Details

analyze2.3s (27.3%)

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

Compiler

Compiled 30 to 24 computations (20% saved)

sample47.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms	248×	body	128	valid
2.0ms	5×	body	512	valid
1.0ms	3×	body	1024	invalid
1.0ms	4×	body	512	invalid
1.0ms	9×	body	128	invalid
1.0ms	1×	body	1024	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4960	43
1	4960	43

prune13.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.4b

Counts

2 → 2

Compiler

Compiled 142 to 112 computations (21.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
14×	`add-log-exp_binary64`
11×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`diff-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`associate--r+_binary64` `associate-r_binary64` `difference-of-squares_binary64` `cos-sum_binary64`
3×	`pow-unpow_binary64` `sub-neg_binary64` `associate-l_binary64`
2×	`associate-*r/_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `unpow2_binary64` `associate--r-_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `prod-exp_binary64` `times-frac_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

29.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))

series566.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

278.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
142.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
97.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
49.0ms	(*.f64 K (+.f64 m n))

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4951	1819
1	4951	1819

prune291.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 1.6b

Counts

100 → 7

Compiler

Compiled 6326 to 3757 computations (40.6% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
8×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
6×	`diff-log_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64`
4×	`associate--r+_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64`
2×	`sub-neg_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `neg-sub0_binary64` `unpow2_binary64` `associate--r-_binary64` `pow-pow_binary64` `sqr-pow_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 51

Calls

2 calls:

29.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series367.0ms (4.3%)

Counts

2 → 6

Calls

2 calls:

256.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
112.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5022	1230

prune115.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Merged error: 1.6b

Counts

64 → 7

Compiler

Compiled 2435 to 1506 computations (38.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sub-neg_binary64` `cos-diff_binary64` `cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 47

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

series978.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

546.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
147.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
143.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
142.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4920	1248
1	4920	1248

prune161.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	59	7	66

Merged error: 1.6b

Counts

66 → 7

Compiler

Compiled 4059 to 2114 computations (47.9% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sub-neg_binary64` `cos-diff_binary64` `cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 47

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

series949.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

543.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
139.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
136.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
132.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4920	1248
1	4920	1248

prune160.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	59	7	66

Merged error: 1.6b

Counts

66 → 7

Compiler

Compiled 3974 to 2088 computations (47.5% saved)

regimes143.0ms (1.7%)

Compiler: Compiled 1628 to 1260 computations (22.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	159	26
1	159	26

end0.0ms (0%)

sample1.7s (19.7%)

Algorithm

1×

intervals

Results

878.0ms	7854×	body	128	valid
50.0ms	99×	body	1024	invalid
34.0ms	67×	body	1024	valid
33.0ms	305×	body	128	invalid
32.0ms	99×	body	512	invalid
23.0ms	51×	body	512	valid
15.0ms	21×	body	2048	invalid
14.0ms	65×	body	256	invalid
6.0ms	27×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 307 to 239 computations (22.1% saved)

Details

analyze2.3s (27.3%)

sample47.0ms (0.6%)

simplify66.0ms (0.8%)

prune13.0ms (0.2%)

localize23.0ms (0.3%)

rewrite75.0ms (0.9%)

series566.0ms (6.6%)

simplify100.0ms (1.2%)

prune291.0ms (3.4%)

localize18.0ms (0.2%)

rewrite47.0ms (0.6%)

series367.0ms (4.3%)

simplify76.0ms (0.9%)

prune115.0ms (1.4%)

localize29.0ms (0.3%)

rewrite47.0ms (0.6%)

series978.0ms (11.5%)

simplify78.0ms (0.9%)

prune161.0ms (1.9%)

localize31.0ms (0.4%)

rewrite48.0ms (0.6%)

series949.0ms (11.1%)

simplify80.0ms (0.9%)

prune160.0ms (1.9%)

regimes143.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (19.7%)

Profiling