Details

sample205.0ms

Algorithm

intervals

Results

96.0ms	470×	body	80	nan
51.0ms	291×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	693
2	157
1	50
0	21

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize48.0ms

Local error

Found 4 expressions with local error:

7.4b	(/ (* l l) Om)
7.8b	(* (* n (pow (/ l Om) 2)) (- U U*))
10.7b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
18.9b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite282.0ms

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:

15.0ms	(/ (* l l) Om)
39.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
138.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
85.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* l l) Om)
115.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
471.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.4s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	2000
2	2000
1	1172
0	376

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.7b

localize51.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) 2))
7.8b	(* (* n (pow (/ l Om) 2)) (- U U*))
10.7b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
18.9b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite306.0ms

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:

13.0ms	(* n (pow (/ l Om) 2))
29.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
147.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
114.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

56.0ms	(* n (pow (/ l Om) 2))
138.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
565.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.2s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	1216
0	406

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 20.2b

localize74.0ms

Local error

Found 4 expressions with local error:

6.5b	(* n (/ l Om))
7.8b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
10.7b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
18.9b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite350.0ms

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:

10.0ms	(* n (/ l Om))
89.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
139.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
107.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

25.0ms	(* n (/ l Om))
130.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
462.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.6s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify2.0s

Counts

222 → 222

Iterations

Iter	Nodes
done	2000
2	2000
1	1637
0	530

prune2.0s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 17.6b

localize46.0ms

Local error

Found 4 expressions with local error:

6.0b	(* (/ l Om) (- U U*))
6.5b	(* n (/ l Om))
10.7b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
18.9b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

111×	`associate-*r/`
49×	`add-sqr-sqrt`
44×	`frac-sub`
42×	`flip3--` `flip--`
39×	`*-un-lft-identity`
38×	`frac-times`
37×	`add-cube-cbrt`
30×	`prod-diff`
27×	`pow1`
24×	`sqrt-div`
23×	`add-cbrt-cube` `add-exp-log`
21×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
20×	`times-frac`
17×	`associate-l`
14×	`pow-prod-down`
13×	`associate-*l/`
10×	`prod-exp` `associate--l+` `cbrt-unprod`
6×	`sub-neg`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`cbrt-undiv` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

28.0ms	(* (/ l Om) (- U U*))
17.0ms	(* n (/ l Om))
226.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
118.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (/ l Om) (- U U*))
21.0ms	(* n (/ l Om))
536.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
1.8s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

simplify1.8s

Counts

218 → 218

Iterations

Iter	Nodes
done	2006
2	2006
1	1599
0	526

prune2.0s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 17.3b

regimes1.9s

Accuracy

4.2% (9.5b remaining)

Error of 29.1b against oracle of 19.6b and baseline of 29.5b

bsearch445.0ms

Steps

Iters	Range		Point
2	4.524631729034864e-46	5.261133834597946e-46	5.16907107140256e-46
6	1.395635143726827e-182	5.762617986989897e-182	1.5047052485579951e-182
8	2.5343482852449933e-258	2.0248104990010824e-254	1.8088620139970252e-254

simplify24.0ms

Iterations

Iter	Nodes
done	54
1	54
0	40

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.8s	14938×	body	80	nan
2.8s	9232×	body	80	valid