Details

sample53.0ms

Algorithm

intervals

Results

22.0ms	51×	body	2560	valid
9.0ms	42×	body	1280	valid
7.0ms	51×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	19×	body	160	valid

simplify15.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b	(- 1.0 (cos x))
14.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite33.0ms

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:

11.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series61.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: done (1.5s)

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

prune134.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/720 (pow x 4) 1/2)
12.8b	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

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:

0.0ms	(fma 1/720 (pow x 4) 1/2)
0.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

series126.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma 1/720 (pow x 4) 1/2)
44.0ms	(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify1.7s

Counts

26 → 26

Iterations

Useful iterations: 2 (23.0ms)

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

prune80.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.4b	(- 1.0 (cos x))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
46×	`times-frac`
36×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `prod-diff`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 132

Calls

3 calls:

18.0ms	(/ (- 1.0 (cos x)) x)
38.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
7.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- 1.0 (cos x)) x)
42.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

141 → 141

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	219	1855
1	556	1581
2	1734	1364
done	5001	1323

prune261.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
0.2b	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
1.4b	(- 1.0 (cos x))
1.4b	(- 1.0 (cos x))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
48×	`add-exp-log`
42×	`add-cube-cbrt`
37×	`times-frac`
30×	`add-cbrt-cube`
29×	`associate-r`
25×	`sqrt-prod`
22×	`prod-exp`
21×	`associate-l`
18×	`prod-diff`
12×	`sqrt-div` `cbrt-unprod`
11×	`pow1` `frac-times` `div-exp`
8×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
7×	`associate-*l/`
6×	`cbrt-undiv` `fma-neg` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`sub-neg` `diff-log` `*-commutative` `div-inv`

Counts

4 → 173

Calls

4 calls:

66.0ms	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
50.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
7.0ms	(- 1.0 (cos x))
8.0ms	(- 1.0 (cos x))

series125.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 1 x) (* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x)))
45.0ms	(* (sqrt (- 1.0 (cos x))) (/ (sqrt (- 1.0 (cos x))) x))
19.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

185 → 185

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	259	3333
1	616	2315
2	2027	1902
done	5000	1784

prune343.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

regimes116.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch64.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.034744172255630555
9	-76786.820650899	-0.0002772006047103471	-0.02623489072028306

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	48
1	33	48
done	33	48

end0.0ms

sample1.6s

Algorithm

intervals

Results

790.0ms	1714×	body	2560	valid
290.0ms	1271×	body	1280	valid
209.0ms	1449×	body	640	valid
92.0ms	911×	body	320	valid
72.0ms	2190×	body	80	valid
33.0ms	465×	body	160	valid