Details

analyze2.5s (39%)

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

sample52.0ms (0.8%)

Algorithm

1×

intervals

Results

28.0ms	252×	body	80	valid
2.0ms	3×	body	1280	invalid
2.0ms	4×	body	640	invalid
1.0ms	2×	body	640	valid
1.0ms	2×	body	320	invalid
1.0ms	1×	body	1280	valid
1.0ms	5×	body	80	invalid
0.0ms	1×	body	160	invalid
0.0ms	1×	body	160	valid

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4986	28
1	4986	28

prune13.0ms (0.2%)

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: 15.2b

Counts

2 → 1

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* K (/ (+ m n) 2.0))
0.0b	(- (* K (/ (+ m n) 2.0)) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.0b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
14×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `cos-diff` `pow-to-exp` `cos-sum` `flip3--` `pow-pow` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `pow-exp` `-commutative` `flip--` `div-inv` `distribute-lft-out--` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

12.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(* K (/ (+ m n) 2.0))
7.0ms	(- (* K (/ (+ m n) 2.0)) M)

series85.0ms (1.4%)

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)
8.0ms	(* K (/ (+ m n) 2.0))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4925	951
1	4925	951

prune247.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.8b

Counts

88 → 4

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 36

Calls

2 calls:

15.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
13.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series85.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
41.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5087	706

prune108.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Merged error: 0.8b

Counts

46 → 4

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

16.0b	(cbrt (* K (/ (+ m n) 2.0)))
16.0b	(cbrt (* K (/ (+ m n) 2.0)))
16.0b	(cbrt (* K (/ (+ m n) 2.0)))
33.0b	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (* K (/ (+ m n) 2.0)))) M))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

11.0ms	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (* K (/ (+ m n) 2.0)))) M))
6.0ms	(cbrt (* K (/ (+ m n) 2.0)))
5.0ms	(cbrt (* K (/ (+ m n) 2.0)))
5.0ms	(cbrt (* K (/ (+ m n) 2.0)))

series152.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (* K (/ (+ m n) 2.0)))
39.0ms	(cbrt (* K (/ (+ m n) 2.0)))
37.0ms	(cbrt (* K (/ (+ m n) 2.0)))
33.0ms	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (* K (/ (+ m n) 2.0)))) M))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4838	480
1	4838	480

prune176.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	52	3	55

Merged error: 0.7b

Counts

55 → 3

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

16.0b	(cbrt (* K (/ (+ m n) 2.0)))
16.0b	(cbrt (* K (/ (+ m n) 2.0)))
16.0b	(cbrt (* K (/ (+ m n) 2.0)))
33.2b	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (* (* (cbrt (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (cbrt (* K (/ (+ m n) 2.0))))) (cbrt (cbrt (* K (/ (+ m n) 2.0)))))) (cbrt (* K (/ (+ m n) 2.0)))) M))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

25.0ms	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (* (* (cbrt (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (cbrt (* K (/ (+ m n) 2.0))))) (cbrt (cbrt (* K (/ (+ m n) 2.0)))))) (cbrt (* K (/ (+ m n) 2.0)))) M))
6.0ms	(cbrt (* K (/ (+ m n) 2.0)))
6.0ms	(cbrt (* K (/ (+ m n) 2.0)))
5.0ms	(cbrt (* K (/ (+ m n) 2.0)))

series149.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (* K (/ (+ m n) 2.0)))
38.0ms	(cbrt (* K (/ (+ m n) 2.0)))
37.0ms	(cbrt (* K (/ (+ m n) 2.0)))
33.0ms	(cos (- (* (* (cbrt (* K (/ (+ m n) 2.0))) (* (* (cbrt (cbrt (* K (/ (+ m n) 2.0)))) (cbrt (cbrt (* K (/ (+ m n) 2.0))))) (cbrt (cbrt (* K (/ (+ m n) 2.0)))))) (cbrt (* K (/ (+ m n) 2.0)))) M))

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4850	456
1	4850	456

prune215.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	51	3	54

Merged error: 0.7b

Counts

54 → 3

regimes343.0ms (5.5%)

Accuracy

Total 0.1b remaining (11.4%)

Threshold costs 0.1b (11.4%)

bsearch0.0ms (0%)

simplify1.0ms (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

1.1s	7832×	body	80	valid
41.0ms	66×	body	1280	invalid
37.0ms	81×	body	640	invalid
34.0ms	51×	body	1280	valid
31.0ms	68×	body	640	valid
25.0ms	76×	body	320	invalid
25.0ms	229×	body	80	invalid
12.0ms	35×	body	320	valid
6.0ms	26×	body	160	invalid
3.0ms	3×	body	2560	invalid
3.0ms	14×	body	160	valid

Details

analyze2.5s (39%)

sample52.0ms (0.8%)

simplify44.0ms (0.7%)

prune13.0ms (0.2%)

localize22.0ms (0.3%)

rewrite40.0ms (0.6%)

series85.0ms (1.4%)

simplify86.0ms (1.4%)

prune247.0ms (3.9%)

localize15.0ms (0.2%)

rewrite28.0ms (0.5%)

series85.0ms (1.4%)

simplify27.0ms (0.4%)

prune108.0ms (1.7%)

localize28.0ms (0.4%)

rewrite28.0ms (0.4%)

series152.0ms (2.4%)

simplify59.0ms (0.9%)

prune176.0ms (2.8%)

localize32.0ms (0.5%)

rewrite43.0ms (0.7%)

series149.0ms (2.4%)

simplify103.0ms (1.6%)

prune215.0ms (3.4%)

regimes343.0ms (5.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.7s (26.3%)

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