Details

sample85.0ms

Algorithm

intervals

Results

29.0ms	287×	body	80	valid
14.0ms	34×	body	640	valid
14.0ms	24×	body	1280	valid
7.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	67	16
3	241	16
4	1097	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.8b	(* (* x (pow sin 2.0)) x)
6.4b	(* x (pow sin 2.0))
17.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite233.0ms

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:

85.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
34.0ms	(* (* x (pow sin 2.0)) x)
16.0ms	(* x (pow sin 2.0))
91.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

400.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
181.0ms	(* (* x (pow sin 2.0)) x)
148.0ms	(* x (pow sin 2.0))
368.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (343.0ms)

Iter	Nodes	Cost
0	179	2045
1	421	1897
2	1445	1617
done	5000	1617

prune478.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.6b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite703.0ms

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:

39.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
265.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
119.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
267.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.3s

Counts

4 → 12

Calls

4 calls:

221.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
465.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
172.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
395.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.3s

Counts

206 → 206

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	211	5143
1	545	3013
2	2109	2569
done	5000	2565

prune449.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.2b

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

17.6b

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

rewrite357.0ms

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:

80.0ms

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

103.0ms

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

148.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

219.0ms

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

462.0ms

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

468.0ms

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

simplify1.3s

Counts

193 → 193

Iterations

Useful iterations: 2 (390.0ms)

Iter	Nodes	Cost
0	188	5240
1	480	3102
2	1864	2616
done	5000	2616

prune425.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.6b

localize39.0ms

Local error

Found 3 expressions with local error:

0.2b

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

4.9b

(* (* (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))))

rewrite284.0ms

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:

97.0ms

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

118.0ms

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

55.0ms

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

series1.2s

Counts

3 → 9

Calls

3 calls:

448.0ms

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

463.0ms

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

306.0ms

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

simplify1.2s

Counts

191 → 191

Iterations

Useful iterations: 2 (457.0ms)

Iter	Nodes	Cost
0	191	5082
1	510	3288
2	1910	2764
done	5000	2764

prune320.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

regimes482.0ms

Accuracy

0% (2.1b remaining)

Error of 6.6b against oracle of 4.5b and baseline of 6.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	9189×	body	80	valid
747.0ms	990×	body	640	valid
747.0ms	618×	body	320	valid
572.0ms	783×	body	1280	valid
112.0ms	274×	body	160	valid