Details

analyze2.3s (32%)

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)

sample49.0ms (0.7%)

Algorithm

1×

intervals

Results

29.0ms	249×	body	128	valid
2.0ms	4×	body	1024	valid
1.0ms	4×	body	512	invalid
1.0ms	9×	body	128	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	2048	invalid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

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

Merged error: 13.1b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(*.f64 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_782`
16×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795`
7×	`add-exp-log_binary64_798` `pow1_binary64_821`
6×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`difference-of-squares_binary64_729` `associate-l_binary64_701` `pow-unpow_binary64_837`
2×	`distribute-lft-out--_binary64_712` `associate-*r/_binary64_702` `sub-neg_binary64_753`
1×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `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` `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 → 72

Calls

4 calls:

11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
7.0ms	(*.f64 K (+.f64 m n))

series200.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
55.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
46.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
25.0ms	(*.f64 K (+.f64 m n))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5114	1313

prune178.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	5	85

Merged error: 1.4b

Counts

85 → 5

Compiler

Compiled 2969 to 1460 computations (50.8% saved)

localize12.0ms (0.2%)

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)

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

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×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
3×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837`
2×	`diff-log_binary64_852` `sum-log_binary64_851`
1×	`unpow2_binary64_825` `flip3-+_binary64_763` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `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

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)

series303.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

136.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
111.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
57.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5488	1364

prune77.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Merged error: 1.4b

Counts

67 → 5

Compiler

Compiled 1677 to 932 computations (44.4% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
33.8b	(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))

rewrite36.0ms (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:

19.0ms	(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))

series481.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(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))
107.0ms	(cbrt.f64 (+.f64 m n))
104.0ms	(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

prune108.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	65	6	71

Merged error: 1.4b

Counts

71 → 6

Compiler

Compiled 2987 to 1298 computations (56.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
13.8b	(cbrt.f64 (*.f64 K (+.f64 m n)))
33.9b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-div_binary64_792` `associate-*r/_binary64_702`
5×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
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` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `flip-+_binary64_734` `cbrt-prod_binary64_791`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753`

Counts

4 → 45

Calls

4 calls:

12.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
5.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))

series402.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
106.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
103.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
87.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.f64 (*.f64 K (+.f64 m n)))) 2) M))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4831	840
1	4831	840

prune89.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	57	6	63

Merged error: 1.3b

Counts

63 → 6

Compiler

Compiled 2527 to 938 computations (62.9% saved)

regimes363.0ms (5%)

Compiler: Compiled 5060 to 3654 computations (27.8% 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%)

sample2.0s (27.5%)

Algorithm

1×

intervals

Results

788.0ms	7846×	body	128	valid
44.0ms	101×	body	1024	invalid
32.0ms	314×	body	128	invalid
28.0ms	83×	body	512	invalid
28.0ms	62×	body	1024	valid
21.0ms	53×	body	512	valid
10.0ms	19×	body	2048	invalid
10.0ms	51×	body	256	invalid
8.0ms	38×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 879 to 638 computations (27.4% saved)

Details

analyze2.3s (32%)

sample49.0ms (0.7%)

simplify138.0ms (1.9%)

prune5.0ms (0.1%)

localize23.0ms (0.3%)

rewrite44.0ms (0.6%)

series200.0ms (2.8%)

simplify69.0ms (1%)

prune178.0ms (2.5%)

localize12.0ms (0.2%)

rewrite49.0ms (0.7%)

series303.0ms (4.2%)

simplify48.0ms (0.7%)

prune77.0ms (1.1%)

localize22.0ms (0.3%)

rewrite36.0ms (0.5%)

series481.0ms (6.7%)

simplify73.0ms (1%)

prune108.0ms (1.5%)

localize22.0ms (0.3%)

rewrite33.0ms (0.5%)

series402.0ms (5.6%)

simplify81.0ms (1.1%)

prune89.0ms (1.2%)

regimes363.0ms (5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (27.5%)

Profiling