Details

sample90.0ms

Algorithm

intervals

Results

34.0ms	288×	body	80	valid
14.0ms	39×	body	640	valid
13.0ms	24×	body	1280	valid
5.0ms	17×	body	320	valid
2.0ms	9×	body	160	valid

simplify972.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	242	16
4	1255	16
done	5001	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.7b	(* (* x (pow sin 2.0)) x)
8.6b	(* x (pow sin 2.0))
15.7b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite258.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 123

Calls

4 calls:

100.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
36.0ms	(* (* x (pow sin 2.0)) x)
20.0ms	(* x (pow sin 2.0))
93.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

414.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
177.0ms	(* (* x (pow sin 2.0)) x)
146.0ms	(* x (pow sin 2.0))
356.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	179	2045
1	457	1907
2	2414	1649
done	5001	1649

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.7b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite762.0ms

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` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
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×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 194

Calls

4 calls:

47.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
313.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
113.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
272.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
447.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
190.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
335.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.1s

Counts

206 → 206

Iterations

Useful iterations: 2 (629.0ms)

Iter	Nodes	Cost
0	211	5143
1	597	3013
2	3852	2569
done	5001	2569

prune443.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.6b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.4b

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

15.7b

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

rewrite471.0ms

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` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv`
5×	`pow1`
3×	`expm1-log1p-u` `unpow-prod-down` `times-frac` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

3 → 184

Calls

3 calls:

76.0ms

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

185.0ms

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

185.0ms

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

series1.0s

Counts

3 → 9

Calls

3 calls:

216.0ms

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

435.0ms

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

383.0ms

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

simplify2.0s

Counts

193 → 193

Iterations

Useful iterations: 2 (512.0ms)

Iter	Nodes	Cost
0	188	5240
1	546	3102
2	2918	2616
done	5001	2616

prune286.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.4b

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

6.3b

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

11.3b

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

rewrite337.0ms

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×	`cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`expm1-log1p-u` `unpow-prod-down` `times-frac` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

3 → 182

Calls

3 calls:

119.0ms

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

127.0ms

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

65.0ms

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

series1.2s

Counts

3 → 9

Calls

3 calls:

440.0ms

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

381.0ms

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

346.0ms

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

simplify2.6s

Counts

191 → 191

Iterations

Useful iterations: 2 (668.0ms)

Iter	Nodes	Cost
0	191	5082
1	586	3288
2	3140	2764
done	5000	2764

prune364.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.4b

regimes577.0ms

Accuracy

0% (1.6b remaining)

Error of 6.5b against oracle of 4.9b and baseline of 6.5b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	21	32
done	21	32

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	9053×	body	80	valid
648.0ms	987×	body	640	valid
628.0ms	776×	body	1280	valid
278.0ms	566×	body	320	valid
73.0ms	323×	body	160	valid