Details

sample136.0ms

Algorithm

intervals

Results

57.0ms	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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize20.0ms

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)

rewrite223.0ms

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×	`expm1-log1p-u` `associate-r` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `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 → 145

Calls

4 calls:

23.0ms	(* (* x sin) (* x sin))
7.0ms	(cos (* 2 x))
79.0ms	(/ (/ (cos (* 2 x)) cos) (* (* (* x sin) (* x sin)) cos))
111.0ms	(* (* (* x sin) (* x sin)) cos)

series158.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* x sin) (* x sin))
9.0ms	(cos (* 2 x))
76.0ms	(/ (/ (cos (* 2 x)) cos) (* (* (* x sin) (* x sin)) cos))
40.0ms	(* (* (* x sin) (* x sin)) cos)

simplify2.0s

Counts

157 → 157

Iterations

Iter	Nodes
done	5000
2	4467
1	657
0	218

prune499.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.7b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

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-l` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

8.0ms	(cos (* x 2))
78.0ms	(/ (cos (* x 2)) (* (* cos (* x sin)) (* cos (* x sin))))
19.0ms	(* cos (* x sin))
21.0ms	(* cos (* x sin))

series146.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cos (* x 2))
77.0ms	(/ (cos (* x 2)) (* (* cos (* x sin)) (* cos (* x sin))))
30.0ms	(* cos (* x sin))
29.0ms	(* cos (* x sin))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
2	3072
1	428
0	142

prune455.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.7b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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-l` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`associate-r` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 78

Calls

4 calls:

7.0ms	(cos (* x 2))
22.0ms	(/ (cos (* x 2)) (* cos (* x sin)))
14.0ms	(* cos (* x sin))
17.0ms	(* cos (* x sin))

series103.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cos (* x 2))
38.0ms	(/ (cos (* x 2)) (* cos (* x sin)))
27.0ms	(* cos (* x sin))
29.0ms	(* cos (* x sin))

simplify907.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1078
1	227
0	99

prune434.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2))))
1.3b	(/ (cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2)))) (* cos (* x sin)))
4.4b	(* cos (* x sin))
4.4b	(* cos (* x sin))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
20×	`add-cbrt-cube`
14×	`pow1`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `times-frac` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-prod` `cbrt-undiv` `div-exp`
2×	`cbrt-div` `associate-r` `associate-l/` `cos-mult` `-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `pow1/3` `pow3` `rem-cbrt-cube` `div-inv` `associate-/l/`

Counts

4 → 85

Calls

4 calls:

55.0ms	(cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2))))
53.0ms	(/ (cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2)))) (* cos (* x sin)))
14.0ms	(* cos (* x sin))
14.0ms	(* cos (* x sin))

series136.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2))))
53.0ms	(/ (cbrt (* (* (cos (* x 2)) (cos (* x 2))) (cos (* x 2)))) (* cos (* x sin)))
35.0ms	(* cos (* x sin))
36.0ms	(* cos (* x sin))

simplify825.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1307
1	266
0	116

prune406.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.7b

regimes241.0ms

Accuracy

0% (0.4b remaining)

Error of 2.6b against oracle of 2.2b and baseline of 2.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	9117×	body	80	valid
802.0ms	985×	body	640	valid
736.0ms	765×	body	1280	valid
354.0ms	570×	body	320	valid
104.0ms	307×	body	160	valid