Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	289×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	29×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	66	16
3	223	16
4	931	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.7b	(* (* x (pow sin 2.0)) x)
7.6b	(* x (pow sin 2.0))
18.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite72.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 123

Calls

4 calls:

27.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
26.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series888.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
158.0ms	(* (* x (pow sin 2.0)) x)
143.0ms	(* x (pow sin 2.0))
270.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify857.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (199.0ms)

Iter	Nodes	Cost
0	179	2045
1	435	1897
2	1541	1627
done	5000	1627

prune314.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (* x (pow sin 2.0)) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.6b	(* x (pow sin 2.0))

rewrite120.0ms

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×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 154

Calls

4 calls:

9.0ms	(* (* x (pow sin 2.0)) x)
26.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
72.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.0ms	(* x (pow sin 2.0))

series857.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (* x (pow sin 2.0)) x)
276.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
276.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
149.0ms	(* x (pow sin 2.0))

simplify879.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (181.0ms)

Iter	Nodes	Cost
0	171	2944
1	428	2102
2	1405	1850
done	5001	1850

prune332.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.9b

localize17.0ms

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))))
2.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
5.8b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

rewrite686.0ms

Algorithm

rewrite-expression-head

Rules

1410×	`add-exp-log`
1300×	`prod-exp`
338×	`pow-to-exp` `pow-exp`
130×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 402

Calls

4 calls:

257.0ms	(/ (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))))
33.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
94.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
265.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ (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))))
162.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
283.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
284.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify1.0s

Counts

414 → 414

Iterations

Useful iterations: 2 (336.0ms)

Iter	Nodes	Cost
0	267	13999
1	796	6515
2	2679	5853
done	5000	5853

prune342.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
5.8b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
5.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

1691×	`add-exp-log`
1549×	`prod-exp`
399×	`pow-to-exp` `pow-exp`
157×	`div-exp`
92×	`add-cbrt-cube`
59×	`cbrt-unprod`
15×	`associate-l`
12×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-undiv` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 478

Calls

4 calls:

14.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
114.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
42.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
117.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
318.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))))
287.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))
285.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

simplify884.0ms

Counts

490 → 490

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	280	16529
1	755	7721
2	2297	6917
done	5000	6917

prune329.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.7b

regimes344.0ms

Accuracy

0% (1.1b remaining)

Error of 5.6b against oracle of 4.5b and baseline of 5.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	20	32
done	20	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

562.0ms	9026×	body	80	valid
279.0ms	789×	body	1280	valid
240.0ms	943×	body	640	valid
106.0ms	576×	body	320	valid
39.0ms	317×	body	160	valid