Details

sample6.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0.925829%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

27.0ms	250×	body	80	valid
3.0ms	4×	body	1280	valid
2.0ms	3×	body	1280	invalid
1.0ms	8×	body	80	invalid
1.0ms	2×	body	320	invalid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	invalid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15

prune31.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 15.2b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

21.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series116.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	465	677
1	1514	631
2	5002	627

prune174.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Merged error: 1.2b

Counts

91 → 4

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
15×	`add-log-exp`
14×	`add-sqr-sqrt`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `add-cbrt-cube`
2×	`flip3--` `distribute-rgt-neg-in` `neg-log` `flip--` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `associate--r-` `sqr-pow`

Counts

3 → 58

Calls

3 calls:

3.0ms	(- l (fabs (- m n)))
20.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series87.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(- l (fabs (- m n)))
40.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
42.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify90.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	347	567
1	942	542
2	3728	530
3	5001	527

prune118.0ms

Filtered

45 candidates to 67 candidates (-48.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 1.2b

Counts

71 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
36.3b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
16.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series124.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (+ m n))
31.0ms	(cbrt (+ m n))
34.0ms	(cbrt (+ m n))
28.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify164.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	207	539
1	429	499
2	1164	478
3	4632	454
4	5001	454

prune154.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	64	5	69

Merged error: 1.1b

Counts

69 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (cbrt (+ m n)))
36.4b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 55

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
4.0ms	(cbrt (cbrt (+ m n)))
18.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

series131.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (+ m n))
31.0ms	(cbrt (+ m n))
41.0ms	(cbrt (cbrt (+ m n)))
28.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))))) (cbrt (+ m n))) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	296	714
1	651	656
2	2004	633
3	5001	610

prune143.0ms

Filtered

54 candidates to 67 candidates (-24.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	67	5	72

Merged error: 1.1b

Counts

72 → 5

regimes397.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10

end0.0ms

sample8.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0.925829%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

887.0ms	7832×	body	80	valid
52.0ms	78×	body	1280	invalid
42.0ms	97×	body	640	invalid
28.0ms	62×	body	640	valid
26.0ms	41×	body	1280	valid
25.0ms	230×	body	80	invalid
21.0ms	68×	body	320	invalid
14.0ms	42×	body	320	valid
6.0ms	27×	body	160	invalid
5.0ms	23×	body	160	valid
4.0ms	5×	body	2560	invalid

Details

sample6.9s

simplify61.0ms

prune31.0ms

localize23.0ms

rewrite47.0ms

series116.0ms

simplify44.0ms

prune174.0ms

localize15.0ms

rewrite35.0ms

series87.0ms

simplify90.0ms

prune118.0ms

localize28.0ms

rewrite26.0ms

series124.0ms

simplify164.0ms

prune154.0ms

localize36.0ms

rewrite28.0ms

series131.0ms

simplify60.0ms

prune143.0ms

regimes397.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.5s

Profiling