Details

sample77.0ms

Algorithm

intervals

Results

37.0ms	52×	body	2560	valid
14.0ms	46×	body	1280	valid
7.0ms	37×	body	640	valid
5.0ms	39×	body	320	valid
3.0ms	64×	body	80	valid
2.0ms	18×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
15.6b	(/ (- 1.0 (cos x)) (* x x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 58

Calls

2 calls:

8.0ms	(- 1.0 (cos x))
26.0ms	(/ (- 1.0 (cos x)) (* x x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- 1.0 (cos x))
77.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	116	808
1	269	678
2	747	566
3	2669	526
done	5001	517

prune203.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 1/720 (pow x 4) 1/2)
11.2b	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/720 (pow x 4) 1/2)
1.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

series183.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(fma 1/720 (pow x 4) 1/2)
58.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify2.6s

Counts

26 → 26

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	35	298
1	55	292
2	140	255
3	556	255
4	3220	255
done	5000	255

prune121.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

23.0ms	(/ (/ (- 1.0 (cos x)) x) x)
44.0ms	(/ (- 1.0 (cos x)) x)
15.0ms	(- 1.0 (cos x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (/ (- 1.0 (cos x)) x) x)
73.0ms	(/ (- 1.0 (cos x)) x)
33.0ms	(- 1.0 (cos x))

simplify3.5s

Counts

174 → 174

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	259	2577
1	583	2358
2	1462	2183
3	4765	2121
done	5000	2121

prune501.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
360×	`add-sqr-sqrt` `*-un-lft-identity`
310×	`sqrt-prod`
232×	`add-cube-cbrt`
64×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r*`
22×	`sqrt-div`
21×	`associate-/r/`
18×	`prod-diff`
13×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube` `div-inv` `associate-/l*`
8×	`add-log-exp`
6×	`fma-neg`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 404

Calls

4 calls:

14.0ms	(/ x (sqrt (- 1.0 (cos x))))
60.0ms	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
16.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ x (sqrt (- 1.0 (cos x))))
62.0ms	(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
38.0ms	(- 1.0 (cos x))
39.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

416 → 416

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	462	10179
1	943	8950
2	3024	8128
done	5000	7825

prune982.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes84.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 32.0b

bsearch75.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.03981852127604897
8	-11.923248480236845	-0.0008047768791668974	-0.030846791202208904

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	46
1	30	44
done	30	44

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	1589×	body	2560	valid
603.0ms	1241×	body	1280	valid
480.0ms	1496×	body	640	valid
234.0ms	953×	body	320	valid
138.0ms	2253×	body	80	valid
115.0ms	468×	body	160	valid