Details

analyze3.2s (34.8%)

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 (24.1%)

Symmetry

(sort m n)

Results

1.8s	8075×	body	128	valid
90.0ms	108×	body	1024	invalid
76.0ms	84×	body	1024	valid
63.0ms	290×	body	128	invalid
51.0ms	82×	body	512	invalid
30.0ms	54×	body	512	valid
24.0ms	18×	body	2048	invalid
22.0ms	42×	body	256	valid
19.0ms	49×	body	256	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify61.0ms (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

18.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.4b	(.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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	35.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series341.0ms (3.7%)

Counts

4 → 180

Calls

4 calls:

295.0ms	(.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))
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(*.f64 K (+.f64 m n))

rewrite69.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
243×	`add-log-exp_binary64`
241×	`add-cube-cbrt_binary64`
241×	`add-cbrt-cube_binary64`

Counts

4 → 67

Calls

4 calls:

68.0ms	(*.f64 K (+.f64 m n))
68.0ms	(.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))))
68.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
68.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	78
1	502	78
2	4831	78
3	5033	78
0	0	0
1	0	0

simplify172.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-def_binary64`
368×	`associate-+l+_binary64`
365×	`*-commutative_binary64`
298×	`associate-r_binary64`
197×	`associate--r+_binary64`

Counts

247 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	13345
1	2180	12084
2	5164	12084

prune250.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	2	173

Error

0.6b

Counts

173 → 2

Alt Table

Status	Error	Program
	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	0.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Status

Error

Program

18.4b

(*.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

▶

0.6b

(*.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 16301 to 8010 computations (50.9% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)

series39.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

39.0ms

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

rewrite58.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

525×	`fma-def_binary64`
264×	`fma-neg_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`

Counts

1 → 44

Calls

1 calls:

57.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	259	16
2	3403	16
3	4905	16
0	0	0
1	0	0

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`sub-neg_binary64`
388×	`associate-+l-_binary64`
378×	`associate--l+_binary64`
371×	`fma-def_binary64`
362×	`associate-+l+_binary64`

Counts

92 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	1394
1	210	1226
2	551	1215
3	1881	1213
4	3391	1213
5	4940	1213
6	5141	1213

prune93.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Error

0.6b

Counts

117 → 2

Alt Table

Status	Error	Program
▶	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Status

Error

Program

▶

18.4b

(*.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

✓

0.6b

(*.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 3184 to 1524 computations (52.1% saved)

localize22.0ms (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)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3)
✓	19.4b	(cbrt.f64 (*.f64 K (+.f64 m n)))
✓	36.0b	(cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M))

series1.2s (13.2%)

Counts

3 → 120

Calls

3 calls:

961.0ms	(pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3)
219.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
27.0ms	(cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M))

rewrite73.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`
241×	`fma-neg_binary64`
153×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`

Counts

3 → 98

Calls

3 calls:

70.0ms	(pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3)
70.0ms	(cbrt.f64 (*.f64 K (+.f64 m n)))
70.0ms	(cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 3) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	306	31
2	3898	31
3	4851	31
0	0	0
1	0	0

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
313×	`associate-r_binary64`
216×	`associate-l_binary64`
207×	`fma-def_binary64`
197×	`*-commutative_binary64`

Counts

218 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3773
1	897	3617
2	3083	3510
3	5079	3510

prune256.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	244	3	247

Error

0.5b

Counts

247 → 3

Alt Table

Status	Error	Program
▶	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 2) (cbrt.f64 K)) (cbrt.f64 (+.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))))
✓	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.6b	(*.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 10744 to 5713 computations (46.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (+.f64 m n))
✓	0.6b	(cbrt.f64 K)
	19.4b	(cbrt.f64 (*.f64 K (+.f64 m n)))
✓	35.5b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 2) (cbrt.f64 K)) (cbrt.f64 (+.f64 m n))) 2) M))

series83.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

35.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 2) (cbrt.f64 K)) (cbrt.f64 (+.f64 m n))) 2) M))
31.0ms	(cbrt.f64 K)
16.0ms	(cbrt.f64 (+.f64 m n))

rewrite82.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

312×	`log1p-udef_binary64`
179×	`add-sqr-sqrt_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
168×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

80.0ms	(cbrt.f64 (+.f64 m n))
80.0ms	(cbrt.f64 K)
80.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 K (+.f64 m n))) 2) (cbrt.f64 K)) (cbrt.f64 (+.f64 m n))) 2) M))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	357	24
2	4531	24
3	4944	24
0	0	0
1	0	0

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Rules

557×	`cancel-sign-sub-inv_binary64`
359×	`fma-neg_binary64`
348×	`times-frac_binary64`
279×	`associate-r_binary64`
233×	`distribute-rgt-neg-in_binary64`

Counts

156 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2465
1	666	2297
2	2386	2168
3	4985	2168
4	5134	2168

prune239.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	215	3	218

Error

0.5b

Counts

218 → 3

Alt Table

Status	Error	Program
✓	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 2) (cbrt.f64 K)) (cbrt.f64 (+.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))))
✓	18.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.6b	(*.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 11352 to 5963 computations (47.5% saved)

regimes287.0ms (3.1%)

Accuracy

Total 0.2b remaining (12.4%)

Threshold costs 0.2b (12.4%)

Counts

40 → 1

Compiler

Compiled 6914 to 5004 computations (27.6% 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

end94.0ms (1%)

Remove: (sort m n)
Compiler: Compiled 205 to 144 computations (29.8% saved)

Details

analyze3.2s (34.8%)

sample2.2s (24.1%)

simplify61.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series341.0ms (3.7%)

rewrite69.0ms (0.8%)

simplify172.0ms (1.9%)

prune250.0ms (2.7%)

localize13.0ms (0.1%)

series39.0ms (0.4%)

rewrite58.0ms (0.6%)

simplify90.0ms (1%)

prune93.0ms (1%)

localize22.0ms (0.2%)

series1.2s (13.2%)

rewrite73.0ms (0.8%)

simplify96.0ms (1%)

prune256.0ms (2.8%)

localize25.0ms (0.3%)

series83.0ms (0.9%)

rewrite82.0ms (0.9%)

simplify89.0ms (1%)

prune239.0ms (2.6%)

regimes287.0ms (3.1%)

simplify3.0ms (0%)

end94.0ms (1%)

Profiling