Details

sample109.0ms

Algorithm

intervals

Results

42.0ms	309×	body	80	valid
24.0ms	21×	body	1280	valid
15.0ms	27×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2531
6	2531
5	1352
4	542
3	196
2	66
1	28
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (* sin cos)) (* x (* sin cos)))
0.3b	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
6.8b	(* x (* sin cos))
6.8b	(* x (* sin cos))

rewrite230.0ms

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×	`insert-posit16` `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 → 138

Calls

4 calls:

92.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
92.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
23.0ms	(* x (* sin cos))
19.0ms	(* x (* sin cos))

series240.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
98.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
32.0ms	(* x (* sin cos))
37.0ms	(* x (* sin cos))

simplify876.0ms

Counts

150 → 150

Iterations

Iter	Nodes
done	2010
2	2010
1	401
0	141

prune479.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* x 2)) (* sin (* cos x))) (* sin (* cos x)))
0.9b	(/ (cos (* x 2)) (* sin (* cos x)))
3.4b	(* sin (* cos x))
3.4b	(* sin (* cos x))

rewrite105.0ms

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-l` `pow-prod-down`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative`
1×	`associate-/l/`

Counts

4 → 113

Calls

4 calls:

48.0ms	(/ (/ (cos (* x 2)) (* sin (* cos x))) (* sin (* cos x)))
26.0ms	(/ (cos (* x 2)) (* sin (* cos x)))
16.0ms	(* sin (* cos x))
13.0ms	(* sin (* cos x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (/ (cos (* x 2)) (* sin (* cos x))) (* sin (* cos x)))
51.0ms	(/ (cos (* x 2)) (* sin (* cos x)))
33.0ms	(* sin (* cos x))
37.0ms	(* sin (* cos x))

simplify875.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
2	2000
1	437
0	153

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* x 2)) sin)
0.2b	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* sin (* cos x)))
3.4b	(* sin (* cos x))
3.5b	(/ (/ (cos (* x 2)) sin) (* cos x))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
92×	`add-cbrt-cube` `add-exp-log`
43×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
33×	`associate-/l*`
26×	`prod-exp` `cbrt-unprod`
9×	`pow1` `div-inv`
5×	`associate-/r*`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down`
2×	`associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 171

Calls

4 calls:

21.0ms	(/ (cos (* x 2)) sin)
49.0ms	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* sin (* cos x)))
21.0ms	(* sin (* cos x))
28.0ms	(/ (/ (cos (* x 2)) sin) (* cos x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (cos (* x 2)) sin)
90.0ms	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* sin (* cos x)))
28.0ms	(* sin (* cos x))
54.0ms	(/ (/ (cos (* x 2)) sin) (* cos x))

simplify1.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	2004
2	2004
1	699
0	267

prune741.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* x 2)) sin)
0.2b	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* (* cos x) sin))
3.4b	(* (* cos x) sin)
3.5b	(/ (/ (cos (* x 2)) sin) (* cos x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
92×	`add-cbrt-cube` `add-exp-log`
43×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
33×	`associate-/l*`
26×	`prod-exp` `cbrt-unprod`
9×	`pow1` `div-inv`
5×	`associate-/r*`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down`
2×	`associate-/l/`
1×	`associate-l` `*-commutative`

Counts

4 → 171

Calls

4 calls:

12.0ms	(/ (cos (* x 2)) sin)
54.0ms	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* (* cos x) sin))
20.0ms	(* (* cos x) sin)
15.0ms	(/ (/ (cos (* x 2)) sin) (* cos x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (cos (* x 2)) sin)
87.0ms	(/ (/ (/ (cos (* x 2)) sin) (* cos x)) (* (* cos x) sin))
33.0ms	(* (* cos x) sin)
46.0ms	(/ (/ (cos (* x 2)) sin) (* cos x))

simplify1.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	2000
2	2000
1	735
0	268

prune938.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes258.0ms

Accuracy

0% (2.5b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 2.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.4s	9077×	body	80	valid
911.0ms	798×	body	1280	valid
841.0ms	950×	body	640	valid
517.0ms	596×	body	320	valid
103.0ms	282×	body	160	valid