Details

sample123.0ms

Algorithm

intervals

Results

49.0ms	297×	body	80	valid
25.0ms	28×	body	1280	valid
17.0ms	23×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid

simplify749.0ms

Counts

1 → 1

Iterations

Iter	Nodes
7	610
6	610
5	603
4	447
3	163
2	53
1	28
0	12

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* sin x) cos) (* (* sin x) cos))
0.6b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-l` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 138

Calls

4 calls:

97.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
109.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
30.0ms	(* (* sin x) cos)
29.0ms	(* (* sin x) cos)

series257.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
95.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
35.0ms	(* (* sin x) cos)
44.0ms	(* (* sin x) cos)

simplify12.6s

Counts

150 → 150

Iterations

Iter	Nodes
3	16995
2	1803
1	412
0	143

prune802.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.3b	(/ (cos (* 2 x)) (* (* sin x) cos))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-cbrt-cube` `add-exp-log`
30×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp`
16×	`times-frac`
14×	`pow1`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`associate-/l*`
6×	`associate-r` `pow-prod-down`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`div-sub`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `cos-2`
1×	`associate-/l/`

Counts

4 → 115

Calls

4 calls:

53.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
46.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
33.0ms	(* (* sin x) cos)
17.0ms	(* (* sin x) cos)

series258.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
56.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
47.0ms	(* (* sin x) cos)
45.0ms	(* (* sin x) cos)

simplify822.0ms

Counts

127 → 127

Iterations

Iter	Nodes
2	2275
1	470
0	161

prune949.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* (sin x) (sin x)) (* (* sin x) cos))
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)
5.6b	(* (* sin x) cos)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
18×	`prod-exp` `cbrt-unprod`
9×	`associate-r` `pow-prod-down`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-undiv` `div-exp`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `div-sub` `sqr-sin` `div-inv` `sin-mult` `associate-/l` `associate-/l/`

Counts

4 → 85

Calls

4 calls:

38.0ms	(/ (* (sin x) (sin x)) (* (* sin x) cos))
29.0ms	(* (* sin x) cos)
29.0ms	(* (* sin x) cos)
29.0ms	(* (* sin x) cos)

series203.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (* (sin x) (sin x)) (* (* sin x) cos))
47.0ms	(* (* sin x) cos)
44.0ms	(* (* sin x) cos)
39.0ms	(* (* sin x) cos)

simplify4.7s

Counts

97 → 97

Iterations

Iter	Nodes
3	11427
2	1399
1	273
0	95

prune898.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
0.6b	(/ (cos (* 2 x)) (* sin x))
5.5b	(/ (/ (cos (* 2 x)) (* sin x)) cos)
5.6b	(* (* sin x) cos)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

121×	`times-frac`
77×	`add-cbrt-cube` `add-exp-log`
51×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
35×	`associate-/l*`
34×	`cbrt-undiv` `div-exp`
20×	`prod-exp` `cbrt-unprod`
15×	`div-inv`
9×	`pow1`
6×	`div-sub`
5×	`associate-/r*`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `cos-2`
2×	`associate-/l/`
1×	`associate-l` `*-commutative`

Counts

4 → 180

Calls

4 calls:

43.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
15.0ms	(/ (cos (* 2 x)) (* sin x))
27.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)
30.0ms	(* (* sin x) cos)

series287.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (/ (/ (cos (* 2 x)) (* sin x)) cos) (* (* sin x) cos))
58.0ms	(/ (cos (* 2 x)) (* sin x))
60.0ms	(/ (/ (cos (* 2 x)) (* sin x)) cos)
38.0ms	(* (* sin x) cos)

simplify1.3s

Counts

192 → 192

Iterations

Iter	Nodes
2	3227
1	846
0	296

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes252.0ms

Accuracy

0% (2.9b remaining)

Error of 3.0b against oracle of 0.1b and baseline of 3.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.4s	9122×	body	80	valid
1.1s	872×	body	1280	valid
990.0ms	937×	body	640	valid
792.0ms	587×	body	320	valid
115.0ms	302×	body	160	valid