Details

sample47.0ms

Algorithm

intervals

Results

24.0ms	263×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	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	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.8b

Counts

2 → 1

localize21.0ms

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	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
32.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite50.0ms

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))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
12.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series518.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
259.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
24.0ms	(* K (+ m n))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

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

prune321.0ms

Filtered

89 candidates to 60 candidates (67.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 1.2b

Counts

90 → 6

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)

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:

24.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series439.0ms

Counts

2 → 6

Calls

2 calls:

182.0ms	(- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
257.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	277	469
1	798	444
2	3368	435
3	5002	432

prune157.0ms

Filtered

50 candidates to 34 candidates (68.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	49	7	56

Merged error: 1.2b

Counts

56 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
32.5b	(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))

series477.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (+ m n))
128.0ms	(cbrt (+ m n))
125.0ms	(cbrt (+ m n))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify150.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (143.0ms)

Iter	Nodes	Cost
0	186	485
1	416	445
2	1213	439
3	4532	439
4	5003	433

prune326.0ms

Filtered

64 candidates to 52 candidates (81.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	65	6	71

Merged error: 1.2b

Counts

71 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2)))
0.5b	(+ (* 1.0 (* m M)) (* 1.0 (* M n)))
4.0b	(- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2))
32.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity`
8×	`exp-prod` `difference-of-squares`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `diff-log` `add-cbrt-cube`
3×	`sub-neg` `exp-sum` `sum-log` `rem-exp-log`
2×	`unpow-prod-down` `cos-sum` `associate--l+` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`+-commutative` `cos-diff` `flip3--` `flip3-+` `exp-diff` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

11.0ms	(exp (- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2)))
5.0ms	(+ (* 1.0 (* m M)) (* 1.0 (* M n)))
10.0ms	(- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2))
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series221.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(exp (- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2)))
71.0ms	(+ (* 1.0 (* m M)) (* 1.0 (* M n)))
37.0ms	(- (+ (* 1.0 (* m M)) (* 1.0 (* M n))) (pow M 2))
54.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify52.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	291	668
1	1028	601
2	5001	569

prune272.0ms

Filtered

75 candidates to 57 candidates (76.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Merged error: 1.2b

Counts

81 → 6

regimes218.0ms

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

sample1.3s

Algorithm

intervals

Results

823.0ms	8132×	body	80	valid
66.0ms	151×	body	640	valid
62.0ms	102×	body	1280	valid
37.0ms	121×	body	320	valid
12.0ms	55×	body	160	valid
1.0ms	1×	body	2560	valid

Details

sample47.0ms

simplify48.0ms

prune9.0ms

localize21.0ms

rewrite50.0ms

series518.0ms

simplify44.0ms

prune321.0ms

localize14.0ms

rewrite35.0ms

series439.0ms

simplify82.0ms

prune157.0ms

localize30.0ms

rewrite26.0ms

series477.0ms

simplify150.0ms

prune326.0ms

localize20.0ms

rewrite36.0ms

series221.0ms

simplify52.0ms

prune272.0ms

regimes218.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling