Details

sample110.0ms

Algorithm

intervals

Results

38.0ms	307×	body	80	valid
20.0ms	28×	body	1280	valid
16.0ms	32×	body	640	valid
5.0ms	14×	body	320	valid
2.0ms	7×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4217
4	728
3	160
2	57
1	26
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b	(* (* x (pow sin 2.0)) x)
8.0b	(* x (pow sin 2.0))
17.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite124.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
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×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 115

Calls

4 calls:

47.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
19.0ms	(* (* x (pow sin 2.0)) x)
10.0ms	(* x (pow sin 2.0))
44.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

442.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
214.0ms	(* (* x (pow sin 2.0)) x)
183.0ms	(* x (pow sin 2.0))
293.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1502
1	414
0	166

prune621.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.3b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite449.0ms

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` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
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×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 186

Calls

4 calls:

22.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
160.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
58.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
198.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
321.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
210.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
344.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.7s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1830
1	556
0	198

prune477.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.1b

localize29.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
3.6b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
7.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
8.0b	(* x (pow sin 2.0))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

158.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
63.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
26.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
20.0ms	(* x (pow sin 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
378.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
319.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))
189.0ms	(* x (pow sin 2.0))

simplify2.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
2	1490
1	432
0	158

prune742.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 6.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
3.5b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
3.6b	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
7.5b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1442×	`add-exp-log`
1342×	`prod-exp`
354×	`pow-to-exp` `pow-exp`
124×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 406

Calls

4 calls:

604.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
516.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
178.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
77.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

459.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
410.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
387.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
358.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.7s

Counts

418 → 418

Iterations

Iter	Nodes
done	5032
2	2538
1	757
0	254

prune695.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

regimes764.0ms

Accuracy

0% (3.4b remaining)

Error of 8.4b against oracle of 5.0b and baseline of 8.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	8961×	body	80	valid
1.1s	842×	body	1280	valid
904.0ms	958×	body	640	valid
253.0ms	623×	body	320	valid
67.0ms	301×	body	160	valid