Details

sample48.0ms

Algorithm

intervals

Results

19.0ms	43×	body	2560	valid
8.0ms	37×	body	1280	valid
8.0ms	54×	body	640	valid
3.0ms	78×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	20×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize6.0ms

Local error

Found 2 expressions with local error:

2.8b	(- 1.0 (cos x))
14.5b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune115.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.2b	(/ (- 1.0 (cos x)) x)
2.8b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 147

Calls

3 calls:

14.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series104.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
18.0ms	(- 1.0 (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	531	1270
1	1899	1197
2	5001	1186

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
0.3b	(cbrt (pow (- 1.0 (cos x)) 3))
0.4b	(pow (- 1.0 (cos x)) 3)
2.8b	(- 1.0 (cos x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
72×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
46×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3--` `flip--`
3×	`pow-unpow` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

17.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
5.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
5.0ms	(pow (- 1.0 (cos x)) 3)
3.0ms	(- 1.0 (cos x))

series127.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
23.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
43.0ms	(pow (- 1.0 (cos x)) 3)
18.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	409	1242
1	1611	1149
2	5002	1118

prune297.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
2.8b	(- 1.0 (cos x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 47

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
3.0ms	(- 1.0 (cos x))

series555.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
174.0ms	(cbrt x)
181.0ms	(cbrt x)
18.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	126	193
1	315	179
2	921	173
3	5001	173

prune148.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

regimes57.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.3b

bsearch68.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	0.03326480281497669
9	-13600.963204601821	-0.00047371797307045637	-0.02973539225823786

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

705.0ms	1542×	body	2560	valid
296.0ms	1302×	body	1280	valid
225.0ms	1512×	body	640	valid
102.0ms	926×	body	320	valid
76.0ms	2266×	body	80	valid
34.0ms	452×	body	160	valid