Details

analyze572.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample61.0ms

Algorithm

intervals

Results

21.0ms	41×	body	1280	valid
12.0ms	40×	body	640	valid
8.0ms	150×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	8×	body	640	invalid
2.0ms	4×	body	1280	invalid
2.0ms	12×	body	160	valid
2.0ms	8×	body	320	invalid
0.0ms	3×	body	160	invalid
0.0ms	5×	body	80	nan
0.0ms	1×	body	80	invalid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
6.7b	(pow (/ x (+ x y)) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

5.0ms	(/ x (+ x y))
10.0ms	(/ (pow (/ x (+ x y)) x) x)
6.0ms	(pow (/ x (+ x y)) x)

series46.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ x (+ x y))
20.0ms	(/ (pow (/ x (+ x y)) x) x)
21.0ms	(pow (/ x (+ x y)) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5011	2849

prune192.0ms

Filtered

134 candidates to 181 candidates (-35.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	8	182

Merged error: 1.1b

Counts

182 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (sqrt (/ x (+ x y))) x)
0.6b	(pow (sqrt (/ x (+ x y))) x)
6.3b	(sqrt (/ x (+ x y)))
6.3b	(sqrt (/ x (+ x y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
64×	`*-un-lft-identity`
50×	`times-frac`
46×	`add-sqr-sqrt`
42×	`unpow-prod-down`
40×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
8×	`associate-/r/`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 136

Calls

4 calls:

7.0ms	(pow (sqrt (/ x (+ x y))) x)
7.0ms	(pow (sqrt (/ x (+ x y))) x)
5.0ms	(sqrt (/ x (+ x y)))
5.0ms	(sqrt (/ x (+ x y)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (/ x (+ x y))) x)
33.0ms	(pow (sqrt (/ x (+ x y))) x)
11.0ms	(sqrt (/ x (+ x y)))
8.0ms	(sqrt (/ x (+ x y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5551	2408

prune185.0ms

Filtered

108 candidates to 148 candidates (-37.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	149	7	156

Merged error: 1.1b

Counts

156 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (/ x (+ x y))) x) (pow (/ x (+ x y)) (* x 1/2)))
0.6b	(pow (sqrt (/ x (+ x y))) x)
6.3b	(sqrt (/ x (+ x y)))
6.7b	(pow (/ x (+ x y)) (* x 1/2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

100×	`unpow-prod-down`
92×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
62×	`sqrt-prod`
49×	`add-cube-cbrt`
28×	`add-exp-log`
25×	`associate-l`
22×	`associate-r`
20×	`unswap-sqr`
15×	`distribute-lft-out`
13×	`pow-exp` `sqr-pow`
12×	`prod-exp`
10×	`associate-/r/`
9×	`pow-to-exp`
8×	`pow1`
6×	`add-cbrt-cube`
5×	`flip3-+` `flip-+` `div-inv`
4×	`pow-unpow` `pow-pow` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sqrt-div` `*-commutative` `sqrt-pow2` `cbrt-unprod`

Counts

4 → 187

Calls

4 calls:

27.0ms	(* (pow (sqrt (/ x (+ x y))) x) (pow (/ x (+ x y)) (* x 1/2)))
7.0ms	(pow (sqrt (/ x (+ x y))) x)
5.0ms	(sqrt (/ x (+ x y)))
6.0ms	(pow (/ x (+ x y)) (* x 1/2))

series131.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (pow (sqrt (/ x (+ x y))) x) (pow (/ x (+ x y)) (* x 1/2)))
33.0ms	(pow (sqrt (/ x (+ x y))) x)
8.0ms	(sqrt (/ x (+ x y)))
19.0ms	(pow (/ x (+ x y)) (* x 1/2))

simplify48.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5008	4859

prune328.0ms

Filtered

143 candidates to 199 candidates (-39.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	199	7	206

Merged error: 1.1b

Counts

206 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
0.6b	(pow (sqrt (/ (cbrt x) (cbrt (+ x y)))) x)
6.7b	(pow (/ x (+ x y)) (* x 1/2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

72×	`unpow-prod-down`
62×	`*-un-lft-identity`
54×	`times-frac`
48×	`cbrt-prod` `sqrt-prod`
44×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log` `distribute-lft-out`
8×	`pow1`
7×	`pow-unpow`
5×	`pow-pow`
4×	`pow-exp` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`cbrt-div` `flip3-+` `flip-+` `div-inv`
1×	`sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `sqrt-pow2`

Counts

4 → 127

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
12.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ x y)))) x)
6.0ms	(pow (/ x (+ x y)) (* x 1/2))

series82.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
12.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
29.0ms	(pow (sqrt (/ (cbrt x) (cbrt (+ x y)))) x)
19.0ms	(pow (/ x (+ x y)) (* x 1/2))

simplify74.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4929	2601
1	4929	2601

prune215.0ms

Filtered

105 candidates to 139 candidates (-32.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Merged error: 1.1b

Counts

146 → 7

regimes137.0ms

Accuracy

58.3% (4.3b remaining)

Error of 5.1b against oracle of 0.7b and baseline of 11.1b

bsearch200.0ms

Steps

Iters	Range		Point
10	1.0014567996717007e+254	5.496890872391325e+265	1.3882841915962162e+254
7	1.8794214866373997e+20	8.838201700038181e+21	1.9116918545050105e+20
9	-9.650792050718139e+82	-8.808528268941804e+73	-1.1947019381196716e+74

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	114	143
1	114	143

end0.0ms

sample1.9s

Algorithm

intervals

Results

734.0ms	1448×	body	1280	valid
371.0ms	1218×	body	640	valid
235.0ms	4307×	body	80	valid
146.0ms	720×	body	320	valid
70.0ms	233×	body	640	invalid
44.0ms	99×	body	1280	invalid
40.0ms	307×	body	160	valid
37.0ms	197×	body	320	invalid
15.0ms	126×	body	160	invalid
9.0ms	152×	body	80	invalid
8.0ms	201×	body	80	nan

Details

analyze572.0ms

sample61.0ms

simplify35.0ms

prune7.0ms

localize6.0ms

rewrite29.0ms

series46.0ms

simplify62.0ms

prune192.0ms

localize9.0ms

rewrite29.0ms

series84.0ms

simplify40.0ms

prune185.0ms

localize12.0ms

rewrite54.0ms

series131.0ms

simplify48.0ms

prune328.0ms

localize24.0ms

rewrite27.0ms

series82.0ms

simplify74.0ms

prune215.0ms

regimes137.0ms

bsearch200.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling