Details

sample131.0ms

Algorithm

intervals

Results

52.0ms	294×	body	80	valid
22.0ms	22×	body	1280	valid
22.0ms	29×	body	640	valid
13.0ms	23×	body	320	valid
4.0ms	12×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	3046
3	405
2	93
1	28
0	12

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x sin) (* x sin))
0.2b	(cos (* 2 x))
4.5b	(/ (/ (cos (* 2 x)) cos) (* (* (* x sin) (* x sin)) cos))
6.6b	(* (* (* x sin) (* x sin)) cos)

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-cbrt-cube` `add-exp-log`
61×	`pow1`
47×	`prod-exp` `cbrt-unprod`
31×	`times-frac`
30×	`pow-prod-down`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`cbrt-undiv` `div-exp`
13×	`associate-/l*`
4×	`associate-r` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`pow-plus` `div-sub` `associate-l` `*-commutative` `cos-2`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `swap-sqr` `unswap-sqr` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

22.0ms	(* (* x sin) (* x sin))
7.0ms	(cos (* 2 x))
69.0ms	(/ (/ (cos (* 2 x)) cos) (* (* (* x sin) (* x sin)) cos))
75.0ms	(* (* (* x sin) (* x sin)) cos)

series186.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x sin) (* x sin))
12.0ms	(cos (* 2 x))
91.0ms	(/ (/ (cos (* 2 x)) cos) (* (* (* x sin) (* x sin)) cos))
40.0ms	(* (* (* x sin) (* x sin)) cos)

simplify2.2s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	4487
1	654
0	210

prune575.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2 x))
0.5b	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

13.0ms	(cos (* 2 x))
111.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
15.0ms	(* (* sin x) cos)
25.0ms	(* (* sin x) cos)

series196.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cos (* 2 x))
111.0ms	(/ (cos (* 2 x)) (* (* (* sin x) cos) (* (* sin x) cos)))
30.0ms	(* (* sin x) cos)
46.0ms	(* (* sin x) cos)

simplify1.8s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	3098
1	447
0	142

prune549.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2 x))
1.3b	(/ (cos (* 2 x)) (* (* sin x) cos))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

369.0ms	(cos (* 2 x))
46.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
29.0ms	(* (* sin x) cos)
14.0ms	(* (* sin x) cos)

series153.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cos (* 2 x))
70.0ms	(/ (cos (* 2 x)) (* (* sin x) cos))
31.0ms	(* (* sin x) cos)
35.0ms	(* (* sin x) cos)

simplify2.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1534
1	261
0	99

prune468.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* (cos x) (cos x)) (* (sin x) (sin x)))
1.3b	(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* (* sin x) cos))
4.4b	(* (* sin x) cos)
4.4b	(* (* sin x) cos)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `pow-prod-down` `add-log-exp`
4×	`times-frac` `cos-mult` `insert-posit16` `sin-mult` `associate-/l*` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `difference-of-squares`
2×	`flip3--` `associate-l` `*-commutative` `frac-sub` `flip--` `sub-div`
1×	`sqr-cos` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `2-cos` `diff-log` `div-sub` `associate--l+` `sqr-sin` `div-inv` `associate--r-`

Counts

4 → 88

Calls

4 calls:

33.0ms	(- (* (cos x) (cos x)) (* (sin x) (sin x)))
41.0ms	(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* (* sin x) cos))
36.0ms	(* (* sin x) cos)
17.0ms	(* (* sin x) cos)

series202.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* (cos x) (cos x)) (* (sin x) (sin x)))
82.0ms	(/ (- (* (cos x) (cos x)) (* (sin x) (sin x))) (* (* sin x) cos))
35.0ms	(* (* sin x) cos)
35.0ms	(* (* sin x) cos)

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	3249
1	442
0	142

prune654.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes279.0ms

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	16
1	16
0	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	9117×	body	80	valid
1.3s	985×	body	640	valid
836.0ms	765×	body	1280	valid
372.0ms	570×	body	320	valid
158.0ms	307×	body	160	valid