Details

sample54.0ms

Algorithm

intervals

Results

23.0ms	49×	body	2560	valid
10.0ms	49×	body	1280	valid
7.0ms	52×	body	640	valid
2.0ms	24×	body	320	valid
2.0ms	62×	body	80	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: 33.1b

localize7.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite33.0ms

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))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- 1.0 (cos x))
44.0ms	(/ (- 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

prune132.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(* 1/24 (pow x 2))
10.2b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

12.0ms	(* 1/24 (pow x 2))
0.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series72.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(* 1/24 (pow x 2))
47.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify103.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	139	194
1	532	171
2	2601	171
3	5001	170

prune110.0ms

Pruning

9 alts after pruning (8 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)
1.8b	(- 1.0 (cos x))

rewrite55.0ms

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

series110.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (43.0ms)

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

prune285.0ms

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 (/ (- (cos x) 1.0) x)) x)
0.1b	(/ (- (cos x) 1.0) x)
1.8b	(- (cos x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r` `associate-/l`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `mul-1-neg` `diff-log` `div-sub` `associate-*r/` `distribute-frac-neg`

Counts

3 → 95

Calls

3 calls:

16.0ms	(/ (* -1 (/ (- (cos x) 1.0) x)) x)
20.0ms	(/ (- (cos x) 1.0) x)
8.0ms	(- (cos x) 1.0)

series132.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (* -1 (/ (- (cos x) 1.0) x)) x)
47.0ms	(/ (- (cos x) 1.0) x)
21.0ms	(- (cos x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	446	680
1	2049	544
2	5001	536

prune172.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes45.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch57.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.03384107969428519
9	-3096.4512561506854	-0.0006592480666379122	-0.033917851243536225

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	39	15
2	39	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

709.0ms	1569×	body	2560	valid
284.0ms	1248×	body	1280	valid
210.0ms	1497×	body	640	valid
96.0ms	967×	body	320	valid
73.0ms	2257×	body	80	valid
33.0ms	462×	body	160	valid