Details

sample94.0ms

Algorithm

intervals

Results

29.0ms	287×	body	80	valid
14.0ms	24×	body	1280	valid
14.0ms	34×	body	640	valid
11.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1097	16
done	5000	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.8b	(* (* x (pow sin 2.0)) x)
6.4b	(* x (pow sin 2.0))
17.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite222.0ms

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:

61.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
32.0ms	(* (* x (pow sin 2.0)) x)
19.0ms	(* x (pow sin 2.0))
104.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

393.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
236.0ms	(* (* x (pow sin 2.0)) x)
175.0ms	(* x (pow sin 2.0))
366.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 2 (325.0ms)

Iter	Nodes	Cost
0	171	1959
1	407	1811
2	1424	1531
done	5001	1531

prune425.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite699.0ms

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:

31.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
307.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
106.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
238.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
559.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
262.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
387.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.6s

Counts

198 → 198

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	203	4993
1	527	2927
2	2088	2483
done	5000	2479

prune432.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.2b

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

17.6b

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

rewrite339.0ms

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:

41.0ms

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

126.0ms

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

148.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

188.0ms

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

452.0ms

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

446.0ms

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

simplify1.3s

Counts

187 → 187

Iterations

Useful iterations: 2 (415.0ms)

Iter	Nodes	Cost
0	182	5118
1	461	3028
2	1847	2552
done	5000	2552

prune356.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b

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

4.9b

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

14.2b

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

rewrite285.0ms

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:

102.0ms

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

143.0ms

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

27.0ms

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

series1.2s

Counts

3 → 9

Calls

3 calls:

479.0ms

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

396.0ms

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

337.0ms

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

simplify1.4s

Counts

185 → 185

Iterations

Useful iterations: 2 (487.0ms)

Iter	Nodes	Cost
0	185	4968
1	498	3206
2	1913	2672
done	5001	2672

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

regimes585.0ms

Accuracy

0% (1.7b remaining)

Error of 6.6b against oracle of 4.9b and baseline of 6.6b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.9s	9189×	body	80	valid
609.0ms	990×	body	640	valid
582.0ms	783×	body	1280	valid
265.0ms	618×	body	320	valid
66.0ms	274×	body	160	valid