Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	271×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	29×	body	640	valid
3.0ms	16×	body	320	valid
1.0ms	12×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	66	16
3	223	16
4	997	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.8b	(* (* x (pow sin 2.0)) x)
10.1b	(* x (pow sin 2.0))
18.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite71.0ms

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:

27.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
25.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series857.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
155.0ms	(* (* x (pow sin 2.0)) x)
137.0ms	(* x (pow sin 2.0))
263.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.0s

Counts

127 → 127

Iterations

Useful iterations: 2 (196.0ms)

Iter	Nodes	Cost
0	171	1959
1	428	1811
2	1553	1531
done	5000	1531

prune263.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite238.0ms

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:

11.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
90.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
31.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
93.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series855.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
292.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
151.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
269.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.1s

Counts

198 → 198

Iterations

Useful iterations: 2 (312.0ms)

Iter	Nodes	Cost
0	203	4993
1	581	2927
2	2286	2483
done	5000	2483

prune273.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.5b

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

18.7b

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

rewrite110.0ms

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:

14.0ms

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

40.0ms

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

43.0ms

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

series730.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms

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

310.0ms

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

268.0ms

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

simplify846.0ms

Counts

187 → 187

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	182	5118
1	539	3028
2	1914	2542
done	5000	2542

prune203.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.5b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b

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

4.8b

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

12.8b

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

rewrite92.0ms

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:

34.0ms

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

32.0ms

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

11.0ms

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

series799.0ms

Counts

3 → 9

Calls

3 calls:

307.0ms

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

277.0ms

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

214.0ms

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

simplify1.1s

Counts

185 → 185

Iterations

Useful iterations: 2 (235.0ms)

Iter	Nodes	Cost
0	185	4968
1	579	3206
2	2002	2672
done	5000	2672

prune185.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.4b

regimes401.0ms

Accuracy

0% (1.8b remaining)

Error of 6.8b against oracle of 5.1b and baseline of 6.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.5s

Algorithm

intervals

Results

546.0ms	8977×	body	80	valid
285.0ms	816×	body	1280	valid
234.0ms	966×	body	640	valid
104.0ms	564×	body	320	valid
39.0ms	321×	body	160	valid