Details

analyze3.7s (37.6%)

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)

sample2.3s (23.6%)

Symmetry

(sort m n)

Results

1.9s	8116×	body	128	valid
65.0ms	276×	body	128	invalid
65.0ms	82×	body	1024	invalid
50.0ms	87×	body	512	invalid
49.0ms	59×	body	1024	valid
32.0ms	48×	body	512	valid
29.0ms	23×	body	2048	invalid
22.0ms	53×	body	256	invalid
13.0ms	33×	body	256	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify79.0ms (0.8%)

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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(.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)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(-.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)
✓	33.2b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series102.0ms (1%)

Counts

4 → 168

Calls

4 calls:

52.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
25.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(*.f64 K (+.f64 m n))

rewrite252.0ms (2.6%)

Algorithm

4×	egg-rewrite

Rules

49×	`egg`
40×	`egg`
36×	`egg`
31×	`egg`

Counts

4 → 156

Calls

4 calls:

78.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
64.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
57.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
48.0ms	(*.f64 K (+.f64 m n))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	261	15
2	3561	15
3	4921	15
0	9	13
1	210	13
2	2676	13
3	5055	13
0	14	24
1	340	22
2	4578	22
3	4978	22
0	6	7
1	134	7
2	1788	7
3	5710	7

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

718×	`cancel-sign-sub-inv_binary64`
639×	`fma-neg_binary64`
483×	`neg-mul-1_binary64`
355×	`sub-neg_binary64`
239×	`fma-def_binary64`

Counts

324 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	4112
1	673	3845
2	2515	3844
3	4393	3836
4	5190	3836

prune402.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	242	7	249

Error

1.2b

Counts

249 → 7

Alt Table

Status	Error	Program
	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.4b	(.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	40.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	37.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 K) (*.f64 (sqrt.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 2)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	1.4b	(*.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 10503 to 5256 computations (50% saved)

localize14.0ms (0.1%)

Local error

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

prune199.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Error

1.2b

Counts

144 → 7

Alt Table

Status	Error	Program
▶	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	14.4b	(.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	40.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	37.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 K) (*.f64 (sqrt.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))))
	14.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (cbrt.f64 (.f64 K (+.f64 m n))) (pow.f64 (cbrt.f64 (.f64 K (+.f64 m n))) 2)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.4b	(*.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 4669 to 2386 computations (48.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 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 (.f64 1/2 (.f64 n K)) M)
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	23.6b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series17.0ms (0.2%)

Counts

2 → 21

Calls

2 calls:

10.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
7.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)

rewrite189.0ms (1.9%)

Algorithm

2×	egg-rewrite

Rules

105×	`egg`
52×	`egg`

Counts

2 → 157

Calls

2 calls:

129.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
56.0ms	(-.f64 (.f64 1/2 (.f64 n K)) M)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	199	12
2	2512	12
3	4678	12
4	4601	12
5	5065	12
0	8	10
1	173	10
2	2139	10
3	4958	10

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

572×	`neg-mul-1_binary64`
514×	`fma-neg_binary64`
401×	`distribute-rgt-neg-in_binary64`
397×	`distribute-lft-neg-in_binary64`
329×	`associate-r_binary64`

Counts

178 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	415
1	144	409
2	451	378
3	1854	356
4	4722	356
5	5182	356

prune485.0ms (5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	312	7	319

Error

1.2b

Counts

319 → 7

Alt Table

Status	Error	Program
✓	9.4b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	14.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	28.7b	(.f64 (cos.f64 (expm1.f64 (log1p.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	44.2b	(.f64 (cos.f64 (.f64 (-.f64 (.f64 1/8 (pow.f64 (.f64 n K) 3)) (pow.f64 M 3)) (/.f64 1 (+.f64 (.f64 1/4 (pow.f64 (.f64 n K) 2)) (.f64 M (fma.f64 1/2 (.f64 n K) M)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	40.4b	(.f64 (cos.f64 (-.f64 (/.f64 (pow.f64 (pow.f64 (.f64 K (+.f64 m n)) 3) 1/3) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	37.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 K) (*.f64 (sqrt.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))))
✓	1.4b	(*.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 12148 to 6185 computations (49.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 m n)) 2)
✓	0.5b	(cbrt.f64 (+.f64 m n))
✓	32.9b	(cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M))

series95.0ms (1%)

