Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	56×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	114×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	23×	body	160	valid

simplify20.0ms

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

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: 33.4b

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))
6.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite53.0ms

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))
8.0ms	(/ (+ x 1.0) (- x 1.0))
36.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune189.0ms

Filtered

113 candidates to 76 candidates (67.3%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.9b	(/ (- 1.0) (pow x 2))
6.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

61.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
93.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
38.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	738	1754
1	3448	1596
2	5001	1578

prune351.0ms

Filtered

246 candidates to 133 candidates (54.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	245	6	251

Merged error: 0b

Counts

251 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 3.0 (pow x 3))
0.9b	(/ (- 1.0) (pow x 2))
2.6b	(log (exp (/ (- 1.0) (pow x 2))))
10.3b	(- (- (log (exp (/ (- 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

200×	`times-frac`
138×	`add-sqr-sqrt`
132×	`*-un-lft-identity`
125×	`add-cube-cbrt`
86×	`log-pow`
84×	`exp-prod`
76×	`unpow-prod-down`
51×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
26×	`sqr-pow`
21×	`unpow2`
20×	`associate-/r*`
17×	`neg-mul-1`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*`
8×	`associate--l+` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `log-prod` `div-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`cube-mult` `unpow3`
3×	`diff-log` `distribute-frac-neg` `div-inv`
2×	`cbrt-undiv` `neg-sub0` `exp-neg` `pow-to-exp` `sub-neg` `log-div` `flip3--` `frac-2neg` `div-sub` `pow-exp` `clear-num` `frac-sub` `flip--`
1×	`associate--l-` `exp-diff` `rem-log-exp` `log-rec`

Counts

4 → 307

Calls

4 calls:

5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
17.0ms	(log (exp (/ (- 1.0) (pow x 2))))
95.0ms	(- (- (log (exp (/ (- 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
25.0ms	(log (exp (/ (- 1.0) (pow x 2))))
37.0ms	(- (- (log (exp (/ (- 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	847	1976
1	3414	1734
2	5003	1703

prune566.0ms

Filtered

319 candidates to 185 candidates (58.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	319	6	325

Merged error: 0b

Counts

325 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.2b	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.7b	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
6.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite119.0ms

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:

8.0ms	(/ (+ x 1.0) (- x 1.0))
37.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
31.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
36.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
214.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
132.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (36.0ms)

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

prune211.0ms

Filtered

142 candidates to 88 candidates (62.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	142	6	148

Merged error: 0b

Counts

148 → 6

regimes56.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.3b

bsearch104.0ms

Steps

Iters	Range		Point
9	62623256.830634765	2087876908255263.8	63442066.52193849
10	-206683631373.734	-17.831791951177678	-19229.509282320705

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	42	23

end0.0ms

sample629.0ms

Algorithm

intervals

Results

217.0ms	1702×	body	1280	valid
127.0ms	1284×	body	640	valid
114.0ms	4091×	body	80	valid
48.0ms	635×	body	320	valid
15.0ms	288×	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

sample24.0ms

simplify20.0ms

prune2.0ms

localize6.0ms

rewrite53.0ms

series201.0ms

simplify43.0ms

prune189.0ms

localize11.0ms

rewrite177.0ms

series165.0ms

simplify96.0ms

prune351.0ms

localize13.0ms

rewrite140.0ms

series126.0ms

simplify96.0ms

prune566.0ms

localize9.0ms

rewrite119.0ms

series519.0ms

simplify56.0ms

prune211.0ms

regimes56.0ms

bsearch104.0ms

simplify2.0ms

end0.0ms

sample629.0ms

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