Details

sample868.0ms

Algorithm

intervals

Results

276.0ms	128×	body	1280	valid
232.0ms	35×	body	5120	valid
203.0ms	74×	body	2560	valid
70.0ms	68×	body	640	valid
27.0ms	40×	body	320	valid
15.0ms	71×	body	80	valid
10.0ms	20×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (pow t 3.0))
0.4b	(* (pow (/ k t) 2.0) (tan k))
17.9b	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
29.4b	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

rewrite170.0ms

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:

6.0ms	(/ 2.0 (pow t 3.0))
38.0ms	(* (pow (/ k t) 2.0) (tan k))
82.0ms	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
23.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

series2.2s

Counts

4 → 12

Calls

4 calls:

572.0ms	(/ 2.0 (pow t 3.0))
269.0ms	(* (pow (/ k t) 2.0) (tan k))
921.0ms	(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
476.0ms	(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

simplify1.8s

Counts

304 → 304

Iterations

Iter	Nodes
done	5000
1	1212
0	433

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
0.7b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
6.2b	(* (pow t 1.0) (pow k 2.0))
15.0b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

rewrite193.0ms

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:

17.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
23.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
24.0ms	(* (pow t 1.0) (pow k 2.0))
96.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

451.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
127.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
444.0ms	(* (pow t 1.0) (pow k 2.0))
521.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))

simplify7.6s

Counts

371 → 371

Iterations

Iter	Nodes
done	5004
2	3675
1	1252
0	432

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
3.5b	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
5.3b	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))
6.2b	(* (pow t 1.0) (pow k 2.0))

rewrite572.0ms

Algorithm

rewrite-expression-head

Rules

4980×	`add-exp-log`
3013×	`prod-exp`
2037×	`div-exp`
1200×	`pow-exp`
480×	`pow-to-exp`
456×	`rec-exp` `1-exp`
140×	`add-cbrt-cube`
135×	`times-frac`
95×	`associate-l`
92×	`add-sqr-sqrt`
80×	`*-un-lft-identity` `add-cube-cbrt`
59×	`cbrt-unprod`
47×	`cbrt-undiv`
12×	`pow1` `unpow-prod-down`
9×	`associate-r` `div-inv` `unswap-sqr`
8×	`sqr-pow`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`associate-/r/`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-r/` `pow-flip` `inv-pow`

Counts

4 → 1055

Calls

4 calls:

30.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
251.0ms	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
81.0ms	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))
24.0ms	(* (pow t 1.0) (pow k 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

522.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
602.0ms	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0)))
619.0ms	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) 2.0))
471.0ms	(* (pow t 1.0) (pow k 2.0))

simplify9.3s

Counts

1067 → 1067

Iterations

Iter	Nodes
done	5001
1	2868
0	934

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (/ (sin k) l))
0.4b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
3.5b	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
5.3b	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

15827×	`add-exp-log`
10951×	`prod-exp`
5925×	`div-exp`
4356×	`pow-exp`
2124×	`pow-to-exp`
1359×	`rec-exp` `1-exp`
210×	`times-frac`
147×	`add-cbrt-cube`
118×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
88×	`associate-l`
60×	`cbrt-unprod`
51×	`cbrt-undiv`
14×	`associate-/r*` `div-inv`
12×	`pow1`
6×	`associate-/l*`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`frac-times` `associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 2660

Calls

4 calls:

13.0ms	(/ (cos k) (/ (sin k) l))
56.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
444.0ms	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
128.0ms	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (cos k) (/ (sin k) l))
428.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
604.0ms	(* (/ 1 (/ (sin k) l)) (* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0)))
605.0ms	(* (/ (cos k) (/ (sin k) l)) (* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) 2.0))

simplify11.0s

Counts

2672 → 2672

Iterations

Iter	Nodes
done	5002
1	4156
0	1446

prune3.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

regimes581.0ms

Accuracy

0% (2.2b remaining)

Error of 11.5b against oracle of 9.2b and baseline of 11.5b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample29.2s

Algorithm

intervals

Results

8.9s	4085×	body	1280	valid
7.4s	2294×	body	2560	valid
6.9s	963×	body	5120	valid
3.4s	2405×	body	640	valid
1.3s	1026×	body	320	valid
529.0ms	2002×	body	80	valid
234.0ms	450×	body	160	valid