Details

analyze2.4s (33.8%)

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

27.0ms	249×	body	128	valid
2.0ms	4×	body	1024	invalid
1.0ms	12×	body	128	invalid
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	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify213.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5053	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: 16.0b

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 (*.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))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_772`
14×	`*-un-lft-identity_binary64_751`
12×	`add-exp-log_binary64_786`
11×	`add-cbrt-cube_binary64_784`
10×	`add-cube-cbrt_binary64_783`
7×	`pow1_binary64_809`
6×	`unpow-prod-down_binary64_827`
4×	`add-log-exp_binary64_787` `times-frac_binary64_757` `associate-r/_binary64_695` `associate-r*_binary64_693`
3×	`associate-/r_binary64_697` `associate-l*_binary64_694` `pow-unpow_binary64_825`
2×	`prod-exp_binary64_797` `flip3-+_binary64_754` `associate-/l/_binary64_700` `cbrt-undiv_binary64_782` `cbrt-unprod_binary64_781` `flip-+_binary64_725` `difference-of-squares_binary64_720` `div-exp_binary64_799`
1×	`distribute-lft-out--_binary64_705` `pow-to-exp_binary64_817` `distribute-lft-out_binary64_704` `unswap-sqr_binary64_719` `unpow2_binary64_813` `pow-exp_binary64_816` `cos-sum_binary64_882` `distribute-lft-in_binary64_702` `sqr-pow_binary64_723` `pow-prod-down_binary64_819` `-commutative_binary64_684` `pow-pow_binary64_820` `div-inv_binary64_748` `frac-2neg_binary64_762` `cos-diff_binary64_885` `clear-num_binary64_750` `sub-neg_binary64_744` `associate-/l_binary64_698` `distribute-rgt-in_binary64_703`

Counts

4 → 76

Calls

4 calls:

13.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
7.0ms	(*.f64 K (+.f64 m n))

series386.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
119.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
64.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
45.0ms	(*.f64 K (+.f64 m n))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5052	1189

prune145.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 1.3b

Counts

89 → 5

Compiler

Compiled 3038 to 1530 computations (49.6% saved)

localize14.0ms (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)

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_772`
8×	`*-un-lft-identity_binary64_751`
6×	`unpow-prod-down_binary64_827`
4×	`add-cube-cbrt_binary64_783` `add-log-exp_binary64_787` `difference-of-squares_binary64_720`
3×	`pow1_binary64_809` `add-exp-log_binary64_786` `pow-unpow_binary64_825`
2×	`distribute-lft-out--_binary64_705` `times-frac_binary64_757` `add-cbrt-cube_binary64_784`
1×	`pow-to-exp_binary64_817` `unpow2_binary64_813` `pow-exp_binary64_816` `sqr-pow_binary64_723` `flip--_binary64_726` `pow-pow_binary64_820` `diff-log_binary64_840` `sub-neg_binary64_744` `flip3--_binary64_755`

Counts

2 → 35

Calls

2 calls:

15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
12.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

series138.0ms (2%)

Counts

2 → 6

Calls

2 calls:

103.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
35.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4904	675
1	4904	675

prune55.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 1.3b

Counts

46 → 5

Compiler

Compiled 1162 to 665 computations (42.8% saved)

localize30.0ms (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))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_779`
7×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
4×	`pow1_binary64_809` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`pow1/3_binary64_830`
1×	`cos-sum_binary64_882` `cos-diff_binary64_885` `sub-neg_binary64_744`

Counts

4 → 42

Calls

4 calls:

16.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
2.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)

series679.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
155.0ms	(cbrt.f64 K)
153.0ms	(cbrt.f64 K)
149.0ms	(cbrt.f64 K)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4885	495
1	4885	495

prune84.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	54	5	59

Merged error: 1.3b

Counts

59 → 5

Compiler

Compiled 2146 to 991 computations (53.8% saved)

localize29.0ms (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))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_779`
7×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
4×	`pow1_binary64_809` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`pow1/3_binary64_830`
1×	`cos-sum_binary64_882` `cos-diff_binary64_885` `sub-neg_binary64_744`

Counts

4 → 42

Calls

4 calls:

17.0ms	(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)

series506.0ms (7.2%)

Counts

4 → 6

Calls

4 calls:

506.0ms	(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)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4968	594
1	4968	594

prune84.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	47	6	53

Merged error: 1.3b

Counts

53 → 6

Compiler

Compiled 1785 to 1095 computations (38.7% 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 (23.5%)

Algorithm

1×

intervals

Results

878.0ms	7833×	body	128	valid
37.0ms	77×	body	1024	invalid
31.0ms	288×	body	128	invalid
31.0ms	59×	body	1024	valid
30.0ms	91×	body	512	invalid
22.0ms	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

analyze2.4s (33.8%)

sample49.0ms (0.7%)

simplify213.0ms (3.1%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite48.0ms (0.7%)

series386.0ms (5.5%)

simplify78.0ms (1.1%)

prune145.0ms (2.1%)

localize14.0ms (0.2%)

rewrite31.0ms (0.4%)

series138.0ms (2%)

simplify70.0ms (1%)

prune55.0ms (0.8%)

localize30.0ms (0.4%)

rewrite25.0ms (0.4%)

series679.0ms (9.7%)

simplify89.0ms (1.3%)

prune84.0ms (1.2%)

localize29.0ms (0.4%)

rewrite25.0ms (0.4%)

series506.0ms (7.2%)

simplify70.0ms (1%)

prune84.0ms (1.2%)

regimes109.0ms (1.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (23.5%)

Profiling