Details

sample861.0ms

Algorithm

intervals

Results

244.0ms	79×	body	2560	valid
192.0ms	29×	body	5120	valid
169.0ms	113×	body	1280	valid
121.0ms	81×	body	640	valid
77.0ms	32×	body	320	valid
12.0ms	61×	body	80	valid
7.0ms	17×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5174
4	3622
3	689
2	142
1	44
0	19

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (pow t 3.0))
0.8b	(* (pow (/ k t) 2.0) (tan k))
20.6b	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
29.5b	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

410×	`add-exp-log`
181×	`div-exp`
173×	`prod-exp`
144×	`times-frac`
89×	`add-cbrt-cube`
80×	`add-sqr-sqrt`
72×	`*-un-lft-identity` `add-cube-cbrt`
55×	`pow-exp`
54×	`unpow-prod-down`
47×	`associate-l`
38×	`pow-to-exp`
34×	`cbrt-unprod`
30×	`cbrt-undiv`
28×	`associate-/l*`
15×	`sqr-pow`
9×	`pow1`
8×	`associate-/r*`
7×	`div-inv`
4×	`associate-r` `associate-*r/` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `tan-quot`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`
1×	`frac-times` `associate-/l/`

Counts

4 → 292

Calls

4 calls:

12.0ms	(/ 2.0 (pow t 3.0))
47.0ms	(* (pow (/ k t) 2.0) (tan k))
147.0ms	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
31.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

series2.4s

Counts

4 → 12

Calls

4 calls:

530.0ms	(/ 2.0 (pow t 3.0))
315.0ms	(* (pow (/ k t) 2.0) (tan k))
1.1s	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
489.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

simplify1.9s

Counts

304 → 304

Iterations

Iter	Nodes
done	5000
1	1212
0	433

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.6b	(* (pow t 1.0) (pow k 2.0))
17.5b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

1239×	`add-exp-log`
740×	`prod-exp`
455×	`div-exp`
318×	`pow-exp`
138×	`pow-to-exp`
85×	`add-cbrt-cube`
70×	`rec-exp` `1-exp`
32×	`cbrt-unprod`
29×	`cbrt-undiv`
26×	`add-sqr-sqrt`
17×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`unpow-prod-down`
9×	`times-frac` `unswap-sqr`
8×	`associate-r` `sqr-pow`
7×	`pow1`
6×	`associate-/r/` `associate-/l*`
4×	`add-log-exp`
3×	`associate-*l/` `div-inv`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-r/` `*-commutative`
1×	`pow-prod-down` `pow-flip` `inv-pow`

Counts

4 → 359

Calls

4 calls:

30.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
24.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
15.0ms	(* (pow t 1.0) (pow k 2.0))
132.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
495.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
523.0ms	(* (pow t 1.0) (pow k 2.0))
574.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

simplify7.5s

Counts

371 → 371

Iterations

Iter	Nodes
done	5002
2	3679
1	1252
0	432

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
4.0b	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
5.6b	(* (pow t 1.0) (pow k 2.0))
7.5b	(* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

1014×	`add-exp-log`
716×	`prod-exp`
269×	`pow-exp`
260×	`div-exp`
119×	`pow-to-exp`
70×	`add-cbrt-cube`
60×	`rec-exp` `1-exp`
35×	`cbrt-unprod`
25×	`add-sqr-sqrt`
18×	`associate-l`
14×	`cbrt-undiv`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1` `unpow-prod-down`
9×	`associate-r` `unswap-sqr`
8×	`sqr-pow`
6×	`times-frac`
4×	`pow-prod-down` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`associate-*l/` `div-inv`
1×	`clear-num` `associate-/r*` `frac-2neg` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 313

Calls

4 calls:

27.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
235.0ms	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
23.0ms	(* (pow t 1.0) (pow k 2.0))
52.0ms	(* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

519.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
675.0ms	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
488.0ms	(* (pow t 1.0) (pow k 2.0))
313.0ms	(* l (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

simplify8.5s

Counts

325 → 325

Iterations

Iter	Nodes
done	5002
2	3221
1	1069
0	405

prune977.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos k) (* (/ (sin k) l) (sin k)))
0.4b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
4.0b	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
7.5b	(* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

rewrite692.0ms

Algorithm

rewrite-expression-head

Rules

3243×	`add-exp-log`
2581×	`prod-exp`
974×	`pow-exp`
768×	`div-exp`
509×	`pow-to-exp`
186×	`rec-exp` `1-exp`
81×	`add-cbrt-cube`
38×	`cbrt-unprod`
19×	`cbrt-undiv`
12×	`pow1`
11×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
9×	`times-frac`
6×	`associate-/l*`
4×	`pow-prod-down` `add-log-exp`
3×	`associate-*l/` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `associate-/r/` `-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 675

Calls

4 calls:

21.0ms	(/ (cos k) (* (/ (sin k) l) (sin k)))
81.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
349.0ms	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
116.0ms	(* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (cos k) (* (/ (sin k) l) (sin k)))
503.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
565.0ms	(* (/ (cos k) (* (/ (sin k) l) (sin k))) (* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
279.0ms	(* l (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

simplify7.6s

Counts

687 → 687

Iterations

Iter	Nodes
done	5257
2	4193
1	1519
0	524

prune835.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.1b

regimes823.0ms

Accuracy

0% (2.0b remaining)

Error of 10.7b against oracle of 8.7b and baseline of 10.7b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample31.5s

Algorithm

intervals

Results

8.9s	3998×	body	1280	valid
8.6s	2259×	body	2560	valid
7.8s	926×	body	5120	valid
3.1s	2541×	body	640	valid
965.0ms	2068×	body	80	valid
811.0ms	1034×	body	320	valid
296.0ms	421×	body	160	valid