Details

analyze4.0ms

Algorithm: search

sample24.0ms

Algorithm

intervals

Results

8.0ms	56×	body	1280	valid
5.0ms	39×	body	640	valid
4.0ms	134×	body	80	valid
1.0ms	16×	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

prune6.0ms

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: 28.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
27.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune185.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.0b

Counts

114 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 135

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
10.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	441	990
1	1497	930
2	5001	917

prune207.0ms

Filtered

93 candidates to 147 candidates (-58.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Merged error: 0.0b

Counts

152 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`log-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`difference-of-squares`
16×	`exp-sum`
7×	`add-exp-log`
6×	`pow1` `log-div` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod` `flip3--` `flip--` `associate-/l*`
3×	`exp-diff` `frac-sub`
2×	`associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 130

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
31.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
26.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
9.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	475	1328
1	1529	1251
2	5001	1219

prune207.0ms

Filtered

86 candidates to 142 candidates (-65.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	142	5	147

Merged error: 0.0b

Counts

147 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
18.5b	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `frac-sub` `flip--`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
19.0ms	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(cbrt x)
10.0ms	(- (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	206	412
1	647	370
2	2823	328
3	5001	325

prune67.0ms

Filtered

45 candidates to 58 candidates (-28.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

regimes82.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

analyze4.0ms

Algorithm: search

sample703.0ms

Algorithm

intervals

Results

251.0ms	1646×	body	1280	valid
158.0ms	1336×	body	640	valid
127.0ms	4064×	body	80	valid
57.0ms	631×	body	320	valid
19.0ms	323×	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

analyze4.0ms

sample24.0ms

simplify18.0ms

prune6.0ms

localize6.0ms

rewrite43.0ms

series13.0ms

simplify44.0ms

prune185.0ms

localize9.0ms

rewrite77.0ms

series23.0ms

simplify46.0ms

prune207.0ms

localize9.0ms

rewrite99.0ms

series26.0ms

simplify53.0ms

prune207.0ms

localize10.0ms

rewrite23.0ms

series74.0ms

simplify75.0ms

prune67.0ms

regimes82.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample703.0ms

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