Details

sample79.0ms

Algorithm

intervals

Results

23.0ms	27×	body	1280	valid
19.0ms	273×	body	80	valid
12.0ms	40×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	7×	body	160	valid

simplify914.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	242	16
4	1255	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b	(* (* x (pow sin 2.0)) x)
9.4b	(* x (pow sin 2.0))
17.8b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

100.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
34.0ms	(* (* x (pow sin 2.0)) x)
21.0ms	(* x (pow sin 2.0))
101.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

445.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
220.0ms	(* (* x (pow sin 2.0)) x)
224.0ms	(* x (pow sin 2.0))
413.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.2s

Counts

127 → 127

Iterations

Useful iterations: 2 (311.0ms)

Iter	Nodes	Cost
0	171	1959
1	439	1821
2	2396	1563
done	5000	1563

prune486.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.8b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 186

Calls

4 calls:

35.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
212.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
83.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
286.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
428.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
181.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
361.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.3s

Counts

198 → 198

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	203	4993
1	584	2927
2	3265	2531
done	5002	2525

prune510.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))

0.3b

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

17.8b

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

466×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
8×	`associate-l`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv`
5×	`pow1`
3×	`unpow-prod-down` `times-frac` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

3 → 178

Calls

3 calls:

49.0ms

(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))

168.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

196.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.2s

Counts

3 → 9

Calls

3 calls:

262.0ms

(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))

487.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

437.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.9s

Counts

187 → 187

Iterations

Useful iterations: 2 (498.0ms)

Iter	Nodes	Cost
0	182	5118
1	530	3028
2	2738	2552
done	5000	2552

prune278.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.3b

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

6.0b

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

12.9b

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

455×	`add-exp-log`
371×	`prod-exp`
89×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
53×	`div-exp`
33×	`cbrt-unprod`
8×	`associate-l`
7×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`unpow-prod-down` `times-frac` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

3 → 176

Calls

3 calls:

127.0ms

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

105.0ms

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

35.0ms

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts

3 → 9

Calls

3 calls:

487.0ms

(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))

368.0ms

(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))

296.0ms

(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify2.6s

Counts

185 → 185

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	185	4968
1	583	3206
2	3051	2780
done	5000	2672

prune321.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.6b

regimes539.0ms

Accuracy

0% (1.6b remaining)

Error of 6.8b against oracle of 5.2b and baseline of 6.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	21	32
done	21	32

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	8967×	body	80	valid
713.0ms	828×	body	1280	valid
666.0ms	589×	body	320	valid
520.0ms	1006×	body	640	valid
66.0ms	295×	body	160	valid