Details

analyze7.2s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 0.925829%

Guaranteed chance to sample good point: 37.168142%

sample53.0ms

Algorithm

intervals

Results

33.0ms	252×	body	80	valid
1.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	320	invalid
0.0ms	1×	body	160	valid
0.0ms	2×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

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

prune12.0ms

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: 14.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
35.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite51.0ms

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:

6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series104.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* K (+ m n))
37.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
41.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

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

prune173.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.8b

Counts

90 → 5

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series79.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify86.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	307	479
1	865	454
2	3603	442
3	5003	439

prune93.0ms

Filtered

34 candidates to 50 candidates (-47.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0.8b

Counts

55 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
35.1b	(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))

series119.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (+ m n))
30.0ms	(cbrt (+ m n))
33.0ms	(cbrt (+ m n))
26.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify161.0ms

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

prune156.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	63	6	69

Merged error: 0.8b

Counts

69 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
35.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
17.0ms	(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
17.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series115.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (+ m n))
29.0ms	(cbrt (+ m n))
30.0ms	(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
27.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify47.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	246	798
1	498	723
2	1314	709
3	5001	693

prune149.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	68	6	74

Merged error: 0.8b

Counts

74 → 6

regimes424.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

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

analyze7.2s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 0.925829%

Guaranteed chance to sample good point: 37.168142%

sample1.4s

Algorithm

intervals

Results

893.0ms	7843×	body	80	valid
47.0ms	76×	body	1280	invalid
33.0ms	76×	body	640	invalid
27.0ms	59×	body	640	valid
27.0ms	250×	body	80	invalid
27.0ms	41×	body	1280	valid
26.0ms	64×	body	320	invalid
10.0ms	32×	body	320	valid
7.0ms	34×	body	160	invalid
6.0ms	25×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze7.2s

sample53.0ms

simplify49.0ms

prune12.0ms

localize22.0ms

rewrite51.0ms

series104.0ms

simplify42.0ms

prune173.0ms

localize15.0ms

rewrite35.0ms

series79.0ms

simplify86.0ms

prune93.0ms

localize28.0ms

rewrite26.0ms

series119.0ms

simplify161.0ms

prune156.0ms

localize33.0ms

rewrite42.0ms

series115.0ms

simplify47.0ms

prune149.0ms

regimes424.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze7.2s

sample1.4s

Profiling