n (/ Om l)))
11.0ms	(/ n (/ Om l))
11.0ms	(/ n (/ Om l))
91.0ms	(sqrt (+ (* U (* (* t 2) n)) (* (/ n (/ Om l)) (* (- (- (* l 2) (* (- U* U) (/ n (/ Om l))))) (* 2 U)))))

series3.4s

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (- U* U) (/ n (/ Om l)))
26.0ms	(/ n (/ Om l))
25.0ms	(/ n (/ Om l))
3.2s	(sqrt (+ (* U (* (* t 2) n)) (* (/ n (/ Om l)) (* (- (- (* l 2) (* (- U* U) (/ n (/ Om l))))) (* 2 U)))))

simplify2.9s

Counts

243 → 243

Iterations

Iter	Nodes
2	3836
1	832
0	304

prune2.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 14.9b

regimes1.8s

Accuracy

20.5% (11.2b remaining)

Error of 24.6b against oracle of 13.4b and baseline of 27.5b

bsearch138.0ms

Steps

Iters	Range		Point
7	-1.1161865709419737e-308	1.6416820990279393e-306	1.4828608859501e-310

simplify31.0ms

Iterations

Iter	Nodes
5	82
4	82
3	80
2	69
1	61
0	45

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.5s	14975×	body	80	nan
2.5s	9155×	body	80	valid