Details

sample68.0ms

Algorithm

intervals

Results

23.0ms	272×	body	80	valid
13.0ms	31×	body	1280	valid
7.0ms	24×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	11×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.8b	(* (* x (pow sin 2.0)) x)
9.6b	(* x (pow sin 2.0))
14.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite176.0ms

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:

67.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
25.0ms	(* (* x (pow sin 2.0)) x)
13.0ms	(* x (pow sin 2.0))
64.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

456.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
201.0ms	(* (* x (pow sin 2.0)) x)
187.0ms	(* x (pow sin 2.0))
344.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	1502
1	414
0	166

prune631.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
14.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite538.0ms

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:

25.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
180.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
96.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
226.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
381.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
198.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
437.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify2.0s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	1830
1	556
0	198

prune580.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

0.6b

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

14.6b

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

466×	`add-exp-log`
382×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
52×	`div-exp`
34×	`cbrt-unprod`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`associate-l`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-undiv`
4×	`unpow-prod-down`
3×	`times-frac` `associate-/l*` `add-log-exp` `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

3 → 186

Calls

3 calls:

51.0ms

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

104.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

155.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

series1.2s

Counts

3 → 9

Calls

3 calls:

219.0ms

(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

524.0ms

(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))))

412.0ms

(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))))

simplify2.1s

Counts

195 → 195

Iterations

Iter	Nodes
done	5000
2	1652
1	483
0	174

prune581.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
0.6b	(/ (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))))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

1631×	`add-exp-log`
1472×	`prod-exp`
378×	`pow-to-exp` `pow-exp`
170×	`div-exp`
97×	`add-cbrt-cube`
60×	`cbrt-unprod`
15×	`associate-l`
11×	`pow1`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `add-cube-cbrt`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`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 → 451

Calls

4 calls:

143.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
122.0ms	(/ (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))))))
51.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
29.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

380.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
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))))))
317.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
281.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify2.0s

Counts

463 → 463

Iterations

Iter	Nodes
done	5128
2	2106
1	684
0	236

prune722.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 1.2b

regimes1.0s

Accuracy

0% (0.3b remaining)

Error of 2.6b against oracle of 2.3b and baseline of 2.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.3s	9044×	body	80	valid
950.0ms	852×	body	1280	valid
595.0ms	1001×	body	640	valid
244.0ms	601×	body	320	valid
66.0ms	304×	body	160	valid