Details

analyze3.2s (28.7%)

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)

sample2.3s (20.5%)

Symmetry

(sort m n)

Results

1.8s	8069×	body	128	valid
87.0ms	103×	body	1024	invalid
72.0ms	315×	body	128	invalid
64.0ms	75×	body	1024	valid
40.0ms	72×	body	512	invalid
37.0ms	64×	body	512	valid
28.0ms	24×	body	2048	invalid
25.0ms	61×	body	256	invalid
19.0ms	47×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify66.0ms (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

15.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.2b	(.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)

localize20.0ms (0.2%)

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	(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)
✓	33.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series499.0ms (4.5%)

Counts

4 → 192

Calls

4 calls:

376.0ms	(.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))))
78.0ms	(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))
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite103.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity_binary64`
96×	`add-sqr-sqrt_binary64`
93×	`prod-diff_binary64`
82×	`exp-sum_binary64`
59×	`add-cube-cbrt_binary64`

Counts

4 → 182

Calls

4 calls:

32.0ms	(.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))))
20.0ms	(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))
9.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

simplify445.0ms (4%)

Algorithm

1×	egg-herbie

Rules

546×	`*-commutative_binary64`
379×	`associate-r_binary64`
221×	`+-commutative_binary64`
198×	`fma-def_binary64`
186×	`cancel-sign-sub-inv_binary64`

Counts

374 → 373

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1154	26523
1	3108	23458
2	4872	23447
3	5002	23447

prune757.0ms (6.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	368	5	373
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	369	5	374

Error

1.0b

Counts

374 → 5

Alt Table

Status	Error	Program
▶	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.1b	(.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))))
	43.1b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) (*.f64 (sqrt.f64 M) (sqrt.f64 M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.2b	(.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
	15.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.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 34050 to 16839 computations (50.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series187.0ms (1.7%)

Counts

1 → 48

Calls

1 calls:

187.0ms

(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
44×	`associate-r_binary64`
41×	`exp-sum_binary64`
36×	`prod-diff_binary64`
35×	`add-sqr-sqrt_binary64`

Counts

1 → 62

Calls

1 calls:

28.0ms

(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

simplify149.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-r_binary64`
467×	`associate-l_binary64`
407×	`fma-neg_binary64`
377×	`fma-def_binary64`
295×	`*-commutative_binary64`

Counts

110 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	382	7602
1	1066	6643
2	4503	6643
3	5007	6643

prune529.0ms (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	279	5	284

Error

1.0b

Counts

284 → 5

Alt Table

Status	Error	Program
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	15.1b	(.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))))
	43.1b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (neg.f64 (.f64 (sqrt.f64 M) (sqrt.f64 M))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) (*.f64 (sqrt.f64 M) (sqrt.f64 M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.2b	(.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
	15.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.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 20369 to 10187 computations (50% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (+.f64 n m) (sqrt.f64 2))
✓	0.5b	(/.f64 K (sqrt.f64 2))
✓	32.9b	(sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))
✓	33.4b	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))

series118.0ms (1.1%)

Counts

4 → 64

Calls

4 calls:

52.0ms	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))
46.0ms	(sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))
11.0ms	(/.f64 (+.f64 n m) (sqrt.f64 2))
8.0ms	(/.f64 K (sqrt.f64 2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
27×	`sqrt-prod_binary64`

Counts

4 → 111

Calls

4 calls:

14.0ms	(/.f64 (+.f64 n m) (sqrt.f64 2))
3.0ms	(/.f64 K (sqrt.f64 2))
1.0ms	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))
1.0ms	(sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-def_binary64`
294×	`associate-r_binary64`
274×	`cancel-sign-sub-inv_binary64`
211×	`associate-l_binary64`
196×	`sub-neg_binary64`

Counts

175 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	364	4556
1	970	4388
2	3284	4239
3	5115	4239

prune778.0ms (7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	327	2	329
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	329	5	334

Error

1.0b

Counts

334 → 5

Alt Table

Status	Error	Program
	15.3b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (-.f64 (/.f64 (.f64 n K) (pow.f64 (sqrt.f64 2) 2)) 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))))
▶	15.0b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (-.f64 (/.f64 (.f64 K m) (pow.f64 (sqrt.f64 2) 2)) 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))))
	15.2b	(.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.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 23427 to 14221 computations (39.3% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(/.f64 K (sqrt.f64 2))
✓	1.0b	(pow.f64 (sqrt.f64 2) 2)
✓	24.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M))
	32.9b	(sin.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 n m) (sqrt.f64 2)) (neg.f64 M)))

series25.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

25.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M))
0.0ms	(pow.f64 (sqrt.f64 2) 2)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`cos-sum_binary64`
45×	`prod-diff_binary64`
33×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`

Counts

2 → 85

Calls

2 calls:

12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M))
2.0ms	(pow.f64 (sqrt.f64 2) 2)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
530×	`associate-r_binary64`
468×	`associate-l_binary64`
243×	`*-commutative_binary64`
227×	`associate-/l*_binary64`

Counts

97 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	6257
1	388	2830
2	911	2487
3	4215	2299
4	4952	2299
5	4933	2299

prune603.0ms (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	213	6	219

Error

1.0b

Counts

219 → 6

Alt Table

Status	Error	Program
	9.3b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (-.f64 (/.f64 (.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (neg.f64 M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.3b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (-.f64 (/.f64 (.f64 n K) (pow.f64 (sqrt.f64 2) 2)) 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))))
	15.0b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K m) (pow.f64 (sqrt.f64 2) 2)) M)))) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K m) (pow.f64 (sqrt.f64 2) 2)) 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))))
	15.2b	(.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (.f64 (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))) (cbrt.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))))
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.1b	(.f64 (-.f64 (.f64 (cos.f64 (.f64 M 0)) (cos.f64 (fma.f64 (/.f64 K (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.f64 2)) (neg.f64 M)))) (.f64 (sin.f64 (.f64 M 0)) (sin.f64 (fma.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 n m) (cbrt.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 16690 to 9951 computations (40.4% saved)

regimes726.0ms (6.5%)

Accuracy

Total 0.3b remaining (17.4%)

Threshold costs 0.3b (17.4%)

Counts

81 → 1

Compiler

Compiled 25328 to 17406 computations (31.3% 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

end211.0ms (1.9%)

Remove: (sort m n)
Compiler: Compiled 458 to 326 computations (28.8% saved)

Details

analyze3.2s (28.7%)

sample2.3s (20.5%)

simplify66.0ms (0.6%)

prune4.0ms (0%)

localize20.0ms (0.2%)

series499.0ms (4.5%)

rewrite103.0ms (0.9%)

simplify445.0ms (4%)

prune757.0ms (6.8%)

localize13.0ms (0.1%)

series187.0ms (1.7%)

rewrite42.0ms (0.4%)

simplify149.0ms (1.3%)

prune529.0ms (4.8%)

localize29.0ms (0.3%)

series118.0ms (1.1%)

rewrite24.0ms (0.2%)

simplify109.0ms (1%)

prune778.0ms (7%)

localize39.0ms (0.4%)

series25.0ms (0.2%)

rewrite25.0ms (0.2%)

simplify141.0ms (1.3%)

prune603.0ms (5.4%)

regimes726.0ms (6.5%)

simplify3.0ms (0%)

end211.0ms (1.9%)

Profiling