Details

sample208.0ms

Algorithm

intervals

Results

91.0ms	481×	body	80	nan
76.0ms	303×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3618
3	693
2	157
1	50
0	21

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize41.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* n (pow (/ l Om) 2)) (- U U*))
6.5b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
6.7b	(/ (* l l) Om)
19.2b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

45.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
116.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
9.0ms	(/ (* l l) Om)
87.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
569.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
34.0ms	(/ (* l l) Om)
1.5s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify2.6s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	4623
1	1161
0	376

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 17.7b

localize88.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2))
5.6b	(* (* n (pow (/ l Om) 2)) (- U U*))
6.5b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
19.2b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
26×	`associate-r`
25×	`pow1`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `unpow2` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2))
60.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
198.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
99.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

85.0ms	(* n (pow (/ l Om) 2))
171.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
498.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify3.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	4362
1	1216
0	407

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.5b

localize50.0ms

Local error

Found 4 expressions with local error:

3.5b	(* n (/ l Om))
5.6b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
6.5b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
19.2b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

104×	`associate-*r/`
47×	`add-cbrt-cube` `add-exp-log`
45×	`frac-times`
44×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
34×	`pow1`
32×	`*-un-lft-identity`
30×	`prod-diff` `associate-*l/` `add-cube-cbrt`
25×	`prod-exp` `cbrt-unprod`
24×	`sqrt-div`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
19×	`pow-prod-down`
10×	`times-frac` `associate--l+`
6×	`cbrt-undiv` `sub-neg` `div-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

18.0ms	(* n (/ l Om))
137.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
180.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
122.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.8s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* n (/ l Om))
156.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
954.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.7s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify2.1s

Counts

222 → 222

Iterations

Iter	Nodes
done	5000
1	1642
0	531

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.5b

localize107.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
6.5b	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
19.2b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
19.2b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite680.0ms

Algorithm

rewrite-expression-head

Rules

184×	`associate-*r/`
88×	`frac-sub`
80×	`flip3--` `flip--`
72×	`frac-times`
48×	`sqrt-div` `associate-*l/`
42×	`pow1`
24×	`prod-diff` `pow-prod-down`
22×	`add-cbrt-cube` `add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`prod-exp` `cbrt-unprod`
8×	`sub-neg` `sqrt-pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `associate-l` `*-commutative` `sqrt-prod`

Counts

4 → 216

Calls

4 calls:

188.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
154.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
179.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
153.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series4.7s

Counts

4 → 12

Calls

4 calls:

666.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
552.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.8s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify1.9s

Counts

228 → 228

Iterations

Iter	Nodes
done	5001
1	1138
0	359

prune3.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.5b

regimes1.5s

Accuracy

3.2% (10.4b remaining)

Error of 30.2b against oracle of 19.8b and baseline of 30.5b

bsearch509.0ms

Steps

Iters	Range		Point
7	-1.874519602334236e-263	-8.022724786538369e-265	-2.81317660591196e-264
10	-3.926724493829904e-97	-1.6388301196789607e-107	-8.997037644090019e-101

simplify12.0ms

Iterations

Iter	Nodes
done	58
1	58
0	43

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.3s	15269×	body	80	nan
2.8s	9207×	body	80	valid