Details

sample109.0ms

Algorithm

intervals

Results

32.0ms	300×	body	80	valid
17.0ms	20×	body	320	valid
15.0ms	24×	body	1280	valid
15.0ms	35×	body	640	valid
1.0ms	6×	body	160	valid

simplify1.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.1b	(* (* x (pow sin 2.0)) x)
6.1b	(* x (pow sin 2.0))
21.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite186.0ms

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` `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 → 115

Calls

4 calls:

74.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
22.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
69.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

420.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
193.0ms	(* (* x (pow sin 2.0)) x)
186.0ms	(* x (pow sin 2.0))
344.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.4s

Counts

127 → 127

Iterations

Useful iterations: 2 (424.0ms)

Iter	Nodes	Cost
0	171	1959
1	439	1821
2	2396	1563
done	5000	1563

prune386.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (* x (pow sin 2.0)) x)
6.1b	(* x (pow sin 2.0))
6.7b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
8.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

22.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* x (pow sin 2.0))
62.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
215.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

series997.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (* x (pow sin 2.0)) x)
176.0ms	(* x (pow sin 2.0))
361.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
289.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))

simplify1.8s

Counts

158 → 158

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	163	2848
1	434	2034
2	2225	1810
done	5000	1792

prune342.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
5.1b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
6.7b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
8.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1410×	`add-exp-log`
1300×	`prod-exp`
338×	`pow-to-exp` `pow-exp`
130×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`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 → 394

Calls

4 calls:

674.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
140.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
214.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
610.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
181.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
358.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
308.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))

simplify2.2s

Counts

406 → 406

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	259	13801
1	768	6413
2	3662	5877
done	5000	5817

prune523.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.5b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))))
6.7b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
8.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

rewrite970.0ms

Algorithm

rewrite-expression-head

Rules

1691×	`add-exp-log`
1549×	`prod-exp`
399×	`pow-to-exp` `pow-exp`
157×	`div-exp`
92×	`add-cbrt-cube`
59×	`cbrt-unprod`
15×	`associate-l`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 462

Calls

4 calls:

47.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
340.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))))
150.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
361.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
466.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))))
394.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))
358.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))

simplify2.1s

Counts

474 → 474

Iterations

Useful iterations: 2 (570.0ms)

Iter	Nodes	Cost
0	275	16226
1	809	7516
2	3488	6720
done	5000	6720

prune376.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

regimes457.0ms

Accuracy

0% (1.2b remaining)

Error of 5.9b against oracle of 4.7b and baseline of 5.9b

bsearch0.0ms

simplify6.0ms

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

1.5s	9191×	body	80	valid
983.0ms	818×	body	1280	valid
556.0ms	1002×	body	640	valid
170.0ms	567×	body	320	valid
65.0ms	333×	body	160	valid