Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	308×	body	80	valid
9.0ms	22×	body	1280	valid
8.0ms	27×	body	640	valid
5.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify804.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.3b	(* (* x (pow sin 2.0)) x)
6.4b	(* x (pow sin 2.0))
15.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite219.0ms

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:

91.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
32.0ms	(* (* x (pow sin 2.0)) x)
18.0ms	(* x (pow sin 2.0))
70.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

368.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
181.0ms	(* (* x (pow sin 2.0)) x)
198.0ms	(* x (pow sin 2.0))
356.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.3s

Counts

127 → 127

Iterations

Useful iterations: 2 (410.0ms)

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

prune397.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize24.0ms

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)))
3.3b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite674.0ms

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:

14.0ms	(cos (* 2.0 x))
268.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
119.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
252.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (* 2.0 x))
449.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
225.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
435.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.3s

Counts

175 → 175

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	187	4524
1	539	2705
2	2927	2335
done	5001	2317

prune385.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
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))))
15.1b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite435.0ms

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`
8×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 185

Calls

4 calls:

72.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
8.0ms	(cos (* 2.0 x))
172.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
169.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
25.0ms	(cos (* 2.0 x))
435.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
407.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify2.0s

Counts

197 → 197

Iterations

Useful iterations: 2 (449.0ms)

Iter	Nodes	Cost
0	190	5189
1	547	3099
2	2852	2615
done	5001	2615

prune343.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

localize41.0ms

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)))
4.2b	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
10.2b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

8.0ms	(cos (* 2.0 x))
152.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
116.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
29.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

15.0ms	(cos (* 2.0 x))
499.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
428.0ms	(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
329.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify2.1s

Counts

195 → 195

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	193	5039
1	602	3277
2	3147	2843
done	5001	2735

prune252.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes401.0ms

Accuracy

0% (1.7b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	9059×	body	80	valid
773.0ms	724×	body	1280	valid
664.0ms	1003×	body	640	valid
291.0ms	585×	body	320	valid
75.0ms	302×	body	160	valid