Details

sample126.0ms

Algorithm

intervals

Results

61.0ms	51×	body	2560	valid
35.0ms	86×	body	1280	valid
14.0ms	67×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

22.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

58 → 58

Iterations

Useful iterations: 4 (741.0ms)

Iter	Nodes	Cost
0	106	665
1	235	645
2	531	609
3	1194	609
4	3136	608
done	5000	608

prune154.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.1b	(* 1/24 (pow x 3))
0.3b	(* 1/240 (pow x 5))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

20.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
12.0ms	(* 1/24 (pow x 3))
11.0ms	(* 1/240 (pow x 5))

series162.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
40.0ms	(* 1/24 (pow x 3))
56.0ms	(* 1/240 (pow x 5))

simplify2.6s

Counts

78 → 78

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	123	847
1	304	752
2	956	704
3	4964	704
done	5000	704

prune189.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

543×	`times-frac`
517×	`add-sqr-sqrt`
337×	`*-un-lft-identity`
208×	`difference-of-squares`
205×	`add-cube-cbrt`
159×	`unpow-prod-down` `cube-prod`
105×	`sqr-pow`
81×	`associate-/l*`
65×	`distribute-lft-out--`
13×	`difference-cubes`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `pow-exp` `clear-num` `sum-log` `flip--` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 412

Calls

4 calls:

105.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
3.0ms	(pow (cos x) 3)
7.0ms	(+ (cos x) 1.0)
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series480.0ms

Counts

4 → 12

Calls

4 calls:

383.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))
29.0ms	(pow (cos x) 3)
17.0ms	(+ (cos x) 1.0)
50.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify1.8s

Counts

424 → 424

Iterations

Useful iterations: 2 (839.0ms)

Iter	Nodes	Cost
0	592	16449
1	1404	15551
2	4409	15381
done	5002	15381

prune1.1s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.4b	(+ (cos x) 1.0)
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.4b	(- 1.0 (cos x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1`
10×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`+-commutative` `sqr-cos` `flip3-+` `sum-log` `flip-+`
1×	`pow2` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

10.0ms	(* (cos x) (cos x))
6.0ms	(+ (cos x) 1.0)
12.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series95.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (cos x) (cos x))
11.0ms	(+ (cos x) 1.0)
43.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	125	726
1	285	587
2	843	535
3	2987	529
done	5001	525

prune214.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.2b

regimes106.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.2b

bsearch106.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.024047924432618564
9	-76786.820650899	-0.0002772006047103471	-0.019390100626972877

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	48	102
1	63	100
done	63	100

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1706×	body	2560	valid
1.2s	2759×	body	1280	valid
427.0ms	1810×	body	640	valid
144.0ms	907×	body	320	valid
49.0ms	461×	body	160	valid
29.0ms	7×	body	5120	valid
22.0ms	350×	body	80	valid