Details

analyze2.1s (16.7%)

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

Compiler

Compiled 30 to 24 computations (20% saved)

sample45.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	251×	body	128	valid
2.0ms	4×	body	1024	valid
1.0ms	3×	body	512	invalid
1.0ms	8×	body	128	invalid
1.0ms	1×	body	2048	invalid
0.0ms	1×	body	1024	invalid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0%)

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

Error

14.8b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
35.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite144.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

Rules

15×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`cancel-sign-sub-inv_binary64_726` `unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `add-exp-log_binary64_798`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796`
3×	`difference-of-squares_binary64_729` `pow-unpow_binary64_837`
2×	`sub-neg_binary64_753` `distribute-lft-out--_binary64_712`
1×	`cos-diff_binary64_897` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `+-commutative_binary64_690` `diff-log_binary64_852` `flip3--_binary64_764` `flip--_binary64_735`

Counts

4 → 61

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

Compiler

Compiled 2347 to 1174 computations (50% saved)

series1.4s (11%)

Error

1.4b

Counts

4 → 93

Calls

4 calls:

615.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
288.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
192.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
156.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 8207 to 5583 computations (32% saved)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5014	2991

prune214.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	4	155

Error

1.3b

Counts

155 → 4

Compiler

Compiled 5134 to 2381 computations (53.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite161.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

17×	`*-un-lft-identity_binary64_760`
13×	`add-sqr-sqrt_binary64_782`
10×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`pow1_binary64_821` `add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `add-cbrt-cube_binary64_796` `distribute-lft-out_binary64_711`
2×	`sum-log_binary64_851` `diff-log_binary64_852`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

3 → 53

Calls

3 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 1647 to 852 computations (48.3% saved)

series1.7s (13.1%)

Error

1.3b

Counts

3 → 93

Calls

3 calls:

637.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
619.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
287.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 6452 to 4486 computations (30.5% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4966	3491
1	4966	3491

prune160.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	146	4	150

Error

1.3b

Counts

150 → 4

Compiler

Compiled 3763 to 1690 computations (55.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
28.5b	(cos.f64 (.f64 1/2 (.f64 K n)))

rewrite139.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

18×	`*-un-lft-identity_binary64_760`
14×	`add-sqr-sqrt_binary64_782`
11×	`add-log-exp_binary64_799`
7×	`add-cube-cbrt_binary64_795`
6×	`unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `add-exp-log_binary64_798`
4×	`add-cbrt-cube_binary64_796` `cancel-sign-sub-inv_binary64_726`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `distribute-lft-out_binary64_711`
2×	`sum-log_binary64_851` `diff-log_binary64_852`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `associate--r+_binary64_696`

Counts

4 → 60

Calls

4 calls:

18.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
2.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))

Compiler

Compiled 2076 to 1129 computations (45.6% saved)

series1.7s (13.6%)

Error

1.3b

Counts

4 → 101

Calls

4 calls:

648.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
607.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
281.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
44.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))

Compiler

Compiled 7886 to 5573 computations (29.3% saved)

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4969	3652
1	4969	3652

prune210.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	161	4	165

Error

1.3b

Counts

165 → 4

Compiler

Compiled 4761 to 2355 computations (50.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K n))))
28.5b	(cos.f64 (.f64 1/2 (.f64 K n)))
28.5b	(cos.f64 (.f64 1/2 (.f64 K n)))
28.5b	(cos.f64 (.f64 1/2 (.f64 K n)))

rewrite86.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

5×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
4×	`pow1_binary64_821` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`cbrt-prod_binary64_791`
1×	`pow1/3_binary64_842`

Counts

4 → 32

Calls

4 calls:

3.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))
3.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))
2.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))
2.0ms	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K n))))

Compiler

Compiled 1545 to 909 computations (41.2% saved)

series390.0ms (3.1%)

Error

1.3b

Counts

4 → 32

Calls

4 calls:

178.0ms	(cbrt.f64 (cos.f64 (.f64 1/2 (.f64 K n))))
54.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))
52.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))
52.0ms	(cos.f64 (.f64 1/2 (.f64 K n)))

Compiler

Compiled 3730 to 2715 computations (27.2% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4985	694
1	4985	694

prune119.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	63	5	68

Error

1.3b

Counts

68 → 5

Compiler

Compiled 2772 to 1591 computations (42.6% saved)

regimes768.0ms (6.1%)

Accuracy

Total 0.2b remaining (15.9%)

Threshold costs 0.2b (15.9%)

Compiler

Compiled 9074 to 7902 computations (12.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	33
1	62	33

end0.0ms (0%)

sample2.8s (22%)

Algorithm

1×

intervals

Results

772.0ms	7833×	body	128	valid
33.0ms	84×	body	512	invalid
31.0ms	79×	body	1024	invalid
29.0ms	298×	body	128	invalid
28.0ms	64×	body	1024	valid
20.0ms	64×	body	512	valid
17.0ms	23×	body	2048	invalid
15.0ms	53×	body	256	invalid
8.0ms	38×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 1552 to 1349 computations (13.1% saved)

Details

analyze2.1s (16.7%)

sample45.0ms (0.4%)

simplify144.0ms (1.1%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite144.0ms (1.1%)

series1.4s (11%)

simplify74.0ms (0.6%)

prune214.0ms (1.7%)

localize14.0ms (0.1%)

rewrite161.0ms (1.3%)

series1.7s (13.1%)

simplify76.0ms (0.6%)

prune160.0ms (1.3%)

localize18.0ms (0.1%)

rewrite139.0ms (1.1%)

series1.7s (13.6%)

simplify94.0ms (0.7%)

prune210.0ms (1.7%)

localize24.0ms (0.2%)

rewrite86.0ms (0.7%)

series390.0ms (3.1%)

simplify70.0ms (0.6%)

prune119.0ms (0.9%)

regimes768.0ms (6.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.8s (22%)

Profiling