Details

analyze3.6s (11%)

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)

sample2.7s (8%)

Symmetry

(sort m n)

Results

2.1s	8059×	body	128	valid
90.0ms	85×	body	1024	valid
87.0ms	323×	body	128	invalid
85.0ms	90×	body	1024	invalid
64.0ms	102×	body	512	invalid
50.0ms	70×	body	512	valid
33.0ms	23×	body	2048	invalid
27.0ms	57×	body	256	invalid
18.0ms	41×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify74.0ms (0.2%)

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

16.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.7b	(.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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	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)
✓	33.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series96.0ms (0.3%)

Counts

4 → 168

Calls

4 calls:

44.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
29.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(*.f64 K (+.f64 m n))

rewrite46.0ms (0.1%)

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)
10.0ms	(*.f64 K (+.f64 m n))
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))

simplify139.0ms (0.4%)

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

prune542.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	228	7	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	7	236

Error

1.7b

Counts

236 → 7

Alt Table

Status	Error	Program
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
	9.3b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	31.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
	16.7b	(.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))))
	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))))
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
▶	2.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 10707 to 5135 computations (52% saved)

localize15.0ms (0%)

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)

prune201.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Error

1.7b

Counts

120 → 7

Alt Table

Status	Error	Program
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
	9.3b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	31.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
	16.7b	(.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))))
▶	2.0b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (log.f64 (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))))
	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))))
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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 3718 to 1891 computations (49.1% saved)

localize15.0ms (0%)

Local error

Found 3 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)
✓	1.0b	(log.f64 (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)))

series46.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

46.0ms

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

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`log-pow_binary64`
4×	`log-prod_binary64`
4×	`exp-prod_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 19

Calls

1 calls:

11.0ms

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

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

826×	`sub-neg_binary64`
389×	`associate-+l-_binary64`
384×	`fma-def_binary64`
378×	`associate--l+_binary64`
364×	`associate-+l+_binary64`

Counts

67 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1825
1	256	1605
2	631	1594
3	2096	1592
4	4278	1592
5	5439	1592

prune335.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	178	7	185

Error

1.7b

Counts

185 → 7

Alt Table

Status	Error	Program
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
	9.3b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	31.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
	16.7b	(.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))))
▶	2.0b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))))))
	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))))
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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 5821 to 3050 computations (47.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))))
✓	0.0b	(+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)
✓	1.0b	(log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))

series20.1s (60.8%)

Counts

4 → 180

Calls

4 calls:

14.2s	(log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))
5.9s	(cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))))
46.0ms	(+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))
21.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)

rewrite47.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`cbrt-prod_binary64`
7×	`log-prod_binary64`

Counts

4 → 73

Calls

4 calls:

13.0ms	(cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))))
12.0ms	(+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)

simplify200.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
474×	`associate-r_binary64`
328×	`associate-l_binary64`
291×	`associate-+r+_binary64`
286×	`fma-neg_binary64`

Counts

253 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	417	10631
1	1245	9399
2	4447	9286
3	4975	9286

prune1.1s (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	452	7	459

Error

1.7b

Counts

459 → 7

Alt Table

Status	Error	Program
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (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))))
	9.3b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	31.8b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.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))))
	16.7b	(.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))))
	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))))
	16.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (cbrt.f64 (.f64 K (+.f64 m n)))) (cbrt.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))))
	2.0b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (.f64 2 (log.f64 (*.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2))))) (sqrt.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)))))))))

Compiler

Compiled 29411 to 17539 computations (40.4% saved)

regimes3.5s (10.7%)

Accuracy

Total 0.2b remaining (15%)

Threshold costs 0.2b (15%)

Counts

378 → 1

Compiler

Compiled 95666 to 69042 computations (27.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`*-commutative_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	61
1	38	61
2	55	61
3	77	61
4	95	61
5	106	61
6	115	61
7	120	61
8	122	61
9	120	61

end195.0ms (0.6%)

Remove: (sort m n)
Compiler: Compiled 472 to 320 computations (32.2% saved)

Details

analyze3.6s (11%)

sample2.7s (8%)

simplify74.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series96.0ms (0.3%)

rewrite46.0ms (0.1%)

simplify139.0ms (0.4%)

prune542.0ms (1.6%)

localize15.0ms (0%)

prune201.0ms (0.6%)

localize15.0ms (0%)

series46.0ms (0.1%)

rewrite12.0ms (0%)

simplify86.0ms (0.3%)

prune335.0ms (1%)

localize18.0ms (0.1%)

series20.1s (60.8%)

rewrite47.0ms (0.1%)

simplify200.0ms (0.6%)

prune1.1s (3.2%)

regimes3.5s (10.7%)

simplify5.0ms (0%)

end195.0ms (0.6%)

Profiling