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

sample48.0ms

Algorithm

intervals

Results

27.0ms	252×	body	80	valid
1.0ms	2×	body	1280	invalid
1.0ms	2×	body	640	valid
1.0ms	2×	body	320	invalid
1.0ms	1×	body	1280	valid
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	320	valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5355	28

prune16.0ms

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: 15.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (/ (+ m n) 2.0))
0.0b	(- (* K (/ (+ m n) 2.0)) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.1b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
14×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `cos-diff` `pow-to-exp` `cos-sum` `flip3--` `pow-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `-commutative` `flip--` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

9.0ms	(* K (/ (+ m n) 2.0))
7.0ms	(- (* K (/ (+ m n) 2.0)) M)
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

series84.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* K (/ (+ m n) 2.0))
12.0ms	(- (* K (/ (+ m n) 2.0)) M)
42.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4942	955
1	4942	955

prune184.0ms

Filtered

62 candidates to 87 candidates (-40.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.8b

Counts

88 → 4

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`add-cbrt-cube` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `times-frac` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

2 → 32

Calls

2 calls:

14.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify30.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5124	513

prune82.0ms

Filtered

29 candidates to 38 candidates (-31.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Merged error: 0.8b

Counts

42 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.4b	(cos (- (* (* (cbrt K) (cbrt K)) (* (+ m n) (/ (cbrt K) 2.0))) M))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `sub-neg` `cos-sum`

Counts

4 → 42

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
15.0ms	(cos (- (* (* (cbrt K) (cbrt K)) (* (+ m n) (/ (cbrt K) 2.0))) M))

series97.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt K)
25.0ms	(cbrt K)
23.0ms	(cbrt K)
28.0ms	(cos (- (* (* (cbrt K) (cbrt K)) (* (+ m n) (/ (cbrt K) 2.0))) M))

simplify41.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5323	303

prune105.0ms

Filtered

39 candidates to 54 candidates (-38.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	53	5	58

Merged error: 0.8b

Counts

58 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
0.4b	(/ (+ m n) (sqrt 2.0))
0.5b	(/ K (sqrt 2.0))
33.4b	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
94×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
64×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `cos-sum` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 175

Calls

4 calls:

25.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
7.0ms	(/ (+ m n) (sqrt 2.0))
4.0ms	(/ K (sqrt 2.0))
12.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series80.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
8.0ms	(/ (+ m n) (sqrt 2.0))
5.0ms	(/ K (sqrt 2.0))
43.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify50.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4968	1945
1	4968	1945

prune334.0ms

Filtered

113 candidates to 187 candidates (-65.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	187	5	192

Merged error: 0.8b

Counts

192 → 5

regimes399.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	17
1	20	17

end0.0ms

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

sample1.5s

Algorithm

intervals

Results

880.0ms	7820×	body	80	valid
51.0ms	76×	body	1280	invalid
44.0ms	96×	body	640	invalid
36.0ms	77×	body	640	valid
34.0ms	277×	body	80	invalid
29.0ms	43×	body	1280	valid
29.0ms	74×	body	320	invalid
14.0ms	42×	body	320	valid
9.0ms	42×	body	160	invalid
4.0ms	18×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze2.4s

sample48.0ms

simplify33.0ms

prune16.0ms

localize21.0ms

rewrite36.0ms

series84.0ms

simplify54.0ms

prune184.0ms

localize14.0ms

rewrite25.0ms

series80.0ms

simplify30.0ms

prune82.0ms

localize29.0ms

rewrite19.0ms

series97.0ms

simplify41.0ms

prune105.0ms

localize24.0ms

rewrite56.0ms

series80.0ms

simplify50.0ms

prune334.0ms

regimes399.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.4s

sample1.5s

Profiling