Details

analyze3.1s (24.4%)

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)

sample2.2s (17.1%)

Symmetry

(sort m n)

Results

1.8s	8085×	body	128	valid
74.0ms	327×	body	128	invalid
66.0ms	79×	body	1024	invalid
59.0ms	73×	body	1024	valid
45.0ms	81×	body	512	invalid
29.0ms	54×	body	512	valid
23.0ms	20×	body	2048	invalid
21.0ms	55×	body	256	invalid
16.0ms	41×	body	256	valid
4.0ms	3×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (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

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

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(.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 (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))))
✓	0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	35.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series417.0ms (3.3%)

Counts

4 → 180

Calls

4 calls:

355.0ms	(.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))))
26.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
19.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
57×	`prod-diff_binary64`
44×	`associate-r_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 145

Calls

4 calls:

33.0ms	(.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))))
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

simplify251.0ms (2%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-def_binary64`
458×	`*-commutative_binary64`
308×	`associate-r_binary64`
166×	`+-commutative_binary64`
157×	`cancel-sign-sub-inv_binary64`

Counts

325 → 321

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	997	19371
1	2658	17213
2	4980	17213

prune665.0ms (5.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	313	8	321
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	314	8	322

Error

1.5b

Counts

322 → 8

Alt Table

Status	Error	Program
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.8b	(.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))))
	36.4b	(.f64 (cos.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 K (+.f64 n m)) 2) 3)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	30.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.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))))
	14.8b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (+.f64 m n)) (sqrt.f64 2)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 26102 to 12996 computations (50.2% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 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)

series55.0ms (0.4%)

Counts

2 → 52

Calls

2 calls:

53.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
2.0ms	(cos.f64 M)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-def_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 34

Calls

2 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
1.0ms	(cos.f64 M)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

741×	`distribute-rgt-in_binary64`
493×	`fma-def_binary64`
426×	`fma-neg_binary64`
392×	`associate--l+_binary64`
383×	`associate-+l+_binary64`

Counts

86 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1851
1	345	1637
2	858	1619
3	2936	1617
4	5525	1617

prune252.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	145	8	153

Error

1.5b

Counts

153 → 8

Alt Table

Status	Error	Program
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	10.8b	(.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))))
	36.4b	(.f64 (cos.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 K (+.f64 n m)) 2) 3)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	30.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.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))))
	14.8b	(.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (+.f64 m n)) (sqrt.f64 2)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 4516 to 2315 computations (48.7% saved)

localize17.0ms (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 (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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	26.5b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series313.0ms (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))))
14.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

rewrite52.0ms (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:

29.0ms	(.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))))
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

simplify206.0ms (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

prune580.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	283	1	284
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	284	8	292

Error

1.5b

Counts

292 → 8

Alt Table

Status	Error	Program
▶	10.8b	(.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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	10.8b	(.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))))
	36.4b	(.f64 (cos.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 K (+.f64 n m)) 2) 3)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	30.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (+.f64 m n)) (sqrt.f64 2)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 19715 to 10122 computations (48.7% 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))))
✓	0.4b	(.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)))
	26.5b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series2.2s (17.4%)

Counts

3 → 108

Calls

3 calls:

1.2s

(*.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))))

983.0ms

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

13.0ms

(*.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))))

rewrite28.0ms (0.2%)

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))))

8.0ms

(*.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))))

1.0ms

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

simplify164.0ms (1.3%)

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

prune946.0ms (7.5%)

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	1	1	2
Total	337	8	345

Error

1.5b

Counts

345 → 8

Alt Table

Status	Error	Program
✓	1.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.7b	(.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))))
	10.8b	(.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 M) 2)) (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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 1 (/.f64 2 (.f64 K (+.f64 m n)))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	36.4b	(.f64 (cos.f64 (-.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 K (+.f64 n m)) 2) 3)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	30.3b	(.f64 (cos.f64 (-.f64 (expm1.f64 (log1p.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))))
	14.8b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (+.f64 m n)) (sqrt.f64 2)) (sqrt.f64 2)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.9b	(.f64 (-.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 21219 to 11984 computations (43.5% saved)

regimes718.0ms (5.7%)

Accuracy

Total 0.2b remaining (15%)

Threshold costs 0.2b (15%)

Counts

87 → 1

Compiler

Compiled 20312 to 13134 computations (35.3% 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

end220.0ms (1.7%)

Remove: (sort m n)
Compiler: Compiled 398 to 281 computations (29.4% saved)

Details

analyze3.1s (24.4%)

sample2.2s (17.1%)

simplify62.0ms (0.5%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series417.0ms (3.3%)

rewrite80.0ms (0.6%)

simplify251.0ms (2%)

prune665.0ms (5.3%)

localize13.0ms (0.1%)

series55.0ms (0.4%)

rewrite18.0ms (0.1%)

simplify68.0ms (0.5%)

prune252.0ms (2%)

localize17.0ms (0.1%)

series313.0ms (2.5%)

rewrite52.0ms (0.4%)

simplify206.0ms (1.6%)

prune580.0ms (4.6%)

localize20.0ms (0.2%)

series2.2s (17.4%)

rewrite28.0ms (0.2%)

simplify164.0ms (1.3%)

prune946.0ms (7.5%)

regimes718.0ms (5.7%)

simplify3.0ms (0%)

end220.0ms (1.7%)

Profiling