Details

sample79.0ms

Algorithm

intervals

Results

25.0ms	304×	body	80	valid
11.0ms	23×	body	1280	valid
10.0ms	32×	body	640	valid
5.0ms	23×	body	320	valid
2.0ms	9×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize22.0ms

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))

rewrite168.0ms

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:

71.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
25.0ms	(* (* x (pow sin 2.0)) x)
11.0ms	(* x (pow sin 2.0))
54.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

369.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
157.0ms	(* (* x (pow sin 2.0)) x)
162.0ms	(* x (pow sin 2.0))
348.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.6s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1502
1	414
0	166

prune595.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize34.0ms

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))

rewrite467.0ms

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:

30.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
192.0ms	(/ (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)
172.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
376.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
161.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
351.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.8s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1830
1	556
0	198

prune520.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.6b

localize37.0ms

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)))

rewrite288.0ms

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:

69.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
180.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
9.0ms	(* x (pow sin 2.0))
20.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x)
335.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin 2.0))) x))
175.0ms	(* x (pow sin 2.0))
285.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin 2.0)))

simplify1.3s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	1535
1	432
0	158

prune643.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize55.0ms

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))))

rewrite1.6s

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:

638.0ms	(/ (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)))
259.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
605.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
93.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

453.0ms	(/ (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)))
439.0ms	(* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)
400.0ms	(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
332.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))))

simplify2.1s

Counts

418 → 418

Iterations

Iter	Nodes
done	5002
2	2578
1	767
0	254

prune740.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.8b

regimes965.0ms

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

sample3.9s

Algorithm

intervals

Results

1.5s	9037×	body	80	valid
1.0s	790×	body	1280	valid
494.0ms	982×	body	640	valid
216.0ms	608×	body	320	valid
74.0ms	316×	body	160	valid