Details

sample52.0ms

Algorithm

intervals

Results

25.0ms	57×	body	2560	valid
8.0ms	58×	body	640	valid
6.0ms	28×	body	1280	valid
3.0ms	27×	body	320	valid
2.0ms	75×	body	80	valid
1.0ms	11×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b	(- 1.0 (cos x))
16.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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:

4.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
49.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify34.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (28.0ms)

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

prune129.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	10	65

Merged error: 0.0b

Counts

65 → 10

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)
1.3b	(- 1.0 (cos x))

rewrite28.0ms

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:

9.0ms	(/ (/ (- 1.0 (cos x)) x) x)
7.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series110.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
42.0ms	(/ (- 1.0 (cos x)) x)
22.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (46.0ms)

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

prune248.0ms

Filtered

174 candidates to 113 candidates (64.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 0.0b

Counts

184 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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:

27.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms	(/ (cos x) x)
18.0ms	(- (/ 1.0 x) (/ (cos x) x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- (/ 1.0 x) (/ (cos x) x)) x)
29.0ms	(/ (cos x) x)
62.0ms	(- (/ 1.0 x) (/ (cos x) x))

simplify115.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 2 (71.0ms)

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

prune333.0ms

Filtered

315 candidates to 140 candidates (44.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	314	1	315
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	315	10	325

Merged error: 0.0b

Counts

325 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt` `times-frac`
35×	`*-un-lft-identity`
34×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`fma-neg` `associate-r` `prod-diff`
10×	`add-cbrt-cube`
9×	`div-inv`
6×	`associate-/l/`
5×	`pow1` `distribute-rgt-out--` `associate-*r/` `un-div-inv` `add-log-exp`
4×	`prod-exp` `frac-sub` `associate-/l*` `sub-div`
3×	`expm1-log1p-u` `div-exp` `associate-l` `associate-/r*` `log1p-expm1-u` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `flip--` `cbrt-unprod`
1×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `div-sub` `pow-prod-down` `clear-num` `*-commutative`

Counts

3 → 123

Calls

3 calls:

10.0ms	(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
8.0ms	(* (cos x) (/ 1 x))
8.0ms	(- (/ 1.0 x) (* (cos x) (/ 1 x)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
29.0ms	(* (cos x) (/ 1 x))
63.0ms	(- (/ 1.0 x) (* (cos x) (/ 1 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	520	986
1	2168	833
2	5003	785

prune200.0ms

Filtered

132 candidates to 100 candidates (75.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	131	11	142

Merged error: 0.0b

Counts

142 → 11

regimes54.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch51.0ms

Steps

Iters	Range		Point
6	0.011261476250181132	0.06406876111163662	0.03363822156293231
9	-3.7752751361666412	-2.6386627092684764e-08	-0.0354657383711672

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	11
1	32	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

722.0ms	1603×	body	2560	valid
277.0ms	1241×	body	1280	valid
221.0ms	1541×	body	640	valid
94.0ms	918×	body	320	valid
75.0ms	2208×	body	80	valid
35.0ms	489×	body	160	valid