Details

sample46.0ms

Algorithm

intervals

Results

24.0ms	255×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify48.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 15.0b

Counts

2 → 1

localize21.0ms

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)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
11×	`add-log-exp`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`sub-neg` `pow-unpow` `distribute-lft-out--` `difference-of-squares`
2×	`cos-sum` `associate-+r+` `diff-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `cos-diff` `pow-to-exp` `associate-+r-` `flip3--` `pow-pow` `flip3-+` `times-frac` `pow-exp` `flip--` `flip-+` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
8.0ms	(- (/ (* K (+ m n)) 2.0) M)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series542.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
56.0ms	(- (/ (* K (+ m n)) 2.0) M)
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify119.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	368	603
1	1045	563
2	4794	552
3	5001	552

prune269.0ms

Filtered

73 candidates to 54 candidates (74.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Merged error: 1.5b

Counts

74 → 6

localize13.0ms

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)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

17.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series432.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	253	368
1	720	351
2	2937	346
3	5002	343

prune136.0ms

Filtered

43 candidates to 31 candidates (72.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 1.5b

Counts

49 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite29.0ms

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

series303.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify130.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 6 (122.0ms)

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

prune269.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	52	7	59

Merged error: 1.5b

Counts

59 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series392.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
142.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify127.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 6 (121.0ms)

Iter	Nodes	Cost
0	83	480
1	123	432
2	183	428
3	334	428
4	1040	428
5	3218	428
6	5001	414

prune241.0ms

Filtered

54 candidates to 44 candidates (81.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	53	8	61

Merged error: 1.5b

Counts

61 → 8

regimes257.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

818.0ms	8073×	body	80	valid
65.0ms	153×	body	640	valid
60.0ms	100×	body	1280	valid
36.0ms	118×	body	320	valid
15.0ms	55×	body	160	valid
5.0ms	5×	body	2560	valid