Details

sample121.0ms

Algorithm

intervals

Results

41.0ms	276×	body	80	valid
30.0ms	36×	body	1280	valid
18.0ms	33×	body	640	valid
11.0ms	24×	body	320	valid
2.0ms	6×	body	160	valid

simplify687.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* sin x) cos) (* (* sin x) cos))
0.4b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
4.0b	(* (* sin x) cos)
4.0b	(* (* sin x) cos)

rewrite213.0ms

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×	`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 → 134

Calls

4 calls:

93.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
89.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
13.0ms	(* (* sin x) cos)
13.0ms	(* (* sin x) cos)

series267.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (* (* sin x) cos) (* (* sin x) cos))
115.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
28.0ms	(* (* sin x) cos)
40.0ms	(* (* sin x) cos)

simplify10.5s

Counts

146 → 146

Iterations

Iter	Nodes
3	17644
2	1793
1	402
0	140

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
0.8b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.0b	(* (* sin x) cos)
4.0b	(* (* sin x) cos)

rewrite117.0ms

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×	`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 → 111

Calls

4 calls:

60.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
22.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
17.0ms	(* (* sin x) cos)
13.0ms	(* (* sin x) cos)

series259.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (/ (cos (* 2 x)) (* (* sin x) cos)) (* (* sin x) cos))
46.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
44.0ms	(* (* sin x) cos)
45.0ms	(* (* sin x) cos)

simplify676.0ms

Counts

123 → 123

Iterations

Iter	Nodes
2	2253
1	457
0	158

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos (* 2 x)) (/ 1 (* (* sin x) cos))) (* (* sin x) cos))
0.8b	(/ 1 (* (* sin x) cos))
4.0b	(* (* sin x) cos)
4.0b	(* (* sin x) cos)

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

200×	`add-exp-log`
105×	`prod-exp`
98×	`add-cbrt-cube`
57×	`div-exp`
45×	`cbrt-unprod`
27×	`cbrt-undiv`
20×	`pow1`
12×	`rec-exp` `1-exp`
9×	`pow-prod-down`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`times-frac` `associate-/l*` `add-log-exp`
3×	`pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `div-inv` `associate-/l/`
1×	`associate-*r/` `un-div-inv` `inv-pow`

Counts

4 → 132

Calls

4 calls:

89.0ms	(/ (* (cos (* 2 x)) (/ 1 (* (* sin x) cos))) (* (* sin x) cos))
26.0ms	(/ 1 (* (* sin x) cos))
14.0ms	(* (* sin x) cos)
24.0ms	(* (* sin x) cos)

series177.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* (cos (* 2 x)) (/ 1 (* (* sin x) cos))) (* (* sin x) cos))
22.0ms	(/ 1 (* (* sin x) cos))
38.0ms	(* (* sin x) cos)
31.0ms	(* (* sin x) cos)

simplify1.1s

Counts

144 → 144

Iterations

Iter	Nodes
2	3519
1	552
0	181

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* sin (* cos x)) (* sin (* cos x)))
0.4b	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
3.5b	(* sin (* cos x))
3.5b	(* sin (* cos x))

rewrite239.0ms

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-l`
4×	`add-log-exp`
3×	`times-frac` `pow-plus` `associate-r` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 134

Calls

4 calls:

81.0ms	(* (* sin (* cos x)) (* sin (* cos x)))
105.0ms	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
23.0ms	(* sin (* cos x))
25.0ms	(* sin (* cos x))

series228.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* sin (* cos x)) (* sin (* cos x)))
80.0ms	(/ (cos (* 2 x)) (* (* sin (* cos x)) (* sin (* cos x))))
31.0ms	(* sin (* cos x))
47.0ms	(* sin (* cos x))

simplify14.6s

Counts

146 → 146

Iterations

Iter	Nodes
3	20492
2	1864
1	384
0	138

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes271.0ms

Accuracy

0% (2.4b remaining)

Error of 2.6b against oracle of 0.2b and baseline of 2.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.1s	8981×	body	80	valid
1.3s	789×	body	1280	valid
817.0ms	1005×	body	640	valid
436.0ms	589×	body	320	valid
110.0ms	286×	body	160	valid