Details

sample146.0ms

Algorithm

intervals

Results

53.0ms	294×	body	80	valid
21.0ms	22×	body	1280	valid
20.0ms	29×	body	640	valid
12.0ms	23×	body	320	valid
4.0ms	12×	body	160	valid

simplify9.3s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize138.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.8b	(* (* x (pow sin 2.0)) x)
8.7b	(* x (pow sin 2.0))
16.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite442.0ms

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` `insert-posit16` `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 → 119

Calls

4 calls:

195.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
68.0ms	(* (* x (pow sin 2.0)) x)
24.0ms	(* x (pow sin 2.0))
145.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series2.3s

Counts

4 → 12

Calls

4 calls:

948.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
333.0ms	(* (* x (pow sin 2.0)) x)
271.0ms	(* x (pow sin 2.0))
725.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify3.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1452
1	415
0	170

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.1b

localize168.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.5b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

15.0ms	(cos (* 2.0 x))
579.0ms	(/ (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)
624.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series2.1s

Counts

4 → 12

Calls

4 calls:

30.0ms	(cos (* 2.0 x))
1.0s	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
427.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
674.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify4.1s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	1906
1	515
0	186

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.0b

localize137.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
16.5b	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite801.0ms

Algorithm

rewrite-expression-head

Rules

467×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
59×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`cbrt-undiv`
4×	`unpow-prod-down` `insert-posit16` `add-log-exp`
3×	`times-frac` `associate-/l*` `unswap-sqr`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `swap-sqr` `pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 197

Calls

4 calls:

116.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
17.0ms	(cos (* 2.0 x))
310.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
332.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

376.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
17.0ms	(cos (* 2.0 x))
923.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
773.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify3.8s

Counts

209 → 209

Iterations

Iter	Nodes
done	5001
2	1586
1	481
0	186

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.0b

localize153.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.4b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.4b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

929×	`add-exp-log`
757×	`prod-exp`
196×	`pow-to-exp` `pow-exp`
170×	`div-exp`
61×	`add-cbrt-cube`
33×	`cbrt-unprod`
14×	`associate-l`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `add-cube-cbrt`
6×	`unpow-prod-down`
4×	`pow1` `insert-posit16` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 268

Calls

4 calls:

30.0ms	(cos (* 2.0 x))
367.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
72.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
84.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series2.2s

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (* 2.0 x))
947.0ms	(/ (cos (* 2.0 x)) (* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
612.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
649.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify4.3s

Counts

280 → 280

Iterations

Iter	Nodes
done	5047
2	2082
1	692
0	237

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 1.8b

regimes2.4s

Accuracy

0% (0.4b remaining)

Error of 2.6b against oracle of 2.2b and baseline of 2.6b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	9117×	body	80	valid
620.0ms	985×	body	640	valid
597.0ms	765×	body	1280	valid
297.0ms	570×	body	320	valid
88.0ms	307×	body	160	valid