Details

sample52.0ms

Algorithm

intervals

Results

22.0ms	49×	body	2560	valid
10.0ms	46×	body	1280	valid
5.0ms	41×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	17×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b	(- 1.0 (cos x))
15.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

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

series67.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
48.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317
done	5001	317

prune130.0ms

Pruning

11 alts after pruning (11 fresh and 0 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)
2.5b	(- 1.0 (cos x))

rewrite54.0ms

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:

20.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series111.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (/ (- 1.0 (cos x)) x) x)
43.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify56.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	592	1453
1	2212	1292
2	5001	1283
done	5001	1283

prune292.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (log (exp (- 1.0 (cos x)))) x)
0.1b	(exp (- 1.0 (cos x)))
2.5b	(- 1.0 (cos x))
2.5b	(log (exp (- 1.0 (cos x))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
30×	`exp-prod` `log-pow`
27×	`times-frac` `prod-diff`
22×	`exp-sum`
14×	`log-prod`
9×	`pow1` `associate-/l*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `exp-diff` `fma-neg` `associate-/r*`
2×	`log-div` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 141

Calls

4 calls:

49.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
16.0ms	(exp (- 1.0 (cos x)))
10.0ms	(- 1.0 (cos x))
16.0ms	(log (exp (- 1.0 (cos x))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (log (exp (- 1.0 (cos x)))) x)
45.0ms	(exp (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))
20.0ms	(log (exp (- 1.0 (cos x))))

simplify41.0ms

Counts

153 → 153

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	393	1192
1	1234	873
2	5001	725
done	5001	725

prune271.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b	(/ (cos x) x)
2.5b	(- (/ 1.0 x) (/ (cos x) x))

rewrite144.0ms

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:

79.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
8.0ms	(/ (cos x) x)
35.0ms	(- (/ 1.0 x) (/ (cos x) x))

series187.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
34.0ms	(/ (cos x) x)
56.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify102.0ms

Counts

315 → 315

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	1009	6352
1	3221	4216
2	5001	3627
done	5001	3627

prune367.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.3b

bsearch61.0ms

Steps

Iters	Range		Point
9	0.00021078761332869983	22.544919195950573	0.03662167515047411
8	-1.6220908197114983	-0.002799490342594777	-0.038128431313299106

simplify1.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11
done	28	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

713.0ms	1573×	body	2560	valid
279.0ms	1254×	body	1280	valid
205.0ms	1484×	body	640	valid
105.0ms	944×	body	320	valid
83.0ms	2284×	body	80	valid
33.0ms	461×	body	160	valid