Details

sample48.0ms

Algorithm

intervals

Results

19.0ms	43×	body	2560	valid
8.0ms	37×	body	1280	valid
7.0ms	54×	body	640	valid
3.0ms	78×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	20×	body	160	valid

simplify8.0ms

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))

rewrite15.0ms

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:

3.0ms	(- 1.0 (cos x))
10.0ms	(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- 1.0 (cos x))
47.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

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

prune138.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

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))

rewrite32.0ms

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:

12.0ms	(/ (/ (- 1.0 (cos x)) x) x)
9.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
41.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

simplify59.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (45.0ms)

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

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
79×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
53×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `flip--` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `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 → 183

Calls

4 calls:

20.0ms	(/ (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))

series126.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (cbrt (pow (- 1.0 (cos x)) 3)) x)
18.0ms	(cbrt (pow (- 1.0 (cos x)) 3))
48.0ms	(pow (- 1.0 (cos x)) 3)
18.0ms	(- 1.0 (cos x))

simplify68.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	472	1433
1	1886	1248
2	5002	1217

prune318.0ms

Pruning

10 alts after pruning (9 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))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

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

series555.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
176.0ms	(cbrt x)
183.0ms	(cbrt x)
19.0ms	(- 1.0 (cos x))

simplify93.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	183	370
1	534	270
2	2582	252
3	5001	237

prune173.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes55.0ms

Accuracy

99% (0.3b remaining)

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

bsearch70.0ms

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	30	17
1	30	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

720.0ms	1542×	body	2560	valid
303.0ms	1302×	body	1280	valid
211.0ms	1512×	body	640	valid
93.0ms	926×	body	320	valid
69.0ms	2266×	body	80	valid
31.0ms	452×	body	160	valid