Details

analyze2.9s (34.1%)

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 (25.2%)

Symmetry

(sort m n)

Results

1.7s	8110×	body	128	valid
67.0ms	315×	body	128	invalid
66.0ms	84×	body	1024	invalid
49.0ms	58×	body	1024	valid
44.0ms	78×	body	512	invalid
37.0ms	64×	body	512	valid
27.0ms	59×	body	256	invalid
20.0ms	17×	body	2048	invalid
11.0ms	24×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (0.7%)

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

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(.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))))

Compiler

Compiled 128 to 80 computations (37.5% saved)

localize17.0ms (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	(/.f64 (*.f64 K (+.f64 m n)) 2)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	32.0b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series326.0ms (3.9%)

Counts

4 → 180

Calls

4 calls:

279.0ms	(.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))))
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

rewrite72.0ms (0.9%)

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:

29.0ms	(.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))))
8.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
5.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)

simplify249.0ms (3%)

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

prune600.0ms (7.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	316	5	321
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	317	5	322

Error

0.8b

Counts

322 → 5

Alt Table

Status	Error	Program
	13.0b	(.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))))
	13.0b	(.f64 (log1p.f64 (expm1.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))))
▶	1.1b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	13.0b	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 25886 to 12848 computations (50.4% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)

series54.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

54.0ms

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
41×	`exp-sum_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
21×	`fabs-mul_binary64`

Counts

1 → 62

Calls

1 calls:

22.0ms

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

simplify142.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

419×	`associate-r_binary64`
375×	`fma-def_binary64`
366×	`times-frac_binary64`
317×	`fma-neg_binary64`
310×	`associate-l_binary64`

Counts

110 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	8695
1	993	6748
2	3794	5655
3	5203	5655

prune259.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	165	4	169

Error

0.8b

Counts

169 → 4

Alt Table

Status	Error	Program
	13.0b	(.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))))
▶	1.1b	(*.f64 (cos.f64 M) (/.f64 (exp.f64 (-.f64 m n)) (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))
	16.6b	(.f64 (cos.f64 M) (fma.f64 (+.f64 (.f64 M m) 1) (exp.f64 (-.f64 (fma.f64 n M (-.f64 m n)) (fma.f64 M M (fma.f64 1/4 (.f64 n n) l)))) (.f64 (.f64 n (.f64 m (exp.f64 (-.f64 (fma.f64 n M (-.f64 m n)) (fma.f64 M M (fma.f64 1/4 (*.f64 n n) l)))))) -1/2)))
	13.0b	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 10282 to 5230 computations (49.1% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

16.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
3×	`pow-unpow_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

7.0ms

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

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
510×	`cancel-sign-sub-inv_binary64`
416×	`unswap-sqr_binary64`
402×	`distribute-rgt-in_binary64`
281×	`fma-def_binary64`

Counts

59 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1345
1	225	1225
2	570	1176
3	1953	1170
4	4214	1170
5	4820	1170
6	4968	1170

prune224.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Error

0.8b

Counts

65 → 4

Alt Table

Status	Error	Program
▶	12.6b	(.f64 (cos.f64 M) (/.f64 (exp.f64 (-.f64 m n)) (exp.f64 (+.f64 l (fma.f64 1/2 (.f64 m n) (fma.f64 1/4 (.f64 n n) (.f64 M (-.f64 M (+.f64 m n)))))))))
✓	1.1b	(*.f64 (cos.f64 M) (/.f64 (exp.f64 (-.f64 m n)) (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))
	13.0b	(.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))))
	13.0b	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 1882 to 979 computations (48% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 M (-.f64 M (+.f64 m n)))
✓	1.3b	(fma.f64 1/4 (.f64 n n) (.f64 M (-.f64 M (+.f64 m n))))
✓	3.3b	(fma.f64 1/2 (.f64 m n) (fma.f64 1/4 (.f64 n n) (*.f64 M (-.f64 M (+.f64 m n)))))

series45.0ms (0.5%)

Counts

3 → 108

Calls

3 calls:

20.0ms	(fma.f64 1/2 (.f64 m n) (fma.f64 1/4 (.f64 n n) (*.f64 M (-.f64 M (+.f64 m n)))))
13.0ms	(fma.f64 1/4 (.f64 n n) (.f64 M (-.f64 M (+.f64 m n))))
11.0ms	(*.f64 M (-.f64 M (+.f64 m n)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`
17×	`distribute-lft-in_binary64`

Counts

3 → 79

Calls

3 calls:

7.0ms	(*.f64 M (-.f64 M (+.f64 m n)))
0.0ms	(fma.f64 1/2 (.f64 m n) (fma.f64 1/4 (.f64 n n) (*.f64 M (-.f64 M (+.f64 m n)))))
0.0ms	(fma.f64 1/4 (.f64 n n) (.f64 M (-.f64 M (+.f64 m n))))

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
659×	`fma-def_binary64`
378×	`distribute-rgt-in_binary64`
360×	`distribute-lft-in_binary64`
285×	`exp-sum_binary64`

Counts

187 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	3536
1	338	2869
2	1025	2622
3	3452	2549
4	4492	2549
5	4838	2549

prune213.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	141	4	145

Error

0.8b

Counts

145 → 4

Alt Table

Status	Error	Program
✓	12.6b	(.f64 (cos.f64 M) (/.f64 (exp.f64 (-.f64 m n)) (exp.f64 (+.f64 l (fma.f64 1/2 (.f64 m n) (fma.f64 1/4 (.f64 n n) (.f64 M (-.f64 M (+.f64 m n)))))))))
✓	1.1b	(*.f64 (cos.f64 M) (/.f64 (exp.f64 (-.f64 m n)) (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))
	13.0b	(.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))))
	13.0b	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (+.f64 m n) (cbrt.f64 2))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 5199 to 1726 computations (66.8% saved)

regimes560.0ms (6.7%)

Accuracy

Total 0.2b remaining (17.3%)

Threshold costs 0.2b (17.3%)

Counts

76 → 1

Compiler

Compiled 15980 to 10446 computations (34.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	24	31
2	32	31
3	36	31
4	38	31
5	38	31

end256.0ms (3.1%)

Compiler: Compiled 256 to 175 computations (31.6% saved)

Details

analyze2.9s (34.1%)

sample2.1s (25.2%)

simplify62.0ms (0.7%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series326.0ms (3.9%)

rewrite72.0ms (0.9%)

simplify249.0ms (3%)

prune600.0ms (7.1%)

localize13.0ms (0.1%)

series54.0ms (0.6%)

rewrite32.0ms (0.4%)

simplify142.0ms (1.7%)

prune259.0ms (3.1%)

localize13.0ms (0.2%)

series16.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify90.0ms (1.1%)

prune224.0ms (2.7%)

localize20.0ms (0.2%)

series45.0ms (0.5%)

rewrite15.0ms (0.2%)

simplify121.0ms (1.4%)

prune213.0ms (2.5%)

regimes560.0ms (6.7%)

simplify2.0ms (0%)

end256.0ms (3.1%)

Profiling