Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	260×	body	80	valid
1.0ms	3×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify50.0ms

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

prune13.0ms

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: 15.6b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

7.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series83.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify39.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	495
1	1304	457
2	5001	450

prune167.0ms

Filtered

79 candidates to 56 candidates (29.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Merged error: 0.9b

Counts

80 → 4

localize14.0ms

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)

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

series82.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
42.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (81.0ms)

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

prune93.0ms

Filtered

50 candidates to 34 candidates (32.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0.9b

Counts

54 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
36.5b	(cos (- (/ (* K (+ m n)) 2.0) M))
36.5b	(cos (- (/ (* K (+ m n)) 2.0) M))
36.5b	(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:

1.0ms	(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))
10.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series121.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	86	463
1	132	417
2	213	415
3	406	415
4	1373	415
5	5001	415

prune182.0ms

Filtered

53 candidates to 44 candidates (17.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	53	4	57

Merged error: 0.9b

Counts

57 → 4

localize27.0ms

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)))
36.5b	(cos (- (/ (* K (+ m n)) 2.0) M))
36.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite20.0ms

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

series161.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
58.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	86	478
1	132	430
2	213	426
3	406	426
4	1373	426
5	5001	426

prune145.0ms

Filtered

54 candidates to 44 candidates (18.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	53	5	58

Merged error: 0.9b

Counts

58 → 5

regimes404.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b 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

sample1.6s

Algorithm

intervals

Results

804.0ms	8083×	body	80	valid
211.0ms	131×	body	1280	valid
70.0ms	160×	body	640	valid
33.0ms	108×	body	320	valid
13.0ms	64×	body	160	valid
3.0ms	4×	body	2560	valid

Details

sample57.0ms

simplify50.0ms

prune13.0ms

localize23.0ms

rewrite35.0ms

series83.0ms

simplify39.0ms

prune167.0ms

localize14.0ms

rewrite33.0ms

series82.0ms

simplify88.0ms

prune93.0ms

localize28.0ms

rewrite29.0ms

series121.0ms

simplify63.0ms

prune182.0ms

localize27.0ms

rewrite20.0ms

series161.0ms

simplify60.0ms

prune145.0ms

regimes404.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.6s

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