Details

sample955.0ms

Algorithm

intervals

Results

321.0ms	146×	body	1280	valid
242.0ms	75×	body	2560	valid
163.0ms	22×	body	5120	valid
74.0ms	71×	body	640	valid
23.0ms	32×	body	320	valid
17.0ms	73×	body	80	valid
8.0ms	15×	body	160	valid

simplify908.0ms

Counts

1 → 1

Iterations

Useful iterations: done (907.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	146	25
3	848	23
done	5001	21

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.2b

localize47.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.2b	(* (/ (pow t 3.0) (* l l)) (sin k))
17.0b	(/ (pow t 3.0) (* l l))
28.9b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
272×	`add-exp-log`
153×	`unpow-prod-down`
144×	`add-sqr-sqrt`
137×	`add-cube-cbrt` `*-un-lft-identity`
128×	`div-exp`
103×	`prod-exp`
59×	`add-cbrt-cube`
58×	`associate-*l/`
54×	`associate-/r/`
38×	`tan-quot`
34×	`pow-exp`
32×	`div-inv`
24×	`pow-to-exp`
21×	`cbrt-unprod`
19×	`cbrt-undiv` `frac-times` `associate-*r/`
18×	`associate-/r*`
17×	`associate-/l*`
15×	`sqr-pow`
12×	`associate-l`
11×	`pow1`
6×	`associate-r`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 354

Calls

4 calls:

116.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
50.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
25.0ms	(/ (pow t 3.0) (* l l))
175.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

496.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
356.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
279.0ms	(/ (pow t 3.0) (* l l))
895.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1000.0ms

Counts

366 → 366

Iterations

Useful iterations: done (985.0ms)

Iter	Nodes	Cost
0	662	10242
1	1764	9771
done	5000	9305

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b	(* (pow k 2.0) (pow t 1.0))
5.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.1b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite224.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

18.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
19.0ms	(* (pow k 2.0) (pow t 1.0))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
110.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

465.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
393.0ms	(* (pow k 2.0) (pow t 1.0))
131.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
873.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify741.0ms

Counts

612 → 612

Iterations

Useful iterations: done (720.0ms)

Iter	Nodes	Cost
0	483	15017
1	1356	13309
done	5000	13047

prune1.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 14.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.1b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

4.0ms	(pow (sin k) 2)
49.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
26.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
197.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin k) 2)
477.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
135.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.3s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify848.0ms

Counts

1472 → 1472

Iterations

Useful iterations: done (779.0ms)

Iter	Nodes	Cost
0	597	50343
1	1808	34674
done	5001	32849

prune847.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 12.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.3b	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
5.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.1b	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

13973×	`add-exp-log`
10155×	`prod-exp`
8251×	`pow-exp`
5914×	`div-exp`
4231×	`pow-to-exp`
920×	`rec-exp` `1-exp`
81×	`unpow-prod-down`
64×	`times-frac`
62×	`associate-l`
49×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
37×	`add-cbrt-cube`
21×	`sqrt-prod`
14×	`cbrt-unprod`
12×	`associate-r` `sqr-pow`
9×	`associate-/r*`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`unpow2` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 3203

Calls

4 calls:

19.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
213.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
26.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
125.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

360.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
422.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
118.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
525.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify1.9s

Counts

3215 → 3215

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	1014	126429
1	3124	111754
done	5001	108728

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 11.9b

regimes696.0ms

Accuracy

28.2% (4.9b remaining)

Error of 16.2b against oracle of 11.3b and baseline of 18.2b

bsearch1.4s

Steps

Iters	Range		Point
9	4.1368702715426593e+145	3.8281298477808404e+154	1.1478743484480851e+154
7	-4.073943833331379e+185	-1.8779889896941352e+183	-1.9100655647147183e+183

simplify14.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	46	107
1	58	77
done	58	77

end0.0ms

sample33.0s

Algorithm

intervals

Results

10.6s	2230×	body	2560	valid
9.0s	4089×	body	1280	valid
7.2s	956×	body	5120	valid
3.3s	2533×	body	640	valid
940.0ms	1025×	body	320	valid
673.0ms	2045×	body	80	valid
273.0ms	480×	body	160	valid