Details

sample84.0ms

Algorithm

intervals

Results

27.0ms	294×	body	80	valid
11.0ms	22×	body	1280	valid
10.0ms	29×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid

simplify9.6s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize133.0ms

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))

rewrite548.0ms

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×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `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 → 127

Calls

4 calls:

166.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
92.0ms	(* (* x (pow sin 2.0)) x)
56.0ms	(* x (pow sin 2.0))
215.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.0s	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
325.0ms	(* (* x (pow sin 2.0)) x)
320.0ms	(* x (pow sin 2.0))
776.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify4.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5004
2	1482
1	434
0	178

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.1b

localize192.0ms

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))

rewrite2.0s

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×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `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 → 175

Calls

4 calls:

27.0ms	(cos (* 2.0 x))
610.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
242.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
1.1s	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series2.3s

Counts

4 → 12

Calls

4 calls:

25.0ms	(cos (* 2.0 x))
1.1s	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
365.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
801.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify4.6s

Counts

187 → 187

Iterations

Iter	Nodes
done	5018
2	1922
1	529
0	194

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.6b

localize155.0ms

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)))))

rewrite891.0ms

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×	`expm1-log1p-u` `unpow-prod-down` `insert-posit16` `log1p-expm1-u` `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 → 205

Calls

4 calls:

127.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
31.0ms	(cos (* 2.0 x))
334.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
354.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
30.0ms	(cos (* 2.0 x))
1.0s	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))
771.0ms	(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify4.1s

Counts

217 → 217

Iterations

Iter	Nodes
done	5001
2	1645
1	507
0	194

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.0b

localize203.0ms

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))))

rewrite696.0ms

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×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `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 → 276

Calls

4 calls:

35.0ms	(cos (* 2.0 x))
422.0ms	(/ (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))))))
89.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
85.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series2.3s

Counts

4 → 12

Calls

4 calls:

19.0ms	(cos (* 2.0 x))
1.0s	(/ (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))))))
654.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
635.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify5.1s

Counts

288 → 288

Iterations

Iter	Nodes
done	5006
2	2042
1	690
0	243

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.8b

regimes2.4s

Accuracy

0% (0.5b remaining)

Error of 2.6b against oracle of 2.1b and baseline of 2.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	9117×	body	80	valid
1.0s	765×	body	1280	valid
642.0ms	985×	body	640	valid
314.0ms	570×	body	320	valid
127.0ms	307×	body	160	valid