Details

sample52.0ms

Algorithm

intervals

Results

28.0ms	261×	body	80	valid
3.0ms	8×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 16.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (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)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite52.0ms

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:

25.0ms	(- (- (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))

series538.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
30.0ms	(* K (+ m n))
268.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	435	667
1	1447	621
2	5001	620

prune311.0ms

Filtered

89 candidates to 60 candidates (67.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 1.1b

Counts

90 → 4

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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:

21.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series460.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
271.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5001	432

prune144.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Merged error: 1.1b

Counts

54 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite27.0ms

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:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series302.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify125.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 6 (119.0ms)

Iter	Nodes	Cost
0	83	464
1	123	418
2	183	416
3	334	416
4	1040	416
5	3218	416
6	5001	397

prune267.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	52	6	58

Merged error: 1.1b

Counts

58 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt K)
0.5b	(cbrt K)
0.5b	(cbrt K)
34.7b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite32.0ms

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:

2.0ms	(cbrt K)
2.0ms	(cbrt K)
2.0ms	(cbrt K)
24.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series641.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt K)
174.0ms	(cbrt K)
178.0ms	(cbrt K)
102.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify96.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	111	309
1	265	279
2	681	273
3	3070	273
4	5001	273

prune232.0ms

Filtered

55 candidates to 46 candidates (83.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	55	6	61

Merged error: 1.1b

Counts

61 → 6

regimes192.0ms

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

sample1.5s

Algorithm

intervals

Results

978.0ms	8095×	body	80	valid
72.0ms	126×	body	1280	valid
65.0ms	160×	body	640	valid
36.0ms	112×	body	320	valid
13.0ms	61×	body	160	valid
3.0ms	3×	body	2560	valid