Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample52.0ms

Algorithm

intervals

Results

27.0ms	252×	body	80	valid
2.0ms	3×	body	1280	invalid
1.0ms	3×	body	640	invalid
1.0ms	11×	body	80	invalid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	invalid
1.0ms	2×	body	320	invalid
0.0ms	1×	body	640	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4986	28
1	4986	28

prune14.0ms

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: 12.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
0.0b	(- (* K (/ (+ m n) 2.0)) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
31.1b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`sub-neg` `pow-unpow` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`flip3--` `flip--`
1×	`cos-diff` `pow-to-exp` `cos-sum` `pow-pow` `times-frac` `pow-exp` `sum-log` `distribute-lft-out` `associate--r+` `sqr-pow`

Counts

4 → 56

Calls

4 calls:

15.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
7.0ms	(- (* K (/ (+ m n) 2.0)) M)
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

series118.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
13.0ms	(- (* K (/ (+ m n) 2.0)) M)
43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

simplify61.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4888	1044
1	4888	1044

prune155.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 0.9b

Counts

69 → 3

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
0.0b	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-log-exp`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
2×	`diff-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `times-frac` `pow-exp` `flip--` `flip-+` `associate--r+` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

13.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
15.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
12.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series121.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
43.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4929	925
1	4929	925

prune106.0ms

Filtered

43 candidates to 57 candidates (-32.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	57	3	60

Merged error: 0.9b

Counts

60 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M))
6.1b	(* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))
31.2b	(cos (/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M)))
36.1b	(/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `times-frac`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-*r/` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`flip3-+` `associate-l` `pow-prod-down` `associate-/r` `flip-+` `associate-/l`
2×	`frac-times` `flip3--` `div-sub` `associate-*l/` `associate-/r/` `flip--` `associate-/l/`
1×	`cos-diff` `sub-neg` `frac-2neg` `diff-log` `associate-r` `clear-num` `*-commutative` `div-inv`

Counts

4 → 78

Calls

4 calls:

18.0ms	(- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M))
16.0ms	(* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))
22.0ms	(cos (/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M)))
29.0ms	(/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M))

series201.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M))
10.0ms	(* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))
71.0ms	(cos (/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M)))
81.0ms	(/ (- (* K (* K (* (+ m n) (/ (/ (+ m n) 2.0) 2.0)))) (* M M)) (+ (* K (/ (+ m n) 2.0)) M))

simplify34.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5523	2085

prune234.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	88	5	93

Merged error: 0.8b

Counts

93 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b	(/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M)))
0.6b	(/ 1 (- (* K (/ (+ m n) 2.0)) M))
33.5b	(cos (/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
63×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
58×	`add-cube-cbrt`
28×	`add-exp-log`
18×	`associate-/r*`
16×	`div-exp`
11×	`associate-/r/` `add-cbrt-cube`
8×	`pow1` `rec-exp` `1-exp`
6×	`unpow-prod-down` `div-inv` `associate-/l*`
5×	`flip3--` `pow-flip` `flip--`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `inv-pow`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `pow-exp` `remove-double-div` `distribute-lft-out--` `sqr-pow`

Counts

4 → 153

Calls

4 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms	(/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M)))
10.0ms	(/ 1 (- (* K (/ (+ m n) 2.0)) M))
11.0ms	(cos (/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
13.0ms	(/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M)))
20.0ms	(/ 1 (- (* K (/ (+ m n) 2.0)) M))
21.0ms	(cos (/ 1 (/ 1 (- (* K (/ (+ m n) 2.0)) M))))

simplify95.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4901	2522
1	4901	2522

prune235.0ms

Filtered

85 candidates to 165 candidates (-94.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	165	5	170

Merged error: 0.8b

Counts

170 → 5

regimes413.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 1.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

860.0ms	7850×	body	80	valid
42.0ms	65×	body	1280	invalid
38.0ms	86×	body	640	invalid
35.0ms	303×	body	80	invalid
26.0ms	57×	body	640	valid
25.0ms	67×	body	320	invalid
25.0ms	39×	body	1280	valid
13.0ms	38×	body	320	valid
7.0ms	33×	body	160	invalid
4.0ms	4×	body	2560	invalid
3.0ms	16×	body	160	valid

Details

analyze2.4s

sample52.0ms

simplify44.0ms

prune14.0ms

localize27.0ms

rewrite42.0ms

series118.0ms

simplify61.0ms

prune155.0ms

localize14.0ms

rewrite42.0ms

series121.0ms

simplify46.0ms

prune106.0ms

localize29.0ms

rewrite87.0ms

series201.0ms

simplify34.0ms

prune234.0ms

localize23.0ms

rewrite53.0ms

series97.0ms

simplify95.0ms

prune235.0ms

regimes413.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

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