Details

sample29.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

9.0ms	64×	body	1280	valid
4.0ms	126×	body	80	valid
4.0ms	33×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

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: 30.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4494	559
3	5003	559

prune128.0ms

Filtered

50 candidates to 77 candidates (-54.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Merged error: 0.2b

Counts

78 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.7b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `frac-sub`
5×	`associate-/r*` `add-log-exp`
4×	`frac-times` `flip3-+` `div-exp` `associate-l` `associate-*l/` `prod-exp` `associate-/r/` `flip-+`
3×	`flip3--` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `distribute-lft-out` `inv-pow`

Counts

3 → 108

Calls

3 calls:

5.0ms	(/ 1 (- x 1.0))
13.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series12.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ 1 (- x 1.0))
3.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	499	779
1	2438	701
2	5001	647

prune123.0ms

Filtered

68 candidates to 117 candidates (-72.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 0.2b

Counts

122 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
0.3b	(/ 1 (pow x 3))
0.3b	(/ (neg 1.0) (pow x 2))
4.6b	(- (/ (neg 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
101×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
45×	`unpow-prod-down`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`add-exp-log` `associate-/r*`
16×	`associate-r`
15×	`sqr-pow`
13×	`associate-/l*`
12×	`cube-prod`
11×	`unpow2`
10×	`unpow3` `add-cbrt-cube`
9×	`neg-mul-1` `div-exp`
7×	`div-inv` `distribute-lft-out`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`distribute-rgt-out`
4×	`cube-mult` `pow-to-exp` `pow-exp`
3×	`rec-exp` `1-exp` `associate-l` `frac-sub`
2×	`cbrt-undiv` `neg-sub0` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `div-sub` `frac-add` `clear-num` `flip-+` `associate--r+`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `pow-prod-down` `distribute-rgt1-in` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 241

Calls

4 calls:

34.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 3))
7.0ms	(/ (neg 1.0) (pow x 2))
23.0ms	(- (/ (neg 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
3.0ms	(/ 1 (pow x 3))
3.0ms	(/ (neg 1.0) (pow x 2))
4.0ms	(- (/ (neg 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

simplify138.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (119.0ms)

Iter	Nodes	Cost
0	792	1515
1	4636	1252
2	5001	1238

prune290.0ms

Filtered

123 candidates to 253 candidates (-105.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	253	5	258

Merged error: 0b

Counts

258 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.3b	(/ 3.0 (pow x 3))
0.3b	(/ (neg 1.0) (pow x 2))
4.6b	(- (/ (neg 1.0) (pow x 2)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
113×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
46×	`unpow-prod-down`
28×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
16×	`sqr-pow`
14×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod` `unpow2`
11×	`add-log-exp`
9×	`neg-mul-1` `unpow3`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-exp`
5×	`difference-of-squares`
4×	`pow1` `cube-mult` `distribute-rgt-out` `div-inv` `distribute-lft-out--`
3×	`frac-sub`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `pow-exp` `clear-num` `sum-log` `flip-+`
1×	`+-commutative` `associate--l-` `sub-neg` `flip3--` `distribute-frac-neg` `distribute-rgt1-in` `flip--` `associate--r+`

Counts

4 → 228

Calls

4 calls:

26.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (neg 1.0) (pow x 2))
84.0ms	(- (/ (neg 1.0) (pow x 2)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
4.0ms	(/ 3.0 (pow x 3))
3.0ms	(/ (neg 1.0) (pow x 2))
7.0ms	(- (/ (neg 1.0) (pow x 2)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify98.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	749	1634
1	3913	1435
2	5001	1433

prune294.0ms

Filtered

132 candidates to 240 candidates (-81.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	240	5	245

Merged error: 0b

Counts

245 → 5

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch52.0ms

Steps

Iters	Range		Point
11	6.5916173492213286e-09	1894315959611.4365	7922.853945838826
9	-1231365629.8151755	-6.487422286971009	-6970.534977222905

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21

end0.0ms

sample718.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

268.0ms	1736×	body	1280	valid
154.0ms	1247×	body	640	valid
126.0ms	4093×	body	80	valid
59.0ms	637×	body	320	valid
17.0ms	287×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Details

sample29.0ms

simplify18.0ms

prune2.0ms

localize6.0ms

rewrite44.0ms

series10.0ms

simplify145.0ms

prune128.0ms

localize7.0ms

rewrite31.0ms

series12.0ms

simplify64.0ms

prune123.0ms

localize13.0ms

rewrite77.0ms

series17.0ms

simplify138.0ms

prune290.0ms

localize11.0ms

rewrite131.0ms

series21.0ms

simplify98.0ms

prune294.0ms

regimes46.0ms

bsearch52.0ms

simplify1.0ms

end0.0ms

sample718.0ms

Profiling

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6