Details

analyze3.0s (24.2%)

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)

sample2.4s (19.2%)

Symmetry

(sort m n)

Results

1.9s	8063×	body	128	valid
86.0ms	96×	body	1024	invalid
83.0ms	52×	body	256	invalid
70.0ms	81×	body	1024	valid
65.0ms	296×	body	128	invalid
49.0ms	87×	body	512	invalid
44.0ms	75×	body	512	valid
23.0ms	19×	body	2048	invalid
16.0ms	36×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify59.0ms (0.5%)

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

prune6.0ms (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

17.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.5b	(.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)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	33.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series99.0ms (0.8%)

Counts

4 → 168

Calls

4 calls:

51.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
25.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(*.f64 K (+.f64 m n))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64`
57×	`prod-diff_binary64`
42×	`add-cube-cbrt_binary64`
26×	`fabs-mul_binary64`

Counts

4 → 156

Calls

4 calls:

20.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
4.0ms	(*.f64 K (+.f64 m n))

simplify205.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
385×	`associate-r_binary64`
362×	`associate-l_binary64`
329×	`fma-def_binary64`
268×	`*-commutative_binary64`

Counts

324 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	11388
1	1288	8942
2	4458	8942
3	5047	8942

prune443.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	299	6	305
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	300	6	306

Error

1.3b

Counts

306 → 6

Alt Table

Status	Error	Program
	17.5b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (*.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.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 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
	17.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
	33.2b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 n m)) 3)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 15224 to 7419 computations (51.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 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	(-.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)

series53.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

44.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
9.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
50×	`times-frac_binary64`
48×	`prod-diff_binary64`

Counts

2 → 108

Calls

2 calls:

11.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
9.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

simplify135.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-l_binary64`
397×	`associate--l+_binary64`
393×	`associate-+l+_binary64`
337×	`associate-r_binary64`
215×	`associate-+r+_binary64`

Counts

192 → 162

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	204	4358
1	487	3519
2	1353	2862
3	4455	2838
4	4747	2837
5	4914	2837

prune485.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	345	0	345
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	345	6	351

Error

1.3b

Counts

351 → 6

Alt Table

Status	Error	Program
	17.5b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (*.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.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 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
	17.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
	33.2b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 n m)) 3)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 12812 to 6135 computations (52.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	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)
✓	20.8b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series311.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

299.0ms	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
11.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
44×	`associate-r_binary64`
41×	`exp-sum_binary64`
39×	`prod-diff_binary64`
38×	`add-sqr-sqrt_binary64`

Counts

2 → 79

Calls

2 calls:

32.0ms	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
5.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

simplify205.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
594×	`*-commutative_binary64`
381×	`associate-+r+_binary64`
274×	`fma-neg_binary64`
257×	`associate-+l+_binary64`

Counts

151 → 156

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	633	12389
1	1730	10998
2	4889	10998
3	5125	10998

prune655.0ms (5.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	338	7	345

Error

1.3b

Counts

345 → 7

Alt Table

Status	Error	Program
▶	10.2b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
	17.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
	33.2b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 n m)) 3)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	18.1b	(.f64 (+.f64 (neg.f64 l) 1) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (exp.f64 (-.f64 (fma.f64 M m (fma.f64 M n (fabs.f64 (-.f64 m n)))) (fma.f64 1/4 (.f64 m m) (fma.f64 1/2 (.f64 n m) (fma.f64 M M (.f64 (.f64 n n) 1/4))))))))
	17.5b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (*.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 23777 to 12213 computations (48.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))
✓	0.3b	(.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))
✓	0.5b	(cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))
	20.8b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series2.1s (16.9%)

Counts

3 → 108

Calls

3 calls:

1.1s

(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))

912.0ms

(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

68.0ms

(*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))

rewrite83.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))

6.0ms

(*.f64 (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M))))

2.0ms

(cbrt.f64 (cos.f64 (-.f64 (*.f64 1/2 (*.f64 n K)) M)))

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

674×	`cancel-sign-sub-inv_binary64`
484×	`unswap-sqr_binary64`
355×	`associate-r_binary64`
296×	`associate-l_binary64`
291×	`neg-mul-1_binary64`

Counts

201 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	5480
1	679	4979
2	2486	4825
3	4750	4764
4	5070	4764

prune879.0ms (7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	336	8	344

Error

1.3b

Counts

344 → 8

Alt Table

Status	Error	Program
	18.1b	(.f64 (+.f64 (neg.f64 l) 1) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (exp.f64 (-.f64 (fma.f64 M m (fma.f64 M n (fabs.f64 (-.f64 m n)))) (fma.f64 1/4 (.f64 m m) (fma.f64 1/2 (.f64 n m) (fma.f64 M M (.f64 (.f64 n n) 1/4))))))))
	10.2b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) 5) (cbrt.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
	17.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
	33.2b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 n m)) 3)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	17.5b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (*.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.3b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (cbrt.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (cbrt.f64 (cos.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 21283 to 12015 computations (43.5% saved)

regimes817.0ms (6.5%)

Accuracy

Total 0.2b remaining (14.5%)

Threshold costs 0.2b (14.5%)

Counts

113 → 1

Compiler

Compiled 23978 to 15930 computations (33.6% saved)

simplify3.0ms (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	31
1	28	31
2	45	31
3	60	31
4	69	31
5	72	31
6	72	31

end204.0ms (1.6%)

Remove: (sort m n)
Compiler: Compiled 462 to 312 computations (32.5% saved)

Details

analyze3.0s (24.2%)

sample2.4s (19.2%)

simplify59.0ms (0.5%)

prune6.0ms (0%)

localize17.0ms (0.1%)

series99.0ms (0.8%)

rewrite59.0ms (0.5%)

simplify205.0ms (1.6%)

prune443.0ms (3.5%)

localize13.0ms (0.1%)

series53.0ms (0.4%)

rewrite32.0ms (0.3%)

simplify135.0ms (1.1%)

prune485.0ms (3.8%)

localize17.0ms (0.1%)

series311.0ms (2.5%)

rewrite55.0ms (0.4%)

simplify205.0ms (1.6%)

prune655.0ms (5.2%)

localize20.0ms (0.2%)

series2.1s (16.9%)

rewrite83.0ms (0.7%)

simplify143.0ms (1.1%)

prune879.0ms (7%)

regimes817.0ms (6.5%)

simplify3.0ms (0%)

end204.0ms (1.6%)

Profiling