Details

analyze3.1s (2.1%)

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)

sample2.4s (1.6%)

Symmetry

(sort m n)

Results

2.0s	8098×	body	128	valid
67.0ms	76×	body	1024	invalid
66.0ms	288×	body	128	invalid
50.0ms	58×	body	1024	valid
47.0ms	84×	body	512	invalid
43.0ms	63×	body	512	valid
30.0ms	75×	body	256	invalid
26.0ms	22×	body	2048	invalid
14.0ms	35×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify62.0ms (0%)

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

15.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.0b	(.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%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	34.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series73.0ms (0%)

Counts

4 → 168

Calls

4 calls:

29.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
15.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
12.0ms	(*.f64 K (+.f64 m n))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
38×	`add-cube-cbrt_binary64`
25×	`cos-sum_binary64`

Counts

4 → 129

Calls

4 calls:

10.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
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)
4.0ms	(*.f64 K (+.f64 m n))

simplify179.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-neg_binary64`
341×	`associate-r_binary64`
311×	`associate-l_binary64`
240×	`distribute-rgt-neg-in_binary64`
221×	`*-commutative_binary64`

Counts

297 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	7218
1	884	5740
2	3048	5550
3	4877	5550
4	5041	5550

prune260.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	252	3	255

Error

0.5b

Counts

255 → 3

Alt Table

Status	Error	Program
	34.2b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
▶	0.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	15.0b	(.f64 (log.f64 (exp.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 11181 to 5212 computations (53.4% saved)

localize13.0ms (0%)

Local error

Found 1 expressions with local error:

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

prune59.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Error

0.5b

Counts

64 → 3

Alt Table

Status	Error	Program
	34.2b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
✓	0.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	15.0b	(.f64 (log.f64 (exp.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 1783 to 905 computations (49.2% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
✓	0.6b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
	34.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series98.0ms (0.1%)

Counts

2 → 96

Calls

2 calls:

73.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))
25.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`exp-diff_binary64`
50×	`cos-sum_binary64`
42×	`prod-diff_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`

Counts

2 → 82

Calls

2 calls:

13.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
10.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))

simplify175.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-l_binary64`
451×	`*-commutative_binary64`
382×	`fma-def_binary64`
256×	`sub-neg_binary64`
255×	`unswap-sqr_binary64`

Counts

178 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	631	9371
1	1373	7245
2	4100	6992
3	5264	6992

prune443.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	320	3	323

Error

0.5b

Counts

323 → 3

Alt Table

Status	Error	Program
	34.2b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 K (-.f64 (.f64 m m) (.f64 n n))) (-.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))))
✓	0.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	15.2b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (exp.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 19672 to 9548 computations (51.5% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))
✓	0.6b	(.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))))
✓	0.7b	(cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
	34.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series4.1s (2.8%)

Counts

3 → 144

Calls

3 calls:

2.2s

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

1.9s

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

30.0ms

(log.f64 (*.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

rewrite50.6s (33.7%)

Algorithm

1×	rewrite-expression-head

Rules

52025×	`cbrt-div_binary64`
52025×	`exp-diff_binary64`
52025×	`cos-sum_binary64`
43701×	`prod-diff_binary64`
33750×	`frac-times_binary64`

Counts

3 → 18362

Calls

3 calls:

1.2s

(log.f64 (*.f64 (*.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))) (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

41.0ms

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

11.0ms

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

simplify1.5min (58.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69196	5894866

Details

analyze3.1s (2.1%)

sample2.4s (1.6%)

simplify62.0ms (0%)

prune4.0ms (0%)

localize17.0ms (0%)

series73.0ms (0%)

rewrite42.0ms (0%)

simplify179.0ms (0.1%)

prune260.0ms (0.2%)

localize13.0ms (0%)

prune59.0ms (0%)

localize22.0ms (0%)

series98.0ms (0.1%)

rewrite36.0ms (0%)

simplify175.0ms (0.1%)

prune443.0ms (0.3%)

localize26.0ms (0%)

series4.1s (2.8%)

rewrite50.6s (33.7%)

simplify1.5min (58.8%)

Profiling