Details

analyze2.4s (28.1%)

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)

sample46.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	251×	body	128	valid
2.0ms	5×	body	512	invalid
1.0ms	3×	body	512	valid
1.0ms	3×	body	256	invalid
1.0ms	1×	body	2048	invalid
1.0ms	5×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify205.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

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)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 K (+.f64 m n))
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)
36.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_772`
14×	`*-un-lft-identity_binary64_751`
8×	`add-cube-cbrt_binary64_783`
7×	`pow1_binary64_809` `add-exp-log_binary64_786`
6×	`add-log-exp_binary64_787` `unpow-prod-down_binary64_827` `add-cbrt-cube_binary64_784`
4×	`associate-r_binary64_693`
3×	`associate-l_binary64_694` `pow-unpow_binary64_825`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `associate-*r/_binary64_695` `flip-+_binary64_725` `difference-of-squares_binary64_720`
1×	`distribute-lft-out--_binary64_705` `prod-exp_binary64_797` `pow-to-exp_binary64_817` `+-commutative_binary64_683` `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` `times-frac_binary64_757` `pow-pow_binary64_820` `sum-log_binary64_839` `cos-diff_binary64_885` `cbrt-unprod_binary64_781` `sub-neg_binary64_744` `distribute-rgt-in_binary64_703`

Counts

4 → 65

Calls

4 calls:

17.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))

series566.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
152.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
120.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
46.0ms	(*.f64 K (+.f64 m n))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5039	1186

prune125.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Merged error: 1.1b

Counts

78 → 5

Compiler

Compiled 2712 to 1358 computations (49.9% saved)

localize14.0ms (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)

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_751`
12×	`add-sqr-sqrt_binary64_772`
10×	`add-log-exp_binary64_787`
6×	`unpow-prod-down_binary64_827`
5×	`add-cube-cbrt_binary64_783`
4×	`pow1_binary64_809` `add-exp-log_binary64_786`
3×	`distribute-lft-out--_binary64_705` `add-cbrt-cube_binary64_784` `pow-unpow_binary64_825` `difference-of-squares_binary64_720`
2×	`distribute-lft-out_binary64_704` `diff-log_binary64_840` `sum-log_binary64_839`
1×	`pow-to-exp_binary64_817` `+-commutative_binary64_683` `unpow2_binary64_813` `flip3-+_binary64_754` `pow-exp_binary64_816` `sqr-pow_binary64_723` `flip--_binary64_726` `times-frac_binary64_757` `pow-pow_binary64_820` `associate--r+_binary64_689` `sub-neg_binary64_744` `flip3--_binary64_755` `flip-+_binary64_725`

Counts

3 → 49

Calls

3 calls:

18.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
17.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series646.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

276.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
245.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
124.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5055	1313

prune79.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Merged error: 1.1b

Counts

63 → 6

Compiler

Compiled 1625 to 913 computations (43.8% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
36.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_772`
11×	`*-un-lft-identity_binary64_751`
9×	`add-cube-cbrt_binary64_783`
6×	`exp-prod_binary64_800` `pow1_binary64_809` `unpow-prod-down_binary64_827`
5×	`add-log-exp_binary64_787` `add-exp-log_binary64_786`
4×	`add-cbrt-cube_binary64_784` `log-prod_binary64_834` `log-pow_binary64_837`
3×	`cos-sum_binary64_882` `cos-diff_binary64_885` `sub-neg_binary64_744` `pow-unpow_binary64_825`
2×	`exp-diff_binary64_796` `exp-sum_binary64_794` `difference-of-squares_binary64_720`
1×	`distribute-lft-out--_binary64_705` `pow-to-exp_binary64_817` `log-div_binary64_835` `rem-log-exp_binary64_789` `unpow2_binary64_813` `pow-exp_binary64_816` `sqr-pow_binary64_723` `times-frac_binary64_757` `pow-pow_binary64_820` `rem-exp-log_binary64_788`

Counts

4 → 60

Calls

4 calls:

13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
11.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series806.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
264.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
139.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
103.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4905	1380
1	4905	1380

prune121.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	72	6	78

Merged error: 1.1b

Counts

78 → 6

Compiler

Compiled 2747 to 1446 computations (47.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
36.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
36.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`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×	`cbrt-prod_binary64_779` `cos-sum_binary64_882` `cos-diff_binary64_885` `sub-neg_binary64_744`
1×	`pow1/3_binary64_830`

Counts

4 → 38

Calls

4 calls:

11.0ms	(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)))

series981.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

551.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
147.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
142.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
140.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5706	942

prune113.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	49	7	56

Merged error: 1.1b

Counts

56 → 7

Compiler

Compiled 2887 to 1458 computations (49.5% saved)

regimes118.0ms (1.4%)

Compiler: Compiled 1215 to 945 computations (22.2% 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 (19.7%)

Algorithm

1×

intervals

Results

875.0ms	7855×	body	128	valid
36.0ms	77×	body	1024	invalid
31.0ms	92×	body	512	invalid
30.0ms	54×	body	1024	valid
30.0ms	283×	body	128	invalid
19.0ms	56×	body	512	valid
12.0ms	56×	body	256	invalid
11.0ms	15×	body	2048	invalid
8.0ms	34×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 288 to 224 computations (22.2% saved)

Details

analyze2.4s (28.1%)

sample46.0ms (0.6%)

simplify205.0ms (2.4%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite57.0ms (0.7%)

series566.0ms (6.8%)

simplify43.0ms (0.5%)

prune125.0ms (1.5%)

localize14.0ms (0.2%)

rewrite55.0ms (0.7%)

series646.0ms (7.7%)

simplify62.0ms (0.7%)

prune79.0ms (0.9%)

localize30.0ms (0.4%)

rewrite51.0ms (0.6%)

series806.0ms (9.6%)

simplify79.0ms (0.9%)

prune121.0ms (1.4%)

localize27.0ms (0.3%)

rewrite39.0ms (0.5%)

series981.0ms (11.7%)

simplify79.0ms (0.9%)

prune113.0ms (1.3%)

regimes118.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (19.7%)

Profiling