Details

analyze2.4s

Algorithm: search

sample53.0ms

Algorithm

intervals

Results

26.0ms	248×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	5×	body	640	invalid
2.0ms	3×	body	1280	invalid
1.0ms	12×	body	80	invalid
1.0ms	3×	body	320	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	invalid
1.0ms	2×	body	320	invalid

simplify46.0ms

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: 14.9b

Counts

2 → 1

localize27.0ms

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)
31.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite46.0ms

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:

20.0ms	(- (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))

series106.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (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)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify40.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (33.0ms)

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

prune180.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Merged error: 1.6b

Counts

90 → 7

localize15.0ms

Local error

Found 2 expressions with local error:

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)

rewrite32.0ms

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:

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)

series80.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify84.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	307	479
1	865	454
2	3603	442
3	5001	439

prune104.0ms

Filtered

34 candidates to 50 candidates (-47.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 1.6b

Counts

57 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
31.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite17.0ms

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`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
13.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series93.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt K)
23.0ms	(cbrt K)
22.0ms	(cbrt K)
26.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (37.0ms)

Iter	Nodes	Cost
0	130	345
1	254	312
2	456	282
3	1079	279
4	5001	267

prune135.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	54	8	62

Merged error: 1.5b

Counts

62 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
31.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
31.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
31.5b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

1.0ms	(cbrt K)
17.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
13.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
13.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series102.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt K)
26.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
26.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))
26.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify42.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	130	627
1	254	560
2	456	550
3	1079	549
4	5001	545

prune157.0ms

Filtered

44 candidates to 53 candidates (-20.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	52	9	61

Merged error: 1.5b

Counts

61 → 9

regimes540.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

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

analyze2.5s

Algorithm: search

sample1.4s

Algorithm

intervals

Results

846.0ms	7817×	body	80	valid
40.0ms	94×	body	640	invalid
36.0ms	59×	body	1280	invalid
34.0ms	74×	body	640	valid
31.0ms	270×	body	80	invalid
30.0ms	47×	body	1280	valid
21.0ms	65×	body	320	invalid
14.0ms	45×	body	320	valid
8.0ms	35×	body	160	invalid
4.0ms	17×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze2.4s

sample53.0ms

simplify46.0ms

prune12.0ms

localize27.0ms

rewrite46.0ms

series106.0ms

simplify40.0ms

prune180.0ms

localize15.0ms

rewrite32.0ms

series80.0ms

simplify84.0ms

prune104.0ms

localize29.0ms

rewrite17.0ms

series93.0ms

simplify42.0ms

prune135.0ms

localize36.0ms

rewrite45.0ms

series102.0ms

simplify42.0ms

prune157.0ms

regimes540.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.5s

sample1.4s

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