Details

analyze2.3s (33.5%)

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)

sample54.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	249×	body	128	valid
8.0ms	4×	body	1024	invalid
1.0ms	12×	body	128	invalid
1.0ms	1×	body	512	valid
1.0ms	2×	body	1024	valid
1.0ms	4×	body	256	valid
1.0ms	1×	body	2048	invalid
1.0ms	3×	body	256	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify206.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5353	43

prune8.0ms (0.1%)

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: 16.0b

Counts

2 → 1

Compiler

Compiled 113 to 89 computations (21.2% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
32.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_789`
15×	`*-un-lft-identity_binary64_767`
12×	`add-exp-log_binary64_805`
11×	`add-cbrt-cube_binary64_803` `add-cube-cbrt_binary64_802`
7×	`pow1_binary64_828`
6×	`unpow-prod-down_binary64_846`
4×	`associate-r_binary64_707` `cos-sum_binary64_901` `times-frac_binary64_773` `add-log-exp_binary64_806` `associate-*r/_binary64_709`
3×	`associate-l_binary64_708` `associate-/r*_binary64_711` `pow-unpow_binary64_844` `cancel-sign-sub-inv_binary64_733`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `flip-+_binary64_741` `flip3-+_binary64_770` `div-exp_binary64_818` `difference-of-squares_binary64_736`
1×	`frac-2neg_binary64_778` `pow-to-exp_binary64_836` `unswap-sqr_binary64_735` `distribute-lft-out_binary64_718` `sqr-pow_binary64_739` `pow-exp_binary64_835` `sub-neg_binary64_760` `-commutative_binary64_698` `distribute-rgt-in_binary64_717` `associate-/l_binary64_712` `unpow2_binary64_832` `distribute-lft-out--_binary64_719` `cos-diff_binary64_904` `distribute-lft-in_binary64_716` `pow-prod-down_binary64_838` `clear-num_binary64_766` `div-inv_binary64_764` `pow-pow_binary64_839`

Counts

4 → 79

Calls

4 calls:

13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms	(*.f64 K (+.f64 m n))

series371.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
103.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
68.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
47.0ms	(*.f64 K (+.f64 m n))

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5163	1297

prune246.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 1.3b

Counts

92 → 5

Compiler

Compiled 5420 to 3191 computations (41.1% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_789`
9×	`*-un-lft-identity_binary64_767`
6×	`unpow-prod-down_binary64_846`
5×	`add-cube-cbrt_binary64_802`
4×	`add-log-exp_binary64_806` `difference-of-squares_binary64_736`
3×	`add-exp-log_binary64_805` `pow1_binary64_828` `pow-unpow_binary64_844` `cancel-sign-sub-inv_binary64_733`
2×	`times-frac_binary64_773` `distribute-lft-out--_binary64_719` `add-cbrt-cube_binary64_803`
1×	`pow-to-exp_binary64_836` `sqr-pow_binary64_739` `pow-exp_binary64_835` `sub-neg_binary64_760` `diff-log_binary64_859` `unpow2_binary64_832` `flip--_binary64_742` `flip3--_binary64_771` `pow-pow_binary64_839`

Counts

2 → 38

Calls

2 calls:

13.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series144.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

105.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
39.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5037	684

prune66.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 1.3b

Counts

49 → 5

Compiler

Compiled 1420 to 842 computations (40.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
32.5b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_798`
8×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`cos-sum_binary64_901` `add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`pow1/3_binary64_849` `cancel-sign-sub-inv_binary64_733`
1×	`sub-neg_binary64_760` `cos-diff_binary64_904`

Counts

4 → 45

Calls

4 calls:

18.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)

series661.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
157.0ms	(cbrt.f64 K)
145.0ms	(cbrt.f64 K)
141.0ms	(cbrt.f64 K)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4919	603
1	4919	603

prune87.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Merged error: 1.3b

Counts

62 → 5

Compiler

Compiled 2272 to 1045 computations (54% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
32.8b	(cos.f64 (-.f64 (/.f64 (.f64 (+.f64 m n) (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 2)) M))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_798`
8×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`cos-sum_binary64_901` `add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`pow1/3_binary64_849` `cancel-sign-sub-inv_binary64_733`
1×	`sub-neg_binary64_760` `cos-diff_binary64_904`

Counts

4 → 45

Calls

4 calls:

20.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (+.f64 m n) (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 2)) M))
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)

series471.0ms (6.8%)

Counts

4 → 6

Calls

4 calls:

471.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (+.f64 m n) (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 2)) M))
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5074	702

prune122.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	50	6	56

Merged error: 1.3b

Counts

56 → 6

Compiler

Compiled 2621 to 1694 computations (35.4% saved)

regimes109.0ms (1.6%)

Compiler: Compiled 1130 to 895 computations (20.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.6s (23.4%)

Algorithm

1×

intervals

Results

852.0ms	7833×	body	128	valid
38.0ms	59×	body	1024	valid
36.0ms	77×	body	1024	invalid
33.0ms	91×	body	512	invalid
31.0ms	288×	body	128	invalid
21.0ms	65×	body	512	valid
17.0ms	24×	body	2048	invalid
11.0ms	50×	body	256	invalid
10.0ms	43×	body	256	valid

Compiler

Compiled 271 to 214 computations (21% saved)

Details

analyze2.3s (33.5%)

sample54.0ms (0.8%)

simplify206.0ms (3%)

prune8.0ms (0.1%)

localize25.0ms (0.4%)

rewrite47.0ms (0.7%)

series371.0ms (5.4%)

simplify50.0ms (0.7%)

prune246.0ms (3.6%)

localize13.0ms (0.2%)

rewrite30.0ms (0.4%)

series144.0ms (2.1%)

simplify33.0ms (0.5%)

prune66.0ms (1%)

localize25.0ms (0.4%)

rewrite27.0ms (0.4%)

series661.0ms (9.6%)

simplify63.0ms (0.9%)

prune87.0ms (1.3%)

localize25.0ms (0.4%)

rewrite29.0ms (0.4%)

series471.0ms (6.8%)

simplify58.0ms (0.8%)

prune122.0ms (1.8%)

regimes109.0ms (1.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (23.4%)

Profiling