Details

sample54.0ms

Algorithm

intervals

Results

24.0ms	47×	body	2560	valid
9.0ms	45×	body	1280	valid
6.0ms	44×	body	640	valid
4.0ms	38×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	11×	body	160	valid

simplify14.0ms

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: 32.4b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite30.0ms

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:

7.0ms	(- 1.0 (cos x))
21.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 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

prune123.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(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))

series125.0ms

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

prune71.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite56.0ms

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)
18.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series108.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (/ (- 1.0 (cos x)) x) x)
46.0ms	(/ (- 1.0 (cos x)) x)
19.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.1s)

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

prune286.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
0.1b	(/ (- 1.0 (cos x)) x)
2.4b	(- 1.0 (cos x))

rewrite70.0ms

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-l`
17×	`add-cbrt-cube`
13×	`associate-r`
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` `un-div-inv` `*-commutative`

Counts

3 → 133

Calls

3 calls:

39.0ms	(* (/ (- 1.0 (cos x)) x) (/ 1 x))
18.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series105.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify1.3s

Counts

142 → 142

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	219	1855
1	571	1582
2	1612	1359
done	5000	1318

prune222.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes44.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch65.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.03227596253233406
10	-21283307590.397102	-3.152803306627408e-07	-0.03309682507506567

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	39
1	28	30
done	28	30

end0.0ms

sample1.6s

Algorithm

intervals

Results

742.0ms	1602×	body	2560	valid
285.0ms	1266×	body	1280	valid
213.0ms	1456×	body	640	valid
94.0ms	949×	body	320	valid
70.0ms	2234×	body	80	valid
34.0ms	493×	body	160	valid