Details

analyze63.0ms

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
50%	50%	0.1%	5
50%	50%	0.1%	6
71.8%	28.1%	0.1%	7
73.4%	25%	1.7%	8
80.4%	16.4%	3.2%	9
80.8%	14%	5.2%	10
84.1%	8.8%	7.1%	11
84.2%	7.4%	8.4%	12
85.8%	4.5%	9.7%	13
85.8%	3.8%	10.4%	14

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

prune3.0ms

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: 0.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
48×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`distribute-lft-out`
15×	`distribute-rgt-out`
12×	`associate-/r*`
5×	`distribute-lft1-in` `count-2` `distribute-rgt1-in`
4×	`associate-/l*`
3×	`add-exp-log` `add-cbrt-cube`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 80

Calls

1 calls:

8.0ms

(/ (+ x y) (+ y y))

series6.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(/ (+ x y) (+ y y))

simplify59.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5602	942

prune62.0ms

Filtered

47 candidates to 83 candidates (-76.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0b

Counts

84 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (+ x y) (/ 1/2 y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
11×	`*-un-lft-identity`
10×	`times-frac`
9×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-l`
3×	`pow1`
2×	`frac-times` `flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `distribute-lft-out` `add-log-exp`

Counts

1 → 37

Calls

1 calls:

8.0ms

(* (+ x y) (/ 1/2 y))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(* (+ x y) (/ 1/2 y))

simplify49.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5161	366

prune45.0ms

Filtered

29 candidates to 40 candidates (-37.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	40	4	44

Merged error: 0b

Counts

44 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (/ (+ x y) (sqrt y)) (+ (sqrt y) (sqrt y)))
0.2b	(/ (+ x y) (sqrt y))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

1400×	`times-frac`
1255×	`*-un-lft-identity`
919×	`sqrt-prod`
917×	`add-sqr-sqrt`
685×	`add-cube-cbrt`
401×	`distribute-lft-out`
290×	`distribute-rgt-out`
58×	`distribute-lft1-in` `distribute-rgt1-in`
32×	`associate-/r` `associate-/l`
29×	`count-2` `div-inv`
9×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`pow1` `frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `add-log-exp`

Counts

2 → 847

Calls

2 calls:

29.0ms	(/ (/ (+ x y) (sqrt y)) (+ (sqrt y) (sqrt y)))
6.0ms	(/ (+ x y) (sqrt y))

series23.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(/ (/ (+ x y) (sqrt y)) (+ (sqrt y) (sqrt y)))
7.0ms	(/ (+ x y) (sqrt y))

simplify176.0ms

Algorithm

egg-herbie

Counts

853 → 853

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4947	15912
1	4947	15912

prune230.0ms

Filtered

199 candidates to 853 candidates (-328.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	852	1	853
Fresh	1	0	1
Picked	1	0	1
Done	2	0	2
Total	856	1	857

Merged error: 0b

Counts

857 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

6.0ms

(* 1/2 (/ x y))

series4.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* 1/2 (/ x y))

simplify84.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5745	229

prune36.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	1	36

Merged error: 0b

Counts

36 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample301.0ms

Algorithm

intervals

Results

174.0ms	8000×	body	80	valid
4.0ms	197×	body	80	invalid

Details

analyze63.0ms

sample13.0ms

simplify4.0ms

prune3.0ms

localize4.0ms

rewrite12.0ms

series6.0ms

simplify59.0ms

prune62.0ms

localize5.0ms

rewrite10.0ms

series5.0ms

simplify49.0ms

prune45.0ms

localize7.0ms

rewrite113.0ms

series23.0ms

simplify176.0ms

prune230.0ms

localize5.0ms

rewrite8.0ms

series4.0ms

simplify84.0ms

prune36.0ms

simplify1.0ms

end0.0ms

sample301.0ms

Profiling