Details

sample95.0ms

Algorithm

intervals

Results

18.0ms	46×	body	1280	valid
17.0ms	57×	body	640	valid
17.0ms	276×	body	80	nan
14.0ms	121×	body	80	valid
6.0ms	26×	body	320	valid
1.0ms	6×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 20.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
16.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
64.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
14.0ms	(/ 1.0 (sqrt x))
25.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5076	1846

prune512.0ms

Filtered

103 candidates to 145 candidates (-40.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	10	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Merged error: 19.9b

Counts

146 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

rewrite750.0ms

Algorithm

rewrite-expression-head

Rules

2937×	`times-frac`
2554×	`*-un-lft-identity`
1354×	`add-sqr-sqrt`
778×	`add-cube-cbrt`
708×	`distribute-lft-out`
508×	`sqrt-prod`
368×	`distribute-lft-out--`
211×	`div-inv`
144×	`difference-of-squares`
64×	`distribute-rgt-out--`
45×	`associate-/l*`
37×	`associate-/r/`
27×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
2×	`flip3--` `flip3-+` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`sub-neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 751

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
267.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
8.0ms	(/ 1.0 (sqrt x))
186.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
39.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
18.0ms	(/ 1.0 (sqrt x))
8.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify434.0ms

Algorithm

egg-herbie

Counts

763 → 763

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4983	23240
1	4983	23240

prune2.3s

Filtered

283 candidates to 763 candidates (-169.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	759	4	763
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	767	6	773

Merged error: 5.7b

Counts

773 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ 1.0 x)))
0.2b	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1.0 x)))))
0.3b	(/ 1 (sqrt x))
1.9b	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

950×	`*-un-lft-identity`
855×	`times-frac`
452×	`add-sqr-sqrt`
314×	`distribute-lft-out`
236×	`add-cube-cbrt`
220×	`sqrt-prod`
144×	`distribute-lft-out--`
103×	`div-inv`
72×	`difference-of-squares`
29×	`associate-/r*`
21×	`associate-/l*`
14×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`pow1`
6×	`pow-flip` `add-log-exp`
5×	`div-exp` `associate-/r/`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
2×	`rec-exp` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `1-exp` `frac-sub` `flip--` `flip-+` `inv-pow`
1×	`sub-neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 411

Calls

4 calls:

12.0ms	(/ 1 (sqrt (+ 1.0 x)))
90.0ms	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1.0 x)))))
7.0ms	(/ 1 (sqrt x))
26.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ 1.0 x)))
30.0ms	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ 1.0 x)))))
12.0ms	(/ 1 (sqrt x))
7.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

simplify185.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5122	10468

prune1.1s

Filtered

146 candidates to 423 candidates (-189.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	425	4	429

Merged error: 5.7b

Counts

429 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 x))
0.2b	(/ 1 (sqrt (+ 1.0 x)))
0.2b	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (pow x -1/2) (/ 1 (sqrt (+ 1.0 x)))))
1.9b	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

262×	`*-un-lft-identity`
220×	`times-frac`
163×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
61×	`distribute-lft-out`
56×	`distribute-lft-out--`
33×	`div-inv`
28×	`difference-of-squares`
21×	`associate-/l*`
16×	`associate-/r*` `sqrt-prod`
12×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`pow1` `associate-/r/` `add-log-exp`
4×	`div-exp`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
2×	`flip3--` `sqrt-div` `frac-sub` `flip--`
1×	`sub-neg` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `div-sub` `inv-pow`

Counts

4 → 222

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 x))
6.0ms	(/ 1 (sqrt (+ 1.0 x)))
60.0ms	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (pow x -1/2) (/ 1 (sqrt (+ 1.0 x)))))
30.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (+ 1.0 x))
8.0ms	(/ 1 (sqrt (+ 1.0 x)))
47.0ms	(/ (- (/ 1.0 x) (/ 1.0 (+ 1.0 x))) (+ (pow x -1/2) (/ 1 (sqrt (+ 1.0 x)))))
4.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

simplify155.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4930	4978
1	4930	4978

prune791.0ms

Filtered

134 candidates to 234 candidates (-74.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	234	4	238

Merged error: 5.7b

Counts

238 → 4

regimes64.0ms

Accuracy

0% (0.3b remaining)

Error of 5.5b against oracle of 5.3b and baseline of 5.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

538.0ms	1816×	body	640	valid
486.0ms	8017×	body	80	nan
449.0ms	1168×	body	1280	valid
313.0ms	4079×	body	80	valid
141.0ms	640×	body	320	valid
44.0ms	297×	body	160	valid

Details

sample95.0ms

simplify21.0ms

prune11.0ms

localize14.0ms

rewrite104.0ms

series58.0ms

simplify58.0ms

prune512.0ms

localize28.0ms

rewrite750.0ms

series77.0ms

simplify434.0ms

prune2.3s

localize21.0ms

rewrite227.0ms

series58.0ms

simplify185.0ms

prune1.1s

localize30.0ms

rewrite114.0ms

series64.0ms

simplify155.0ms

prune791.0ms

regimes64.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling