Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	302×	body	80	valid
11.0ms	31×	body	1280	valid
6.0ms	23×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify453.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	66	16
3	227	16
4	1013	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.7b	(* (* x (pow sin 2.0)) x)
8.4b	(* x (pow sin 2.0))
19.9b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite70.0ms

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:

24.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
8.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
24.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series825.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
144.0ms	(* (* x (pow sin 2.0)) x)
136.0ms	(* x (pow sin 2.0))
258.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify604.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	171	1959
1	434	1811
2	1672	1531
done	5000	1531

prune264.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.9b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite222.0ms

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))
88.0ms	(/ (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)
89.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series725.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
299.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
150.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
262.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify900.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (211.0ms)

Iter	Nodes	Cost
0	187	4524
1	547	2705
2	2202	2299
done	5000	2299

prune244.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.5b

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))))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
19.9b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite111.0ms

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))))
42.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
40.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series722.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
151.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
294.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
264.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify739.0ms

Counts

205 → 205

Iterations

Useful iterations: 2 (200.0ms)

Iter	Nodes	Cost
0	187	5282
1	509	3194
2	1882	2692
done	5000	2692

prune255.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

localize15.0ms

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)))))
0.4b	(/ (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))))))
5.9b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.9b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite167.0ms

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:

49.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
53.0ms	(/ (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))))))
10.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series995.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
297.0ms	(/ (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))))))
208.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
223.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify1.2s

Counts

463 → 463

Iterations

Useful iterations: 2 (422.0ms)

Iter	Nodes	Cost
0	242	15892
1	732	7616
2	2324	6700
done	5001	6700

prune249.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.9b

regimes284.0ms

Accuracy

0% (0.3b remaining)

Error of 2.6b against oracle of 2.4b and baseline of 2.6b

bsearch0.0ms

simplify2.0ms

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

556.0ms	8936×	body	80	valid
300.0ms	852×	body	1280	valid
245.0ms	987×	body	640	valid
107.0ms	578×	body	320	valid
45.0ms	339×	body	160	valid