Details

analyze2.3s (29.8%)

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)

sample47.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	251×	body	128	valid
2.0ms	18×	body	128	invalid
2.0ms	4×	body	1024	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	2×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify206.0ms (2.7%)

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: 17.4b

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 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_772`
12×	`*-un-lft-identity_binary64_751`
10×	`add-exp-log_binary64_786`
9×	`add-cbrt-cube_binary64_784`
8×	`add-cube-cbrt_binary64_783`
6×	`add-log-exp_binary64_787` `unpow-prod-down_binary64_827`
5×	`pow1_binary64_809`
4×	`times-frac_binary64_757`
3×	`associate-/r*_binary64_697` `pow-unpow_binary64_825` `difference-of-squares_binary64_720`
2×	`distribute-lft-out--_binary64_705` `associate-/l/_binary64_700` `associate-*r/_binary64_695` `cbrt-undiv_binary64_782` `sub-neg_binary64_744` `div-exp_binary64_799`
1×	`prod-exp_binary64_797` `pow-to-exp_binary64_817` `unpow2_binary64_813` `flip3-+_binary64_754` `pow-exp_binary64_816` `cos-sum_binary64_882` `sqr-pow_binary64_723` `flip--_binary64_726` `pow-pow_binary64_820` `div-inv_binary64_748` `diff-log_binary64_840` `frac-2neg_binary64_762` `cos-diff_binary64_885` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `associate-/l*_binary64_698` `flip3--_binary64_755` `flip-+_binary64_725`

Counts

4 → 66

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

series428.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
114.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
92.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
68.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4975	1265
1	4975	1265

prune129.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 1.2b

Counts

79 → 6

Compiler

Compiled 2786 to 1430 computations (48.7% 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)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

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

series380.0ms (4.9%)

Counts

2 → 6

Calls

2 calls:

268.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
112.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5173	1008

prune62.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 1.2b

Counts

49 → 6

Compiler

Compiled 1280 to 730 computations (43% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b	(/.f64 K (/.f64 2 (+.f64 m n)))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

rewrite97.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64_757`
85×	`*-un-lft-identity_binary64_751`
71×	`add-sqr-sqrt_binary64_772`
57×	`add-cube-cbrt_binary64_783`
18×	`associate-/r*_binary64_697`
12×	`distribute-lft-out_binary64_704`
10×	`add-exp-log_binary64_786`
9×	`add-cbrt-cube_binary64_784` `associate-/r/_binary64_699`
6×	`add-log-exp_binary64_787` `unpow-prod-down_binary64_827`
5×	`pow1_binary64_809` `div-inv_binary64_748` `difference-of-squares_binary64_720`
4×	`flip3-+_binary64_754` `flip-+_binary64_725`
3×	`cbrt-undiv_binary64_782` `associate-/l*_binary64_698` `pow-unpow_binary64_825` `div-exp_binary64_799`
2×	`distribute-lft-out--_binary64_705` `sub-neg_binary64_744`
1×	`pow-to-exp_binary64_817` `unpow2_binary64_813` `pow-exp_binary64_816` `cos-sum_binary64_882` `sqr-pow_binary64_723` `flip--_binary64_726` `pow-pow_binary64_820` `diff-log_binary64_840` `frac-2neg_binary64_762` `cos-diff_binary64_885` `clear-num_binary64_750` `flip3--_binary64_755`

Counts

4 → 135

Calls

4 calls:

30.0ms	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
26.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(/.f64 K (/.f64 2 (+.f64 m n)))

series421.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
111.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
99.0ms	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
60.0ms	(/.f64 K (/.f64 2 (+.f64 m n)))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4927	2987
1	4927	2987

prune241.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	148	5	153

Merged error: 1.2b

Counts

153 → 5

Compiler

Compiled 5469 to 2781 computations (49.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

rewrite88.0ms (1.1%)

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:

28.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
26.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
26.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))

series973.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

551.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))
142.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
141.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
138.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5706	942

prune120.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	48	7	55

Merged error: 1.2b

Counts

55 → 7

Compiler

Compiled 2887 to 1618 computations (44% saved)

regimes131.0ms (1.7%)

Compiler: Compiled 1480 to 1130 computations (23.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.7s (21.8%)

Algorithm

1×

intervals

Results

864.0ms	7833×	body	128	valid
36.0ms	79×	body	1024	invalid
34.0ms	315×	body	128	invalid
33.0ms	65×	body	1024	valid
27.0ms	81×	body	512	invalid
25.0ms	62×	body	512	valid
16.0ms	23×	body	2048	invalid
13.0ms	60×	body	256	invalid
9.0ms	37×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 341 to 261 computations (23.5% saved)

Details

analyze2.3s (29.8%)

sample47.0ms (0.6%)

simplify206.0ms (2.7%)

prune5.0ms (0.1%)

localize22.0ms (0.3%)

rewrite49.0ms (0.6%)

series428.0ms (5.5%)

simplify60.0ms (0.8%)

prune129.0ms (1.7%)

localize13.0ms (0.2%)

rewrite35.0ms (0.5%)

series380.0ms (4.9%)

simplify38.0ms (0.5%)

prune62.0ms (0.8%)

localize22.0ms (0.3%)

rewrite97.0ms (1.3%)

series421.0ms (5.4%)

simplify69.0ms (0.9%)

prune241.0ms (3.1%)

localize27.0ms (0.3%)

rewrite88.0ms (1.1%)

series973.0ms (12.6%)

simplify78.0ms (1%)

prune120.0ms (1.5%)

regimes131.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (21.8%)

Profiling