Details

analyze2.1s (31.3%)

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)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	253×	body	128	valid
1.0ms	3×	body	1024	invalid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	2048	invalid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	1024	valid
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)

simplify139.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (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)

localize20.0ms (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))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_419`
19×	`add-sqr-sqrt_binary64_441`
10×	`add-cube-cbrt_binary64_454`
9×	`add-log-exp_binary64_458`
7×	`add-exp-log_binary64_457` `cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
6×	`unpow-prod-down_binary64_498` `add-cbrt-cube_binary64_455`
4×	`cos-sum_binary64_553` `associate-r_binary64_359`
3×	`difference-of-squares_binary64_388` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `associate-l_binary64_360` `pow-unpow_binary64_496`
2×	`sub-neg_binary64_412` `associate-*r/_binary64_361` `diff-log_binary64_511`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `times-frac_binary64_425` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sqr-pow_binary64_391` `sum-log_binary64_510` `flip3--_binary64_423` `pow-to-exp_binary64_488` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `pow-pow_binary64_491` `associate--r+_binary64_355` `flip--_binary64_394` `unpow2_binary64_484` `cos-diff_binary64_556`

Counts

4 → 76

Calls

4 calls:

21.0ms	(-.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)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))

series289.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(-.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))
52.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
27.0ms	(*.f64 K (+.f64 m n))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5708	1646

prune132.0ms (2%)

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)

localize13.0ms (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)

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_419`
12×	`add-sqr-sqrt_binary64_441`
7×	`add-log-exp_binary64_458`
6×	`unpow-prod-down_binary64_498`
5×	`add-cube-cbrt_binary64_454`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `add-exp-log_binary64_457` `pow-unpow_binary64_496` `pow1_binary64_480`
2×	`distribute-lft-out_binary64_370` `add-cbrt-cube_binary64_455` `diff-log_binary64_511`
1×	`times-frac_binary64_425` `sub-neg_binary64_412` `pow-exp_binary64_487` `sqr-pow_binary64_391` `sum-log_binary64_510` `flip3--_binary64_423` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `associate--r+_binary64_355` `flip--_binary64_394` `unpow2_binary64_484`

Counts

2 → 41

Calls

2 calls:

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)

series192.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

134.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
57.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5184	1059

prune59.0ms (0.9%)

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)

localize24.0ms (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))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_553`
9×	`cancel-sign-sub-inv_binary64_385`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`sub-neg_binary64_412` `cbrt-prod_binary64_450` `cos-diff_binary64_556`
1×	`pow1/3_binary64_501`

Counts

4 → 47

Calls

4 calls:

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

series503.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
75.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
74.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
71.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4958	1248
1	4958	1248

prune132.0ms (2%)

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)

localize25.0ms (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))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_419`
12×	`cbrt-prod_binary64_450`
8×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
6×	`cbrt-div_binary64_451`
4×	`cos-sum_binary64_553` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`flip3-+_binary64_422` `pow1/3_binary64_501` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `cancel-sign-sub-inv_binary64_385`
1×	`sub-neg_binary64_412` `cos-diff_binary64_556`

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))

series491.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(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))
124.0ms	(cbrt.f64 (+.f64 m n))
111.0ms	(cbrt.f64 (+.f64 m n))
107.0ms	(cbrt.f64 (+.f64 m n))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4875	997
1	4875	997

prune100.0ms (1.5%)

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)

regimes236.0ms (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%)

sample1.8s (26.2%)

Algorithm

1×

intervals

Results

800.0ms	7842×	body	128	valid
37.0ms	73×	body	1024	invalid
33.0ms	64×	body	1024	valid
27.0ms	261×	body	128	invalid
23.0ms	78×	body	512	invalid
20.0ms	64×	body	512	valid
12.0ms	58×	body	256	invalid
11.0ms	14×	body	2048	invalid
6.0ms	28×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 572 to 424 computations (25.9% saved)

Details

analyze2.1s (31.3%)

sample43.0ms (0.6%)

simplify139.0ms (2.1%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

rewrite55.0ms (0.8%)

series289.0ms (4.3%)

simplify64.0ms (1%)

prune132.0ms (2%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series192.0ms (2.9%)

simplify69.0ms (1%)

prune59.0ms (0.9%)

localize24.0ms (0.4%)

rewrite38.0ms (0.6%)

series503.0ms (7.5%)

simplify83.0ms (1.2%)

prune132.0ms (2%)

localize25.0ms (0.4%)

rewrite34.0ms (0.5%)

series491.0ms (7.3%)

simplify72.0ms (1.1%)

prune100.0ms (1.5%)

regimes236.0ms (3.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (26.2%)

Profiling