Details

analyze3.7s (36.9%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
1.8%	98%	0.2%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample3.4s (33.6%)

Symmetry

(sort m n)

Results

2.0s	8096×	body	128	valid
1.1s	398×	body	8192	exit
57.0ms	63×	body	1024	valid
47.0ms	53×	body	1024	invalid
35.0ms	59×	body	512	valid
28.0ms	48×	body	512	invalid
15.0ms	37×	body	256	valid
14.0ms	34×	body	256	invalid
12.0ms	10×	body	2048	invalid
7.0ms	30×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 69 to 47 computations (31.9% saved)

simplify59.0ms (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

14.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.1b	(.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)

localize19.0ms (0.2%)

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 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	32.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series96.0ms (0.9%)

Counts

4 → 168

Calls

4 calls:

45.0ms	(+.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)
7.0ms	(*.f64 K (+.f64 m n))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
25×	`cos-sum_binary64`
24×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

4 → 108

Calls

4 calls:

11.0ms	(+.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)
5.0ms	(*.f64 K (+.f64 m n))

simplify142.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

326×	`associate-r_binary64`
293×	`fma-neg_binary64`
288×	`associate-l_binary64`
269×	`fma-def_binary64`
238×	`distribute-rgt-neg-in_binary64`

Counts

276 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	461	7167
1	983	5956
2	3264	5823
3	4933	5823

prune247.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	4	236

Error

0.8b

Counts

236 → 4

Alt Table

Status	Error	Program
	41.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.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))))
	14.1b	(.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))))
▶	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 10461 to 4987 computations (52.3% saved)

localize15.0ms (0.1%)

Local error

Found 3 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 (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 (0.5%)

Counts

1 → 48

Calls

1 calls:

53.0ms

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

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
26×	`fabs-mul_binary64`
21×	`add-cube-cbrt_binary64`

Counts

1 → 73

Calls

1 calls:

22.0ms

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

simplify127.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
479×	`distribute-rgt-in_binary64`
424×	`distribute-lft-in_binary64`
346×	`cancel-sign-sub-inv_binary64`
269×	`sub-neg_binary64`

Counts

121 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	6040
1	583	4533
2	1860	3642
3	4530	3634
4	4954	3634

prune262.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	230	5	235

Error

0.8b

Counts

235 → 5

Alt Table

Status	Error	Program
	41.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.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))))
	14.1b	(.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))))
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	25.4b	(.f64 (cos.f64 M) (exp.f64 (fma.f64 m (-.f64 M (.f64 n 1/2)) (.f64 (.f64 m m) -1/4))))
▶	14.1b	(.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 8823 to 4434 computations (49.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.6b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
✓	0.6b	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
✓	32.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))

series225.0ms (2.2%)

Counts

3 → 144

Calls

3 calls:

168.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
30.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
27.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cos-sum_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 83

Calls

3 calls:

13.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
5.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))

simplify203.0ms (2%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-l_binary64`
417×	`fma-def_binary64`
410×	`*-commutative_binary64`
382×	`fma-neg_binary64`
244×	`sub-neg_binary64`

Counts

227 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	542	8711
1	1274	7517
2	4122	7499
3	4910	7499
4	4988	7499

prune311.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	213	5	218

Error

0.8b

Counts

218 → 5

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.1b	(.f64 (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	41.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.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))))
▶	14.1b	(.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))))
	25.4b	(.f64 (cos.f64 M) (exp.f64 (fma.f64 m (-.f64 M (.f64 n 1/2)) (.f64 (.f64 m m) -1/4))))

Compiler

Compiled 12502 to 6576 computations (47.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.3b	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
✓	0.4b	(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
	32.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series116.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

88.0ms	(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
28.0ms	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

873×	`associate-r_binary64`
574×	`associate-l_binary64`
390×	`fma-def_binary64`
210×	`associate-+r+_binary64`
182×	`*-commutative_binary64`

Counts

118 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	361	4961
1	1177	4394
2	5022	4394

prune338.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	236	5	241

Error

0.8b

Counts

241 → 5

Alt Table

Status	Error	Program
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.1b	(.f64 (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) 3)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	41.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 K (+.f64 m n))) (sqrt.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))))
✓	14.1b	(.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))))
	25.4b	(.f64 (cos.f64 M) (exp.f64 (fma.f64 m (-.f64 M (.f64 n 1/2)) (.f64 (.f64 m m) -1/4))))

Compiler

Compiled 13779 to 7002 computations (49.2% saved)

regimes428.0ms (4.2%)

Accuracy

Total 0.2b remaining (15.7%)

Threshold costs 0.2b (15.7%)

Counts

66 → 1

Compiler

Compiled 10856 to 7722 computations (28.9% 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

end119.0ms (1.2%)

Remove: (sort m n)
Compiler: Compiled 260 to 181 computations (30.4% saved)

Details

analyze3.7s (36.9%)

sample3.4s (33.6%)

simplify59.0ms (0.6%)

prune4.0ms (0%)

localize19.0ms (0.2%)

series96.0ms (0.9%)

rewrite40.0ms (0.4%)

simplify142.0ms (1.4%)

prune247.0ms (2.4%)

localize15.0ms (0.1%)

series53.0ms (0.5%)

rewrite33.0ms (0.3%)

simplify127.0ms (1.3%)

prune262.0ms (2.6%)

localize24.0ms (0.2%)

series225.0ms (2.2%)

rewrite26.0ms (0.3%)

simplify203.0ms (2%)

prune311.0ms (3.1%)

localize23.0ms (0.2%)

series116.0ms (1.1%)

rewrite1.0ms (0%)

simplify81.0ms (0.8%)

prune338.0ms (3.3%)

regimes428.0ms (4.2%)

simplify3.0ms (0%)

end119.0ms (1.2%)

Profiling