Counts

4 → 132

Calls

4 calls:

35.0ms	(pow.f64 (cbrt.f64 (+.f64 m n)) 2)
27.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M))
22.0ms	(cbrt.f64 (+.f64 m n))
10.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K))

rewrite310.0ms (3.2%)

Algorithm

4×	egg-rewrite

Rules

44×	`egg`
28×	`egg`
23×	`egg`
21×	`egg`

Counts

4 → 116

Calls

4 calls:

133.0ms	(cbrt.f64 (+.f64 m n))
70.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M))
61.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (.f64 (cbrt.f64 (+.f64 m n)) K))
43.0ms	(pow.f64 (cbrt.f64 (+.f64 m n)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15
1	315	15
2	4030	15
3	5051	15
0	5	6
1	106	6
2	1372	6
3	4838	6
4	4821	6
5	4992	6
6	4935	6
0	7	9
1	149	7
2	1684	7
3	5058	7
0	10	7
1	209	7
2	2421	7
3	4968	7

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
353×	`associate-r_binary64`
237×	`associate-l_binary64`
237×	`fma-def_binary64`
228×	`fma-neg_binary64`

Counts

248 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	3531
1	886	3471
2	3146	3176
3	5190	3176

prune353.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	259	5	264
Fresh	4	0	4
Picked	1	0	1
Done	1	1	2
Total	265	6	271

Error

1.1b

Counts

271 → 6

Alt Table

Status	Error	Program
✓	1.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	23.1b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (cbrt.f64 (.f64 n n)) (.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	10.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 m) 2) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	48.1b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 m n)) 2) (*.f64 (log.f64 (exp.f64 (cbrt.f64 (+.f64 m n)))) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	36.4b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 (+.f64 m n) 1/6) 2) 2) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (fma.f64 2/3 (/.f64 (pow.f64 (.f64 1 (exp.f64 (log.f64 n))) 2/3) (/.f64 n m)) (pow.f64 (.f64 1 (exp.f64 (log.f64 n))) 2/3)) (*.f64 (cbrt.f64 (+.f64 m n)) K)) 2) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 12851 to 6974 computations (45.7% saved)

regimes764.0ms (7.9%)

Accuracy

Total 0.2b remaining (16.4%)

Threshold costs 0.2b (16.4%)

Counts

109 → 1

Compiler

Compiled 20138 to 13968 computations (30.6% 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	18	33
1	32	33
2	47	33
3	61	33
4	69	33
5	72	33
6	72	33

end157.0ms (1.6%)

Remove: (sort m n)
Compiler: Compiled 349 to 243 computations (30.4% saved)

Details

analyze3.7s (37.6%)

sample2.3s (23.6%)

simplify79.0ms (0.8%)

prune4.0ms (0%)

localize19.0ms (0.2%)

series102.0ms (1%)

rewrite252.0ms (2.6%)

simplify123.0ms (1.3%)

prune402.0ms (4.1%)

localize14.0ms (0.1%)

prune199.0ms (2%)

localize18.0ms (0.2%)

series17.0ms (0.2%)

rewrite189.0ms (1.9%)

simplify68.0ms (0.7%)

prune485.0ms (5%)

localize21.0ms (0.2%)

series95.0ms (1%)

rewrite310.0ms (3.2%)

simplify95.0ms (1%)

prune353.0ms (3.6%)

regimes764.0ms (7.9%)

simplify3.0ms (0%)

end157.0ms (1.6%)

Profiling