Details

sample107.0ms

Algorithm

intervals

Results

45.0ms	273×	body	80	valid
16.0ms	40×	body	640	valid
16.0ms	27×	body	1280	valid
6.0ms	19×	body	320	valid
2.0ms	7×	body	160	valid

simplify946.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b	(* (* x (pow sin 2.0)) x)
9.4b	(* x (pow sin 2.0))
17.8b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite195.0ms

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:

72.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
24.0ms	(* (* x (pow sin 2.0)) x)
21.0ms	(* x (pow sin 2.0))
72.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

405.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
154.0ms	(* (* x (pow sin 2.0)) x)
177.0ms	(* x (pow sin 2.0))
403.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.5s

Counts

135 → 135

Iterations

Useful iterations: 2 (412.0ms)

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

prune462.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.8b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite661.0ms

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)))
241.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
94.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
264.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
385.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
204.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
359.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.0s

Counts

206 → 206

Iterations

Useful iterations: 2 (579.0ms)

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

prune376.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.3b

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

0.3b

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

17.8b

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

rewrite335.0ms

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:

46.0ms

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

127.0ms

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

141.0ms

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

series941.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms

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

400.0ms

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

330.0ms

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

simplify1.8s

Counts

193 → 193

Iterations

Useful iterations: 2 (440.0ms)

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

prune280.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.3b

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

6.0b

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

12.9b

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

rewrite287.0ms

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:

109.0ms

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

123.0ms

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

30.0ms

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

series1.0s

Counts

3 → 9

Calls

3 calls:

410.0ms

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

313.0ms

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

289.0ms

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

simplify2.6s

Counts

191 → 191

Iterations

Useful iterations: 2 (583.0ms)

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

prune391.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.6b

regimes658.0ms

Accuracy

0% (1.6b remaining)

Error of 6.8b against oracle of 5.2b and baseline of 6.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	8967×	body	80	valid
689.0ms	1006×	body	640	valid
591.0ms	828×	body	1280	valid
327.0ms	589×	body	320	valid
80.0ms	295×	body	160	valid