Details

sample845.0ms

Algorithm

intervals

Results

265.0ms	140×	body	1280	valid
219.0ms	80×	body	2560	valid
213.0ms	28×	body	5120	valid
76.0ms	73×	body	640	valid
19.0ms	28×	body	320	valid
13.0ms	66×	body	80	valid
8.0ms	17×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (/ k t) 2.0) (tan k))
0.4b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
14.6b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
32.0b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

12307×	`times-frac`
4673×	`add-sqr-sqrt`
4665×	`*-un-lft-identity` `add-cube-cbrt`
1470×	`unpow-prod-down`
954×	`associate-/l*`
487×	`sqr-pow`
358×	`associate-/r*`
350×	`add-exp-log`
328×	`div-inv`
253×	`div-exp`
93×	`associate-/r/`
74×	`add-cbrt-cube`
48×	`prod-exp`
46×	`cbrt-undiv`
45×	`pow-exp`
33×	`pow-to-exp`
17×	`associate-l`
6×	`cbrt-unprod`
4×	`pow1` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`tan-quot` `associate-*r/`
1×	`*-commutative` `associate-/l/`

Counts

4 → 3666

Calls

4 calls:

22.0ms	(* (pow (/ k t) 2.0) (tan k))
98.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
28.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
314.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series1.7s

Counts

4 → 12

Calls

4 calls:

287.0ms	(* (pow (/ k t) 2.0) (tan k))
388.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
315.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
686.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify5.4s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune45.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 19.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
6.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.4b	(* (pow t 1.0) (pow k 2.0))
17.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `associate-r/` `associate-/l`

Counts

4 → 567

Calls

4 calls:

5.0ms	(pow (sin k) 2)
23.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.0ms	(* (pow t 1.0) (pow k 2.0))
78.0ms	(* (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:

27.0ms	(pow (sin k) 2)
124.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
580.0ms	(* (pow t 1.0) (pow k 2.0))
1.4s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.1s

Counts

579 → 579

Iterations

Iter	Nodes
done	5000
1	1162
0	416

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.7b	(/ 1 (pow k 2.0))
8.2b	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))
15.0b	(/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

rewrite473.0ms

Algorithm

rewrite-expression-head

Rules

4520×	`add-exp-log`
2317×	`div-exp`
2252×	`prod-exp`
1706×	`pow-exp`
527×	`pow-to-exp`
396×	`rec-exp` `1-exp`
112×	`add-cbrt-cube`
94×	`add-sqr-sqrt`
90×	`times-frac`
67×	`*-un-lft-identity`
64×	`add-cube-cbrt`
55×	`unpow-prod-down`
42×	`associate-l`
41×	`cbrt-undiv` `cbrt-unprod`
21×	`associate-r`
13×	`swap-sqr` `unswap-sqr`
11×	`pow1` `sqr-pow`
8×	`associate-/r*` `div-inv`
6×	`associate-/r/`
4×	`associate-r/` `associate-/l` `add-log-exp`
3×	`frac-times` `associate-*l/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 1069

Calls

4 calls:

26.0ms	(* (/ (sin k) l) (/ (sin k) l))
13.0ms	(/ 1 (pow k 2.0))
151.0ms	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))
48.0ms	(/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

series2.0s

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ (sin k) l) (/ (sin k) l))
455.0ms	(/ 1 (pow k 2.0))
1.0s	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))
506.0ms	(/ (* (pow (/ 1 (pow k 2.0)) 1.0) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

simplify2.1s

Counts

1081 → 1081

Iterations

Iter	Nodes
done	5001
1	2831
0	835

prune2.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (pow k 2.0))
4.1b	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))) (/ (cos k) (/ (sin k) l)))
6.2b	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
8.8b	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

5812×	`add-exp-log`
3861×	`div-exp`
2577×	`pow-exp`
2425×	`times-frac`
2103×	`prod-exp`
1474×	`add-sqr-sqrt`
1297×	`unpow-prod-down`
1000×	`*-un-lft-identity`
889×	`add-cube-cbrt`
795×	`pow-to-exp`
597×	`rec-exp` `1-exp`
426×	`associate-r`
227×	`sqr-pow`
171×	`unswap-sqr`
94×	`div-inv`
74×	`add-cbrt-cube`
32×	`associate-/l*`
30×	`associate-l`
28×	`cbrt-undiv`
24×	`cbrt-unprod`
20×	`associate-/r*`
6×	`pow1`
4×	`associate-*r/` `add-log-exp`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `pow-prod-down` `associate-*l/` `pow-flip` `inv-pow`

Counts

4 → 2375

Calls

4 calls:

10.0ms	(/ 1 (pow k 2.0))
234.0ms	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))) (/ (cos k) (/ (sin k) l)))
41.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
346.0ms	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

series2.5s

Counts

4 → 12

Calls

4 calls:

544.0ms	(/ 1 (pow k 2.0))
996.0ms	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))) (/ (cos k) (/ (sin k) l)))
361.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
578.0ms	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

simplify3.3s

Counts

2387 → 2387

Iterations

Iter	Nodes
done	5000
0	2212

prune11.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 1.9b

regimes769.0ms

Accuracy

0% (2.1b remaining)

Error of 4.4b against oracle of 2.3b and baseline of 4.4b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample31.5s

Algorithm

intervals

Results

8.8s	4066×	body	1280	valid
8.8s	986×	body	5120	valid
7.9s	2245×	body	2560	valid
3.5s	2547×	body	640	valid
868.0ms	1102×	body	320	valid
699.0ms	2012×	body	80	valid
211.0ms	452×	body	160	valid