Details

analyze2.8s (35.4%)

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)

sample2.0s (25.5%)

Symmetry

(sort m n)

Results

1.7s	8093×	body	128	valid
76.0ms	98×	body	1024	invalid
61.0ms	308×	body	128	invalid
53.0ms	67×	body	1024	valid
40.0ms	70×	body	512	invalid
34.0ms	61×	body	512	valid
25.0ms	61×	body	256	invalid
14.0ms	13×	body	2048	invalid
13.0ms	35×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
251×	`times-frac_binary64`
231×	`cancel-sign-sub-inv_binary64`
219×	`exp-sum_binary64`
202×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	135	43
3	442	43
4	1753	43

Stop Event

1×	node limit

Counts

1 → 2

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

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 128 to 83 computations (35.2% 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	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	31.9b	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

series55.0ms (0.7%)

Counts

4 → 168

Calls

4 calls:

20.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
13.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
7.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

354×	`fma-def_binary64`
241×	`expm1-udef_binary64`
241×	`log1p-udef_binary64`
201×	`fma-neg_binary64`
173×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	51
1	291	43
2	3972	43

Stop Event

1×	node limit

Counts

4 → 173

Calls

4 calls:

57.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)
57.0ms	(fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))
57.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
57.0ms	(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M)))

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
310×	`associate--r+_binary64`
277×	`associate--l+_binary64`
223×	`associate-r_binary64`
185×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3245
1	547	3003
2	2062	2914

Stop Event

1×	node limit

Counts

341 → 257

prune330.0ms (4.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	3	258

Error

0.4b

Counts

258 → 3

Alt Table

Status	Error	Program
	14.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.2b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	0.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 9696 to 4794 computations (50.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series38.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

37.0ms

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

rewrite48.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`fma-def_binary64`
264×	`fma-neg_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	259	16
2	3683	16

Stop Event

1×	node limit

Counts

1 → 43

Calls

1 calls:

46.0ms

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

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

816×	`sub-neg_binary64`
388×	`associate-+l-_binary64`
378×	`associate--l+_binary64`
361×	`fma-def_binary64`
352×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1394
1	228	1226
2	779	1215
3	2517	1213
4	4573	1213

Stop Event

1×	node limit

Counts

91 → 76

prune247.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	239	3	242

Error

0.4b

Counts

242 → 3

Alt Table

Status	Error	Program
	14.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.2b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 6879 to 3256 computations (52.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (.f64 n K)) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(.f64 1/2 (.f64 n K))
✓	24.4b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series22.0ms (0.3%)

Counts

3 → 21

Calls

3 calls:

9.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
7.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)
6.0ms	(.f64 1/2 (.f64 n K))

rewrite54.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`prod-diff_binary64`
295×	`fma-def_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
172×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	199	29
2	2633	29

Stop Event

1×	node limit

Counts

3 → 154

Calls

3 calls:

51.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)
51.0ms	(.f64 1/2 (.f64 n K))
51.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-neg_binary64`
398×	`distribute-rgt-neg-in_binary64`
394×	`distribute-lft-neg-in_binary64`
326×	`associate-r_binary64`
320×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	415
1	147	409
2	483	378
3	2361	368

Stop Event

1×	node limit

Counts

175 → 174

prune292.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	253	3	256

Error

0.4b

Counts

256 → 3

Alt Table

Status	Error	Program
	14.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.0b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (.f64 K (*.f64 1/2 n)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 9100 to 4836 computations (46.9% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))))
✓	0.4b	(expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M)))
✓	24.4b	(cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))

series67.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))))
26.0ms	(expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M)))
9.0ms	(cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

908×	`prod-diff_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
112×	`add-sqr-sqrt_binary64`
109×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	221	38
2	2835	38

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

51.0ms	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))))
51.0ms	(expm1.f64 (cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M)))
51.0ms	(cos.f64 (-.f64 (.f64 K (.f64 1/2 n)) M))

simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
531×	`cancel-sign-sub-inv_binary64`
310×	`associate-r_binary64`
205×	`associate-l_binary64`
204×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2619
1	489	2545
2	2066	2481

Stop Event

1×	node limit

Counts

178 → 83

prune211.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	162	3	165

Error

0.4b

Counts

165 → 3

Alt Table

Status	Error	Program
	14.4b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.5b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	10.0b	(.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 (.f64 K (*.f64 1/2 n)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 6869 to 3773 computations (45.1% saved)

regimes1.3s (16%)

Accuracy

Total 0.1b remaining (9.3%)

Threshold costs 0.1b (9.3%)

Counts

174 → 1

Compiler

Compiled 35030 to 23784 computations (32.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	26	29
2	40	29
3	53	29
4	61	29
5	64	29

Stop Event

1×

saturated

end91.0ms (1.1%)

Remove: (sort m n)
Compiler: Compiled 200 to 141 computations (29.5% saved)

Details

analyze2.8s (35.4%)

sample2.0s (25.5%)

simplify18.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.2%)

series55.0ms (0.7%)

rewrite60.0ms (0.7%)

simplify63.0ms (0.8%)

prune330.0ms (4.1%)

localize12.0ms (0.2%)

series38.0ms (0.5%)

rewrite48.0ms (0.6%)

simplify49.0ms (0.6%)

prune247.0ms (3.1%)

localize16.0ms (0.2%)

series22.0ms (0.3%)

rewrite54.0ms (0.7%)

simplify29.0ms (0.4%)

prune292.0ms (3.6%)

localize21.0ms (0.3%)

series67.0ms (0.8%)

rewrite53.0ms (0.7%)

simplify52.0ms (0.6%)

prune211.0ms (2.6%)

regimes1.3s (16%)

simplify3.0ms (0%)

end91.0ms (1.1%)

Profiling