Details

sample88.0ms

Algorithm

intervals

Results

36.0ms	307×	body	80	valid
16.0ms	36×	body	1280	valid
7.0ms	24×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.6b	(* (* x (pow sin 2.0)) x)
10.5b	(* x (pow sin 2.0))
18.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite190.0ms

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` `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 → 123

Calls

4 calls:

64.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
28.0ms	(* (* x (pow sin 2.0)) x)
14.0ms	(* x (pow sin 2.0))
76.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

374.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
220.0ms	(* (* x (pow sin 2.0)) x)
189.0ms	(* x (pow sin 2.0))
371.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify2.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1436
1	432
0	174

prune859.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
2.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.3b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite744.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 194

Calls

4 calls:

308.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
46.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
98.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
268.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

449.0ms	(/ (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)))
238.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
386.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.9s

Counts

206 → 206

Iterations

Iter	Nodes
done	5002
2	2135
1	557
0	206

prune823.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.4b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

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

18.3b

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

rewrite343.0ms

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×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `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 → 192

Calls

3 calls:

146.0ms

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

38.0ms

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

143.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

487.0ms

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

200.0ms

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

392.0ms

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

simplify1.7s

Counts

201 → 201

Iterations

Iter	Nodes
done	5002
2	1594
1	494
0	180

prune682.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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))))))
0.2b	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite450.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 459

Calls

4 calls:

161.0ms	(/ (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))))))
136.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
38.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
26.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.6s

Counts

4 → 12

Calls

4 calls:

472.0ms	(/ (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))))))
450.0ms	(* (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
348.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
349.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify2.1s

Counts

471 → 471

Iterations

Iter	Nodes
done	5303
2	1985
1	665
0	242

prune762.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.3b

regimes875.0ms

Accuracy

0% (0.5b remaining)

Error of 2.7b against oracle of 2.1b and baseline of 2.7b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	9028×	body	80	valid
614.0ms	816×	body	1280	valid
583.0ms	949×	body	640	valid
449.0ms	309×	body	160	valid
231.0ms	560×	body	320	valid