Details

sample97.0ms

Algorithm

intervals

Results

35.0ms	304×	body	80	valid
15.0ms	23×	body	1280	valid
13.0ms	32×	body	640	valid
8.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.0b	(* (* x (pow sin 2.0)) x)
7.0b	(* x (pow sin 2.0))
20.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite150.0ms

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:

49.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
17.0ms	(* (* x (pow sin 2.0)) x)
9.0ms	(* x (pow sin 2.0))
69.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

425.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
197.0ms	(* (* x (pow sin 2.0)) x)
190.0ms	(* x (pow sin 2.0))
318.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
2	2350
1	430
0	166

prune817.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite411.0ms

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)))
158.0ms	(/ (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)
162.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
368.0ms	(/ (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)
413.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.2s

Counts

198 → 198

Iterations

Iter	Nodes
done	5002
2	3307
1	575
0	198

prune698.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.7b

localize35.0ms

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))
0.7b	(/ (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))))
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))
6.4b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

rewrite608.0ms

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:

105.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
208.0ms	(/ (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))))
217.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))
26.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

series2.4s

Counts

4 → 12

Calls

4 calls:

775.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
473.0ms	(/ (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))))
675.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x)))
473.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

simplify2.6s

Counts

478 → 478

Iterations

Iter	Nodes
done	5000
2	3721
1	866
0	267

prune784.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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))
5.9b	(/ (/ (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)))
6.4b	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

rewrite301.0ms

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:

18.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
89.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
116.0ms	(/ (/ (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)))
41.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

series2.0s

Counts

4 → 12

Calls

4 calls:

269.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
739.0ms	(* (* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x)) (* (pow sin (/ 2.0 2)) x))
480.0ms	(/ (/ (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)))
496.0ms	(* (pow cos (/ 2.0 2)) (* (pow sin (/ 2.0 2)) x))

simplify1.9s

Counts

444 → 444

Iterations

Iter	Nodes
done	5001
1	1201
0	352

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

regimes778.0ms

Accuracy

-0.2% (2.0b remaining)

Error of 2.7b against oracle of 0.7b and baseline of 2.7b

bsearch191.0ms

Steps

Iters	Range		Point
9	1.721851027394304e-131	4.241195356250261e-126	7.441590536785485e-128
7	-84463.33967257517	-1633.4135693106575	-2020.5836627569333

simplify15.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	9037×	body	80	valid
988.0ms	982×	body	640	valid
658.0ms	790×	body	1280	valid
202.0ms	608×	body	320	valid
71.0ms	316×	body	160	valid