Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	297×	body	80	valid
11.0ms	23×	body	1280	valid
11.0ms	31×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	14×	body	160	valid

simplify5.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
6	4062
5	1352
4	542
3	196
2	66
1	28
0	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
0.8b	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
5.1b	(* sin (* x cos))
5.1b	(* sin (* x cos))

rewrite250.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 146

Calls

4 calls:

121.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
86.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
16.0ms	(* sin (* x cos))
18.0ms	(* sin (* x cos))

series261.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
114.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
39.0ms	(* sin (* x cos))
39.0ms	(* sin (* x cos))

simplify1.3s

Counts

158 → 158

Iterations

Iter	Nodes
done	5016
2	1756
1	403
0	147

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* sin (* x cos)))
0.5b	(/ (cos (* 2 x)) (* sin (* x cos)))
5.1b	(* sin (* x cos))
5.1b	(* sin (* x cos))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
32×	`add-cbrt-cube`
20×	`pow1`
18×	`prod-exp`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`div-exp` `pow-prod-down`
6×	`cbrt-undiv` `times-frac` `associate-l` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `div-inv`
1×	`div-sub` `cos-2` `inv-pow`

Counts

4 → 105

Calls

4 calls:

33.0ms	(/ 1 (* sin (* x cos)))
38.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
29.0ms	(* sin (* x cos))
30.0ms	(* sin (* x cos))

series163.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (* sin (* x cos)))
52.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
45.0ms	(* sin (* x cos))
41.0ms	(* sin (* x cos))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1093
1	302
0	128

prune473.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 sin) (* x cos)) (/ (cos (* 2 x)) (* sin (* x cos))))
0.5b	(/ (cos (* 2 x)) (* sin (* x cos)))
5.1b	(* sin (* x cos))
5.1b	(/ (/ 1 sin) (* x cos))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

222×	`add-exp-log`
132×	`add-cbrt-cube`
90×	`div-exp`
89×	`prod-exp`
59×	`times-frac`
51×	`cbrt-unprod`
48×	`cbrt-undiv`
33×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-l`
16×	`associate-/l*`
11×	`pow1`
10×	`rec-exp` `1-exp`
8×	`associate-r`
7×	`div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative`
1×	`frac-times` `div-sub` `associate-l/` `associate-r/` `cos-2` `unswap-sqr` `associate-/l/`

Counts

4 → 197

Calls

4 calls:

79.0ms	(* (/ (/ 1 sin) (* x cos)) (/ (cos (* 2 x)) (* sin (* x cos))))
38.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
27.0ms	(* sin (* x cos))
23.0ms	(/ (/ 1 sin) (* x cos))

series204.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (/ 1 sin) (* x cos)) (/ (cos (* 2 x)) (* sin (* x cos))))
45.0ms	(/ (cos (* 2 x)) (* sin (* x cos)))
28.0ms	(* sin (* x cos))
22.0ms	(/ (/ 1 sin) (* x cos))

simplify1.7s

Counts

209 → 209

Iterations

Iter	Nodes
done	5065
2	3541
1	831
0	293

prune737.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
0.5b	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
5.1b	(* sin (* x cos))
5.1b	(* sin (* x cos))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
35×	`add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
14×	`pow1`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
7×	`times-frac` `associate-/l*`
6×	`cbrt-prod` `associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `div-inv`

Counts

4 → 102

Calls

4 calls:

21.0ms	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
37.0ms	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
21.0ms	(* sin (* x cos))
17.0ms	(* sin (* x cos))

series286.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (cbrt (cos (* 2 x))) (* sin (* x cos)))
127.0ms	(/ (* (cbrt (cos (* 2 x))) (cbrt (cos (* 2 x)))) (* sin (* x cos)))
33.0ms	(* sin (* x cos))
32.0ms	(* sin (* x cos))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1215
1	308
0	129

prune549.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

regimes233.0ms

Accuracy

0% (0.7b remaining)

Error of 2.9b against oracle of 2.2b and baseline of 2.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	16

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.0s	9117×	body	80	valid
659.0ms	851×	body	1280	valid
599.0ms	950×	body	640	valid
219.0ms	582×	body	320	valid
136.0ms	331×	body	160	valid