Details

sample54.0ms

Algorithm

intervals

Results

22.0ms	308×	body	80	valid
7.0ms	19×	body	1280	valid
7.0ms	28×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify596.0ms

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	931	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.3b	(* (* x (pow sin 2.0)) x)
9.5b	(* x (pow sin 2.0))
16.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite73.0ms

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:

25.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
6.0ms	(* x (pow sin 2.0))
28.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
143.0ms	(* (* x (pow sin 2.0)) x)
138.0ms	(* x (pow sin 2.0))
455.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify594.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (167.0ms)

Iter	Nodes	Cost
0	171	1959
1	425	1811
2	1532	1541
done	5001	1541

prune286.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.3b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
92.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
33.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
92.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series727.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
298.0ms	(/ (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)
265.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify731.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (219.0ms)

Iter	Nodes	Cost
0	187	4524
1	539	2705
2	2063	2309
done	5000	2309

prune249.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.3b	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
16.1b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

467×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`cbrt-undiv`
4×	`unpow-prod-down` `add-log-exp`
3×	`times-frac` `associate-/l*` `unswap-sqr`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 193

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
14.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
41.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
44.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
150.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
304.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
268.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify548.0ms

Counts

205 → 205

Iterations

Useful iterations: 2 (155.0ms)

Iter	Nodes	Cost
0	187	5282
1	502	3194
2	1713	2702
done	5000	2702

prune266.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
0.7b	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

1631×	`add-exp-log`
1472×	`prod-exp`
378×	`pow-to-exp` `pow-exp`
170×	`div-exp`
97×	`add-cbrt-cube`
60×	`cbrt-unprod`
15×	`associate-l`
11×	`pow1`
10×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 451

Calls

4 calls:

50.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
51.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series988.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
294.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
217.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify667.0ms

Counts

463 → 463

Iterations

Useful iterations: 2 (219.0ms)

Iter	Nodes	Cost
0	242	15892
1	726	7616
2	2130	6700
done	5001	6700

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

regimes272.0ms

Accuracy

0% (0.3b remaining)

Error of 2.7b against oracle of 2.4b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	17	32
done	17	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

548.0ms	8983×	body	80	valid
277.0ms	795×	body	1280	valid
240.0ms	957×	body	640	valid
106.0ms	608×	body	320	valid
36.0ms	304×	body	160	valid