Details

analyze2.6s (35.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5136	473
0	5	5
1	5	5

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)

sample53.0ms (0.7%)

Algorithm

1×

intervals

Results

28.0ms	253×	body	128	valid
1.0ms	3×	body	1024	invalid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	1024	valid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	512	valid
0.0ms	2×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	43

prune6.0ms (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

Error

16.2b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize22.0ms (0.3%)

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 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_760`
19×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
9×	`add-log-exp_binary64_799`
7×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
6×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`diff-log_binary64_852` `associate-*r/_binary64_702` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `unpow2_binary64_825` `prod-exp_binary64_809` `flip3-+_binary64_763` `distribute-lft-in_binary64_709` `pow-exp_binary64_828` `distribute-rgt-in_binary64_710` `flip-+_binary64_734` `pow-to-exp_binary64_829` `sum-log_binary64_851` `associate--r+_binary64_696` `sqr-pow_binary64_732` `cos-diff_binary64_897` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `times-frac_binary64_766` `*-commutative_binary64_691` `flip--_binary64_735` `pow-pow_binary64_832` `flip3--_binary64_764`

Counts

4 → 76

Calls

4 calls:

16.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(*.f64 K (+.f64 m n))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series283.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
78.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
55.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
23.0ms	(*.f64 K (+.f64 m n))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5708	1646

prune139.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Error

0.7b

Counts

89 → 4

Compiler

Compiled 3092 to 1521 computations (50.8% saved)

localize16.0ms (0.2%)

Local error

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

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

16.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series192.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

139.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
53.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5184	1059

prune62.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	47	4	51

Error

0.7b

Counts

51 → 4

Compiler

Compiled 1284 to 716 computations (44.2% saved)

localize27.0ms (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)))
34.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
34.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
34.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_894`
9×	`cancel-sign-sub-inv_binary64_726`
8×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`cbrt-prod_binary64_791` `cos-diff_binary64_897` `sub-neg_binary64_753`
1×	`pow1/3_binary64_842`

Counts

4 → 47

Calls

4 calls:

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

series511.0ms (7%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
77.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
75.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
71.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4958	1248
1	4958	1248

prune138.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	59	4	63

Error

0.7b

Counts

63 → 4

Compiler

Compiled 3622 to 1830 computations (49.5% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(cbrt.f64 (+.f64 m n))
0.5b	(cbrt.f64 (+.f64 m n))
34.7b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_760`
12×	`cbrt-prod_binary64_791`
8×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
6×	`cbrt-div_binary64_792`
4×	`cos-sum_binary64_894` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`pow1/3_binary64_842` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `flip-+_binary64_734`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 54

Calls

4 calls:

18.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))

series474.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
116.0ms	(cbrt.f64 (+.f64 m n))
112.0ms	(cbrt.f64 (+.f64 m n))
103.0ms	(cbrt.f64 (+.f64 m n))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4875	997
1	4875	997

prune103.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	65	5	70

Error

0.6b

Counts

70 → 5

Compiler

Compiled 2839 to 1195 computations (57.9% saved)

regimes255.0ms (3.5%)

Accuracy

Total 0.3b remaining (19.5%)

Threshold costs 0.3b (19.5%)

Compiler

Compiled 3218 to 2370 computations (26.4% 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%)

sample1.9s (26.4%)

Algorithm

1×

intervals

Results

889.0ms	7842×	body	128	valid
32.0ms	73×	body	1024	invalid
31.0ms	64×	body	1024	valid
29.0ms	261×	body	128	invalid
26.0ms	78×	body	512	invalid
22.0ms	64×	body	512	valid
17.0ms	58×	body	256	invalid
8.0ms	14×	body	2048	invalid
7.0ms	28×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 572 to 424 computations (25.9% saved)

Details

analyze2.6s (35.2%)

sample53.0ms (0.7%)

simplify52.0ms (0.7%)

prune6.0ms (0.1%)

localize22.0ms (0.3%)

rewrite53.0ms (0.7%)

series283.0ms (3.9%)

simplify68.0ms (0.9%)

prune139.0ms (1.9%)

localize16.0ms (0.2%)

rewrite30.0ms (0.4%)

series192.0ms (2.6%)

simplify69.0ms (0.9%)

prune62.0ms (0.8%)

localize27.0ms (0.4%)

rewrite37.0ms (0.5%)

series511.0ms (7%)

simplify84.0ms (1.2%)

prune138.0ms (1.9%)

localize26.0ms (0.4%)

rewrite33.0ms (0.5%)

series474.0ms (6.5%)

simplify73.0ms (1%)

prune103.0ms (1.4%)

regimes255.0ms (3.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (26.4%)

Profiling