Details

sample90.0ms

Algorithm

intervals

Results

26.0ms	272×	body	80	valid
25.0ms	31×	body	1280	valid
10.0ms	24×	body	640	valid
4.0ms	14×	body	320	valid
2.0ms	11×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1263
3	241
2	67
1	26
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.8b	(* (* x (pow sin 2.0)) x)
9.6b	(* x (pow sin 2.0))
14.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite137.0ms

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:

51.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
18.0ms	(* (* x (pow sin 2.0)) x)
10.0ms	(* x (pow sin 2.0))
53.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
203.0ms	(* (* x (pow sin 2.0)) x)
181.0ms	(* x (pow sin 2.0))
361.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.9s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	2350
1	430
0	166

prune681.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
14.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite605.0ms

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:

45.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
240.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
105.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
187.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
418.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
228.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
425.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.3s

Counts

198 → 198

Iterations

Iter	Nodes
done	5002
2	3307
1	575
0	198

prune800.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
4.0b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
4.1b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

1711×	`add-exp-log`
1564×	`prod-exp`
400×	`pow-to-exp` `pow-exp`
160×	`div-exp`
97×	`add-cbrt-cube`
62×	`cbrt-unprod`
15×	`associate-l`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 466

Calls

4 calls:

100.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
227.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
35.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
272.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

series2.4s

Counts

4 → 12

Calls

4 calls:

688.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
488.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))))
478.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
739.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

simplify2.9s

Counts

478 → 478

Iterations

Iter	Nodes
done	5000
2	3700
1	860
0	267

prune887.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
0.2b	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
4.0b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
4.3b	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

1287×	`add-exp-log`
896×	`prod-exp`
374×	`div-exp`
266×	`pow-to-exp` `pow-exp`
97×	`add-cbrt-cube`
88×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`cbrt-unprod`
33×	`unpow-prod-down`
28×	`associate-/l*`
22×	`cbrt-undiv`
11×	`sqr-pow`
8×	`associate-/r` `associate-l*`
6×	`pow1`
4×	`div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`pow-prod-down` `associate-/l/`

Counts

4 → 432

Calls

4 calls:

14.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
103.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
44.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
105.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

series2.3s

Counts

4 → 12

Calls

4 calls:

587.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
757.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
525.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))
419.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))

simplify2.0s

Counts

444 → 444

Iterations

Iter	Nodes
done	5000
1	1212
0	352

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

regimes942.0ms

Accuracy

0% (1.0b remaining)

Error of 2.5b against oracle of 1.5b and baseline of 2.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	9044×	body	80	valid
592.0ms	852×	body	1280	valid
563.0ms	1001×	body	640	valid
268.0ms	601×	body	320	valid
62.0ms	304×	body	160	valid