Details

sample119.0ms

Algorithm

intervals

Results

34.0ms	265×	body	80	valid
21.0ms	29×	body	1280	valid
21.0ms	39×	body	640	valid
6.0ms	17×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	242	16
4	1255	16
done	5001	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.8b	(* (* x (pow sin 2.0)) x)
6.6b	(* x (pow sin 2.0))
19.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite624.0ms

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:

466.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
33.0ms	(* (* x (pow sin 2.0)) x)
20.0ms	(* x (pow sin 2.0))
97.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

527.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
221.0ms	(* (* x (pow sin 2.0)) x)
206.0ms	(* x (pow sin 2.0))
412.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.0s

Counts

127 → 127

Iterations

Useful iterations: 2 (592.0ms)

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

prune671.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 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)))
3.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.5b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite893.0ms

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:

55.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
352.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
128.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
334.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
476.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
231.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
455.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.2s

Counts

198 → 198

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	203	4993
1	584	2927
2	3265	2531
done	5002	2525

prune725.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.0b

localize41.0ms

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))))

19.5b

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

rewrite462.0ms

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:

75.0ms

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

176.0ms

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

182.0ms

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

series1.3s

Counts

3 → 9

Calls

3 calls:

257.0ms

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

545.0ms

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

523.0ms

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

simplify2.7s

Counts

187 → 187

Iterations

Useful iterations: 2 (601.0ms)

Iter	Nodes	Cost
0	182	5118
1	530	3028
2	2738	2552
done	5000	2552

prune600.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.0b

localize52.0ms

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)))

9.4b

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

14.6b

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

rewrite411.0ms

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:

160.0ms

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

156.0ms

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

66.0ms

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

series1.6s

Counts

3 → 9

Calls

3 calls:

597.0ms

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

553.0ms

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

431.0ms

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

simplify3.4s

Counts

185 → 185

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	185	4968
1	583	3206
2	3051	2780
done	5000	2672

prune477.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 6.8b against oracle of 5.0b and baseline of 6.8b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.0s	9034×	body	80	valid
850.0ms	860×	body	1280	valid
771.0ms	963×	body	640	valid
335.0ms	605×	body	320	valid
132.0ms	315×	body	160	valid