Details

analyze2.4s (37.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample54.0ms (0.8%)

Algorithm

1×

intervals

Results

28.0ms	249×	body	80	valid
4.0ms	6×	body	1280	invalid
2.0ms	4×	body	640	valid
1.0ms	3×	body	640	invalid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4986	28
1	4986	28

prune17.0ms (0.3%)

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: 14.0b

Counts

2 → 1

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
35.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite34.0ms (0.5%)

Algorithm

1×	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` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `cos-sum` `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 → 65

Calls

4 calls:

11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
8.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
8.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))

series84.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
13.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4937	829
1	4937	829

prune218.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 1.4b

Counts

78 → 6

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

17.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
13.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series123.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
37.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4929	925
1	4929	925

prune144.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 1.4b

Counts

63 → 6

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

12.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
12.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
43.6b	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`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--` `difference-of-squares`

Counts

4 → 52

Calls

4 calls:

8.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
8.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
8.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
6.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series199.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
58.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
57.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
25.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5420	981

prune228.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	64	6	70

Merged error: 1.4b

Counts

70 → 6

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
35.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
35.2b	(cos (- (/ (* K (+ m n)) 2.0) M))
35.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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` `cos-sum`
1×	`pow1/3`

Counts

4 → 38

Calls

4 calls:

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

series129.0ms (2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
24.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4970	618
1	4970	618

prune181.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	50	6	56

Merged error: 1.4b

Counts

56 → 6

regimes455.0ms (7%)

Accuracy

Total 0.2b remaining (16.6%)

Threshold costs 0.2b (16.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	17
1	61	17

end0.0ms (0%)

sample1.7s (26.3%)

Algorithm

1×

intervals

Results

891.0ms	7824×	body	80	valid
248.0ms	59×	body	320	invalid
46.0ms	74×	body	1280	invalid
45.0ms	98×	body	640	invalid
41.0ms	80×	body	640	valid
29.0ms	37×	body	1280	valid
29.0ms	261×	body	80	invalid
13.0ms	38×	body	320	valid
8.0ms	35×	body	160	invalid
5.0ms	21×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze2.4s (37.7%)

sample54.0ms (0.8%)

simplify50.0ms (0.8%)

prune17.0ms (0.3%)

localize23.0ms (0.4%)

rewrite34.0ms (0.5%)

series84.0ms (1.3%)

simplify65.0ms (1%)

prune218.0ms (3.4%)

localize14.0ms (0.2%)

rewrite42.0ms (0.6%)

series123.0ms (1.9%)

simplify47.0ms (0.7%)

prune144.0ms (2.2%)

localize28.0ms (0.4%)

rewrite30.0ms (0.5%)

series199.0ms (3.1%)

simplify44.0ms (0.7%)

prune228.0ms (3.5%)

localize28.0ms (0.4%)

rewrite28.0ms (0.4%)

series129.0ms (2%)

simplify61.0ms (0.9%)

prune181.0ms (2.8%)

regimes455.0ms (7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (26.3%)

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