Details

sample68.0ms

Algorithm

intervals

Results

23.0ms	304×	body	80	valid
10.0ms	23×	body	1280	valid
10.0ms	32×	body	640	valid
6.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize37.0ms

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))

rewrite174.0ms

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:

66.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
25.0ms	(* (* x (pow sin 2.0)) x)
14.0ms	(* x (pow sin 2.0))
63.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series978.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
152.0ms	(* (* x (pow sin 2.0)) x)
142.0ms	(* x (pow sin 2.0))
361.0ms	(* (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

prune661.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize43.0ms

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))

rewrite480.0ms

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:

33.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
185.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
57.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
186.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
391.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
191.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
308.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.5s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1830
1	556
0	198

prune549.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
7.0b	(* x (pow sin 2.0))
8.2b	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

rewrite230.0ms

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:

56.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
131.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
9.0ms	(* x (pow sin 2.0))
23.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

387.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
408.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
194.0ms	(* x (pow sin 2.0))
319.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	1535
1	432
0	158

prune757.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (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)))
3.8b	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
5.6b	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
8.2b	(* (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:

579.0ms	(/ (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)))
177.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
519.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
70.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

437.0ms	(/ (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)))
343.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
315.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
284.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.3s

Counts

418 → 418

Iterations

Iter	Nodes
done	5002
2	2578
1	767
0	254

prune684.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

regimes1.1s

Accuracy

0% (3.7b remaining)

Error of 8.7b against oracle of 5.0b and baseline of 8.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	9037×	body	80	valid
888.0ms	982×	body	640	valid
462.0ms	790×	body	1280	valid
209.0ms	608×	body	320	valid
104.0ms	316×	body	160	valid