Details

analyze1.7s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 27.253101%

Guaranteed chance to sample good point: 46.087758%

sample63.0ms

Algorithm

intervals

Results

21.0ms	42×	body	1280	valid
9.0ms	32×	body	640	valid
8.0ms	147×	body	80	valid
5.0ms	27×	body	320	valid
4.0ms	15×	body	640	invalid
1.0ms	5×	body	320	invalid
1.0ms	8×	body	160	valid
0.0ms	4×	body	160	invalid
0.0ms	1×	body	1280	invalid
0.0ms	7×	body	80	invalid
0.0ms	2×	body	80	nan

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (6.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

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: 12.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.1b	(pow (/ x (+ x y)) x)

rewrite35.0ms

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:

14.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series45.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

simplify96.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	752	1628
1	3787	1586
2	5001	1586

prune223.0ms

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: 0.7b

Counts

182 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
1.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`add-exp-log`
15×	`*-un-lft-identity`
13×	`unpow-prod-down`
12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
8×	`associate-/r/`
5×	`pow1` `pow-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3` `distribute-lft-out`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series132.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (+ x y))
32.0ms	(cbrt (+ x y))
33.0ms	(cbrt (+ x y))
36.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	579	936
1	2000	885
2	5001	831

prune137.0ms

Filtered

64 candidates to 85 candidates (-32.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 0.7b

Counts

93 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt x)
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))

series119.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
31.0ms	(cbrt (+ x y))
31.0ms	(cbrt (+ x y))
33.0ms	(cbrt (+ x y))

simplify181.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	167	366
1	354	344
2	998	310
3	4983	297
4	5003	297

prune98.0ms

Filtered

53 candidates to 65 candidates (-22.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Merged error: 0.7b

Counts

71 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (pow (/ x (+ x y)) x) x))
7.1b	(pow (/ x (+ x y)) x)
7.1b	(pow (/ x (+ x y)) x)
7.1b	(pow (/ x (+ x y)) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
117×	`*-un-lft-identity`
108×	`unpow-prod-down`
81×	`add-sqr-sqrt` `add-cube-cbrt`
70×	`cbrt-prod`
18×	`distribute-lft-out`
13×	`add-exp-log`
12×	`associate-/r/`
9×	`pow-unpow`
7×	`pow1` `div-inv`
6×	`flip3-+` `pow-exp` `flip-+` `sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-exp`
1×	`cbrt-div` `pow1/3`

Counts

4 → 178

Calls

4 calls:

11.0ms	(cbrt (/ (pow (/ x (+ x y)) x) x))
7.0ms	(pow (/ x (+ x y)) x)
7.0ms	(pow (/ x (+ x y)) x)
9.0ms	(pow (/ x (+ x y)) x)

series99.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (/ (pow (/ x (+ x y)) x) x))
22.0ms	(pow (/ x (+ x y)) x)
18.0ms	(pow (/ x (+ x y)) x)
18.0ms	(pow (/ x (+ x y)) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	919	2341
1	3802	2269
2	5002	2262

prune568.0ms

Filtered

142 candidates to 190 candidates (-33.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	188	8	196

Merged error: 0.7b

Counts

196 → 8

Details

analyze1.7s

sample63.0ms

simplify113.0ms

prune7.0ms

localize7.0ms

rewrite35.0ms

series45.0ms

simplify96.0ms

prune223.0ms

localize17.0ms

rewrite26.0ms

series132.0ms

simplify59.0ms

prune137.0ms

localize13.0ms

rewrite11.0ms

series119.0ms

simplify181.0ms

prune98.0ms

localize12.0ms

rewrite43.0ms

series99.0ms

simplify105.0ms

prune568.0ms

regimes141.0ms

bsearch1.0ms

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