Details

sample89.0ms

Algorithm

intervals

Results

31.0ms	51×	body	2560	valid
23.0ms	40×	body	1280	valid
12.0ms	57×	body	640	valid
4.0ms	27×	body	320	valid
4.0ms	63×	body	80	valid
2.0ms	18×	body	160	valid

simplify33.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize14.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
15.7b	(/ (- 1.0 (cos x)) (* x x))

rewrite88.0ms

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:

40.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 1.0 (cos x)) (* x x))

series124.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- 1.0 (cos x))
94.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: done (2.3s)

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

prune239.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite78.0ms

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:

26.0ms	(/ (/ (- 1.0 (cos x)) x) x)
22.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(- 1.0 (cos x))

series194.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (/ (- 1.0 (cos x)) x) x)
72.0ms	(/ (- 1.0 (cos x)) x)
40.0ms	(- 1.0 (cos x))

simplify3.3s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.8s)

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

prune371.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite115.0ms

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:

59.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
33.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(- 1.0 (cos x))

series150.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
56.0ms	(/ (- 1.0 (cos x)) x)
36.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

141 → 141

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	219	1855
1	556	1581
2	1741	1364
done	5001	1323

prune312.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
1.6b	(- (/ 1.0 x) (/ (cos x) x))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
287×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
227×	`add-cube-cbrt`
169×	`prod-diff`
39×	`div-inv`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/l*`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`distribute-rgt-out--` `add-log-exp`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub`

Counts

3 → 306

Calls

3 calls:

146.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
10.0ms	(/ (cos x) x)
51.0ms	(- (/ 1.0 x) (/ (cos x) x))

series269.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
39.0ms	(/ (cos x) x)
92.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify2.1s

Counts

315 → 315

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	442	10461
1	997	9121
2	2203	6316
done	5001	4297

prune426.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch109.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.029805544534800093
11	-2445851338.3862987	-4.2674702477225e-16	-0.03339438899281232

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	1593×	body	2560	valid
481.0ms	1486×	body	640	valid
474.0ms	1236×	body	1280	valid
201.0ms	946×	body	320	valid
142.0ms	2264×	body	80	valid
95.0ms	475×	body	160	valid