Details

sample834.0ms

Algorithm

intervals

Results

258.0ms	71×	body	2560	valid
198.0ms	34×	body	5120	valid
173.0ms	130×	body	1280	valid
112.0ms	81×	body	640	valid
33.0ms	43×	body	320	valid
12.0ms	58×	body	80	valid
8.0ms	19×	body	160	valid

simplify957.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	832
2	147
1	44
0	19

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin k) l)
0.3b	(pow (/ k t) 2.0)
16.2b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
30.4b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite807.0ms

Algorithm

rewrite-expression-head

Rules

8296×	`times-frac`
3022×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
954×	`associate-/l*`
940×	`unpow-prod-down`
312×	`add-exp-log`
310×	`sqr-pow`
226×	`div-exp`
212×	`div-inv`
60×	`add-cbrt-cube` `associate-/r/`
48×	`associate-/r*`
44×	`prod-exp`
42×	`pow-exp`
37×	`cbrt-undiv`
30×	`pow-to-exp`
5×	`pow1` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
1×	`pow-pow` `tan-quot` `associate-*r/` `associate-/l/`

Counts

4 → 2403

Calls

4 calls:

13.0ms	(/ (sin k) l)
9.0ms	(pow (/ k t) 2.0)
40.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
334.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series1.2s

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin k) l)
90.0ms	(pow (/ k t) 2.0)
262.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
813.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify1.3s

Counts

2415 → 2415

Iterations

Iter	Nodes
done	5043
0	5043

prune30.4s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 13.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.8b	(* (pow t 1.0) (pow k 2.0))
16.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 600

Calls

4 calls:

29.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
30.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
28.0ms	(* (pow t 1.0) (pow k 2.0))
74.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

481.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
162.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
513.0ms	(* (pow t 1.0) (pow k 2.0))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify752.0ms

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
3.2b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
5.8b	(* (pow t 1.0) (pow k 2.0))
16.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`add-exp-log`
660×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
90×	`times-frac`
88×	`add-sqr-sqrt`
80×	`rec-exp` `1-exp`
61×	`add-cbrt-cube`
55×	`*-un-lft-identity` `add-cube-cbrt`
52×	`associate-r`
31×	`associate-l`
21×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
15×	`unswap-sqr`
9×	`sqr-pow`
7×	`pow1` `div-inv`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 440

Calls

4 calls:

14.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
69.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
26.0ms	(* (pow t 1.0) (pow k 2.0))
128.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series2.2s

Counts

4 → 12

Calls

4 calls:

488.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
148.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
497.0ms	(* (pow t 1.0) (pow k 2.0))
1.0s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify1.0s

Counts

452 → 452

Iterations

Iter	Nodes
done	5000
1	1708
0	542

prune1.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin k) (/ (sin k) l))
3.4b	(/ (* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l)) (* (sin k) (/ (sin k) l)))
6.2b	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
8.2b	(* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

1276×	`add-exp-log`
701×	`div-exp`
676×	`times-frac`
532×	`prod-exp`
467×	`unpow-prod-down`
419×	`pow-exp`
331×	`add-sqr-sqrt`
326×	`*-un-lft-identity` `add-cube-cbrt`
186×	`associate-l`
179×	`pow-to-exp`
97×	`sqr-pow`
81×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
26×	`associate-/l*`
20×	`cbrt-unprod`
19×	`div-inv`
16×	`cbrt-undiv`
14×	`associate-r`
8×	`associate-/r*`
6×	`pow1`
4×	`add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `associate-/l/`

Counts

4 → 766

Calls

4 calls:

24.0ms	(* (sin k) (/ (sin k) l))
87.0ms	(/ (* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l)) (* (sin k) (/ (sin k) l)))
27.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
241.0ms	(* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l))

series2.3s

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin k) (/ (sin k) l))
1.1s	(/ (* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l)) (* (sin k) (/ (sin k) l)))
514.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
562.0ms	(* (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0) (* (cos k) l))

simplify1.6s

Counts

778 → 778

Iterations

Iter	Nodes
done	5000
1	3053
0	975

prune4.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 1.7b

regimes852.0ms

Accuracy

0% (1.8b remaining)

Error of 3.9b against oracle of 2.1b and baseline of 3.9b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample31.2s

Algorithm

intervals

Results

9.2s	2308×	body	2560	valid
8.6s	4074×	body	1280	valid
7.3s	920×	body	5120	valid
3.0s	2532×	body	640	valid
873.0ms	447×	body	160	valid
833.0ms	1028×	body	320	valid
559.0ms	2095×	body	80	valid