Details

analyze2.9s (30.4%)

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 35 to 24 computations (31.4% saved)

sample2.1s (21.7%)

Symmetry

(sort m n)

Results

1.7s	8089×	body	128	valid
101.0ms	117×	body	1024	invalid
72.0ms	68×	body	1024	valid
63.0ms	308×	body	128	invalid
41.0ms	60×	body	512	invalid
34.0ms	59×	body	512	valid
31.0ms	29×	body	2048	invalid
20.0ms	57×	body	256	invalid
14.0ms	39×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

691×	`exp-prod_binary64`
507×	`exp-sum_binary64`
446×	`fma-neg_binary64`
375×	`associate-l_binary64`
251×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	129	43
3	384	43
4	1266	43
5	4023	43
6	4945	43
7	5019	43

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

15.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	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)
✓	34.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series99.0ms (1%)

Counts

4 → 180

Calls

4 calls:

43.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
26.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
14.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

rewrite93.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

851×	`prod-diff_binary64`
199×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
186×	`add-log-exp_binary64`

Counts

4 → 120

Calls

4 calls:

90.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
90.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
90.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
90.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	57
1	384	57
2	4847	57
3	6544	57
0	0	0
1	0	0

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary64`
566×	`associate--l+_binary64`
566×	`cancel-sign-sub-inv_binary64`
232×	`fma-def_binary64`
221×	`associate-r_binary64`

Counts

300 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	4422
1	618	3915
2	2187	3816
3	4618	3810
4	5253	3810

prune219.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

0.8b

Counts

207 → 4

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8586 to 4283 computations (50.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
	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)

series7.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(-.f64 (/.f64 (+.f64 m n) 2) M)

rewrite109.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

955×	`prod-diff_binary64`
696×	`fma-udef_binary64`
223×	`fma-neg_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Counts

1 → 58

Calls

1 calls:

108.0ms

(-.f64 (/.f64 (+.f64 m n) 2) M)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	188	10
2	2516	10
3	4665	10
4	4561	10
5	5023	10
0	0	0
1	0	0

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

250×	`fma-def_binary64`
241×	`fma-neg_binary64`
86×	`cancel-sign-sub-inv_binary64`
46×	`sub-neg_binary64`
40×	`associate--r+_binary64`

Counts

94 → 68

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	313
1	27	313
2	44	313
3	68	313
4	108	313
5	167	313
6	315	313
7	433	313
8	508	313
9	555	313
10	567	313
11	569	313
12	541	313

prune180.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Error

0.8b

Counts

166 → 4

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.7b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.3b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 4741 to 2360 computations (50.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
	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)
✓	30.2b	(cos.f64 (.f64 1/2 (.f64 K m)))

series6.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

6.0ms

(cos.f64 (*.f64 1/2 (*.f64 K m)))

rewrite41.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`log1p-expm1-u_binary64`
597×	`expm1-log1p-u_binary64`
343×	`log-prod_binary64`
324×	`prod-diff_binary64`
126×	`expm1-udef_binary64`

Counts

1 → 22

Calls

1 calls:

41.0ms

(cos.f64 (*.f64 1/2 (*.f64 K m)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	9
2	1575	9
3	5157	9
0	0	0
1	0	0

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

612×	`distribute-rgt-neg-in_binary64`
529×	`distribute-lft-neg-in_binary64`
489×	`fma-def_binary64`
356×	`cancel-sign-sub-inv_binary64`
353×	`*-commutative_binary64`

Counts

30 → 29

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	27	184
1	75	176
2	221	168
3	928	164
4	2389	152
5	3661	146
6	4943	128
7	4908	128

prune231.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	191	4	195

Error

0.8b

Counts

195 → 4

Alt Table

Status	Error	Program
▶	10.4b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	10.3b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 6256 to 3349 computations (46.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (*.f64 K m))))))
✓	0.8b	(log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (*.f64 K m)))))))
✓	1.1b	(cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))
	30.2b	(cos.f64 (.f64 1/2 (.f64 K m)))

series2.2s (23.1%)

Counts

3 → 72

Calls

3 calls:

1.2s

(log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))))

564.0ms

(*.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))))

436.0ms

(cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

rewrite57.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

854×	`log1p-expm1-u_binary64`
854×	`expm1-log1p-u_binary64`
341×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
97×	`add-log-exp_binary64`

Counts

3 → 63

Calls

3 calls:

56.0ms

(*.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))))

55.0ms

(log.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))))

55.0ms

(cbrt.f64 (exp.f64 (cos.f64 (*.f64 1/2 (*.f64 K m)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	47
1	211	42
2	2279	42
3	5806	42
0	0	0
1	0	0

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

736×	`distribute-rgt-neg-in_binary64`
699×	`distribute-lft-neg-in_binary64`
615×	`associate-r_binary64`
551×	`associate-l_binary64`
264×	`cancel-sign-sub-inv_binary64`

Counts

135 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	1616
1	212	1532
2	684	1320
3	3180	1320
4	4929	1320
5	4976	1320
6	4936	1320

prune405.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	239	4	243

Error

0.8b

Counts

243 → 4

Alt Table

Status	Error	Program
✓	10.4b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.4b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))) (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m))))))) (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (cos.f64 (.f64 1/2 (.f64 K m)))))) 3))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.6b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 12399 to 7955 computations (35.8% saved)

regimes358.0ms (3.7%)

Accuracy

Total 0.1b remaining (10.9%)

Threshold costs 0.1b (10.9%)

Counts

54 → 1

Compiler

Compiled 9284 to 6720 computations (27.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	30	26
2	46	26
3	61	26
4	70	26
5	73	26
6	72	26

end124.0ms (1.3%)

Remove: (sort m n)
Compiler: Compiled 254 to 184 computations (27.6% saved)

Iter	Nodes	Cost
0	13	313
1	27	313
2	44	313
3	68	313
4	108	313
5	167	313
6	315	313
7	433	313
8	508	313
9	555	313
10	567	313
11	569	313
12	541	313

Iter	Nodes	Cost
0	13	313
1	27	313
2	44	313
3	68	313
4	108	313
5	167	313
6	315	313
7	433	313
8	508	313
9	555	313
10	567	313
11	569	313
12	541	313

Details

analyze2.9s (30.4%)

sample2.1s (21.7%)

simplify59.0ms (0.6%)

prune4.0ms (0%)

localize16.0ms (0.2%)

series99.0ms (1%)

rewrite93.0ms (1%)

simplify123.0ms (1.3%)

prune219.0ms (2.3%)

localize12.0ms (0.1%)

series7.0ms (0.1%)

rewrite109.0ms (1.1%)

simplify39.0ms (0.4%)

prune180.0ms (1.9%)

localize16.0ms (0.2%)

series6.0ms (0.1%)

rewrite41.0ms (0.4%)

simplify71.0ms (0.7%)

prune231.0ms (2.4%)

localize24.0ms (0.3%)

series2.2s (23.1%)

rewrite57.0ms (0.6%)

simplify103.0ms (1.1%)

prune405.0ms (4.2%)

regimes358.0ms (3.7%)

simplify4.0ms (0%)

end124.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	13	313
1	27	313
2	44	313
3	68	313
4	108	313
5	167	313
6	315	313
7	433	313
8	508	313
9	555	313
10	567	313
11	569	313
12	541	313