Details

analyze49.0ms

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
56.2%	43.7%	0.1%	6
65.6%	34.3%	0.1%	7
76.5%	23.4%	0.1%	8
82%	18%	0.1%	9
87.8%	12.1%	0.1%	10
90.7%	9.2%	0.1%	11
93.8%	6.1%	0.1%	12
95.3%	4.6%	0.1%	13
96.8%	3.1%	0.1%	14

sample10.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

prune4.0ms

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: 0.0b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (+ x y) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `add-log-exp`
3×	`sum-log` `distribute-lft-out`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+l+` `flip3-+` `add-cbrt-cube` `flip-+`

Counts

1 → 15

Calls

1 calls:

5.0ms

(+ (+ x y) x)

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(+ (+ x y) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5128	116

prune19.0ms

Filtered

11 candidates to 18 candidates (-63.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	2	19

Merged error: 0.0b

Counts

19 → 2

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x y))
0.0b	(+ x (+ x y))
0.3b	(* (sqrt (+ x (+ x y))) (sqrt (+ x (+ x y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
38×	`sqrt-prod`
30×	`distribute-lft-out`
23×	`add-sqr-sqrt`
18×	`pow1`
16×	`swap-sqr`
13×	`add-log-exp`
12×	`sqrt-div`
11×	`add-cube-cbrt`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `associate-l` `flip-+`
6×	`sum-log`
5×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-+r+` `associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 99

Calls

3 calls:

6.0ms	(+ x (+ x y))
5.0ms	(+ x (+ x y))
14.0ms	(* (sqrt (+ x (+ x y))) (sqrt (+ x (+ x y))))

series14.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x y))
4.0ms	(+ x (+ x y))
7.0ms	(* (sqrt (+ x (+ x y))) (sqrt (+ x (+ x y))))

simplify48.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5358	833

prune63.0ms

Filtered

49 candidates to 108 candidates (-120.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	108	2	110

Merged error: 0.0b

Counts

110 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ x y))
0.3b	(* (sqrt (+ x (+ x y))) (sqrt (+ (+ x x) y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 57

Calls

2 calls:

5.0ms	(+ x (+ x y))
16.0ms	(* (sqrt (+ x (+ x y))) (sqrt (+ (+ x x) y)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ x (+ x y))
7.0ms	(* (sqrt (+ x (+ x y))) (sqrt (+ (+ x x) y)))

simplify31.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4934	648
1	4934	648

prune59.0ms

Filtered

41 candidates to 63 candidates (-53.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	62	3	65

Merged error: 0.0b

Counts

65 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (sqrt (+ (+ x x) y)) (sqrt (+ (+ x x) y)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
38×	`sqrt-prod`
24×	`distribute-lft-out`
21×	`add-sqr-sqrt`
16×	`pow1` `swap-sqr`
12×	`sqrt-div`
9×	`add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `associate-r` `associate-l`
6×	`flip3-+` `flip-+`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`add-exp-log` `pow-prod-down` `pow-sqr` `add-cbrt-cube`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 69

Calls

1 calls:

18.0ms

(* (sqrt (+ (+ x x) y)) (sqrt (+ (+ x x) y)))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (sqrt (+ (+ x x) y)) (sqrt (+ (+ x x) y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4998	631
1	4998	631

prune43.0ms

Filtered

30 candidates to 72 candidates (-140.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	0	0
Picked	1	0	1
Done	2	0	2
Total	74	1	75

Merged error: 0b

Counts

75 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end0.0ms

sample229.0ms

Algorithm

intervals

Results

121.0ms	8000×	body	80	valid
0.0ms	3×	body	80	invalid

Details

analyze49.0ms

sample10.0ms

simplify3.0ms

prune4.0ms

localize3.0ms

rewrite6.0ms

series4.0ms

simplify54.0ms

prune19.0ms

localize5.0ms

rewrite28.0ms

series14.0ms

simplify48.0ms

prune63.0ms

localize11.0ms

rewrite23.0ms

series11.0ms

simplify31.0ms

prune59.0ms

localize5.0ms

rewrite21.0ms

series7.0ms

simplify44.0ms

prune43.0ms

simplify1.0ms

end0.0ms

sample229.0ms

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