Details

sample226.0ms

Algorithm

intervals

Results

118.0ms	448×	body	80	nan
63.0ms	290×	body	80	valid

simplify921.0ms

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: 30.0b

localize43.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (* n (pow (/ l Om) 2)) (- U U*))
7.1b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
7.6b	(/ (* l l) Om)
19.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite216.0ms

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:

28.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
102.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
9.0ms	(/ (* l l) Om)
74.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
470.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
28.0ms	(/ (* l l) Om)
1.4s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

simplify1.1s

Counts

157 → 157

Iterations

Iter	Nodes
done	2002
2	2002
1	1161
0	376

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize55.0ms

Local error

Found 4 expressions with local error:

5.5b	(* n (pow (/ l Om) 2))
6.1b	(* (* n (pow (/ l Om) 2)) (- U U*))
7.1b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
19.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

rewrite321.0ms

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:

21.0ms	(* n (pow (/ l Om) 2))
40.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
161.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))
95.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

53.0ms	(* n (pow (/ l Om) 2))
124.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
524.0ms	(* (* (* 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*)))))

simplify1.4s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	1216
0	406

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.5b

localize66.0ms

Local error

Found 4 expressions with local error:

4.3b	(* n (/ l Om))
6.1b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
7.1b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
19.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite412.0ms

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:

9.0ms	(* n (/ l Om))
97.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
163.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
139.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

23.0ms	(* n (/ l Om))
166.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
587.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))
1.7s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

simplify1.6s

Counts

222 → 222

Iterations

Iter	Nodes
done	2000
2	2000
1	1637
0	530

prune4.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.4b

localize38.0ms

Local error

Found 4 expressions with local error:

4.3b	(* n (/ l Om))
6.9b	(* (/ l Om) (- U U*))
7.1b	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
19.3b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

rewrite462.0ms

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:

16.0ms	(* n (/ l Om))
36.0ms	(* (/ l Om) (- U U*))
237.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
165.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* n (/ l Om))
78.0ms	(* (/ l Om) (- U U*))
584.0ms	(* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))
1.7s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

simplify1.7s

Counts

218 → 218

Iterations

Iter	Nodes
done	2009
2	2009
1	1603
0	526

prune3.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.2b

regimes1.2s

Accuracy

17% (7.7b remaining)

Error of 27.8b against oracle of 20.1b and baseline of 29.3b

bsearch405.0ms

Steps

Iters	Range		Point
7	3.361105384241476e+87	8.317112121772259e+88	6.690071193692508e+87
7	-2.719704927392792e-162	-1.6899825801825173e-164	-2.277408299947311e-162

simplify12.0ms

Iterations

Iter	Nodes
done	51
1	51
0	38

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.1s	14973×	body	80	nan
2.8s	9258×	body	80	valid