Details

sample102.0ms

Algorithm

intervals

Results

25.0ms	313×	body	80	valid
18.0ms	6×	body	160	valid
12.0ms	36×	body	640	valid
12.0ms	25×	body	1280	valid
4.0ms	15×	body	320	valid

simplify9.1s

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: 28.4b

localize40.0ms

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)
8.1b	(* x (pow sin 2.0))
19.1b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite348.0ms

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:

135.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
49.0ms	(* (* x (pow sin 2.0)) x)
27.0ms	(* x (pow sin 2.0))
121.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series2.2s

Counts

4 → 12

Calls

4 calls:

851.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
332.0ms	(* (* x (pow sin 2.0)) x)
372.0ms	(* x (pow sin 2.0))
652.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify3.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1452
1	415
0	170

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 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)
19.1b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.1s

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×	`insert-posit16` `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 → 190

Calls

4 calls:

66.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
403.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
155.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
491.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series2.5s

Counts

4 → 12

Calls

4 calls:

381.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
993.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
451.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
719.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify4.1s

Counts

202 → 202

Iterations

Iter	Nodes
done	5184
2	2129
1	557
0	202

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.5b

localize46.0ms

Local error

Found 3 expressions with local error:

0.3b

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

0.6b

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

19.1b

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

rewrite444.0ms

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`
8×	`associate-l`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-undiv`
5×	`pow1`
3×	`unpow-prod-down` `times-frac` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv` `sqr-pow`

Counts

3 → 181

Calls

3 calls:

73.0ms

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

171.0ms

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

173.0ms

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

series2.3s

Counts

3 → 9

Calls

3 calls:

397.0ms

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

986.0ms

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

872.0ms

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

simplify4.1s

Counts

190 → 190

Iterations

Iter	Nodes
done	5067
2	1835
1	494
0	180

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.7b

localize46.0ms

Local error

Found 3 expressions with local error:

0.6b

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

6.2b

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

14.2b

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

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

455×	`add-exp-log`
371×	`prod-exp`
89×	`pow-to-exp` `pow-exp`
58×	`add-cbrt-cube`
53×	`div-exp`
33×	`cbrt-unprod`
8×	`associate-l`
7×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`unpow-prod-down` `times-frac` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow-prod-down` `div-inv` `sqr-pow`

Counts

3 → 179

Calls

3 calls:

155.0ms

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

132.0ms

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

45.0ms

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

series2.4s

Counts

3 → 9

Calls

3 calls:

1.0s

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

790.0ms

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

619.0ms

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

simplify4.1s

Counts

188 → 188

Iterations

Iter	Nodes
done	5032
2	2013
1	527
0	182

prune998.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.0b

regimes2.3s

Accuracy

0% (2.6b remaining)

Error of 6.7b against oracle of 4.0b and baseline of 6.7b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	8918×	body	80	valid
950.0ms	944×	body	640	valid
544.0ms	848×	body	1280	valid
213.0ms	563×	body	320	valid
67.0ms	300×	body	160	valid