Details

analyze2.9s (31.9%)

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
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)

sample107.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

35.0ms	253×	body	128	valid
1.0ms	2×	body	512	valid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	1024	valid
1.0ms	1×	body	1024	invalid
1.0ms	4×	body	128	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify63.0ms (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

16.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.0b	(.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)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(*.f64 K (+.f64 m n))
✓	35.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series75.0ms (0.8%)

Counts

4 → 168

Calls

4 calls:

28.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
21.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
19.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
6.0ms	(*.f64 K (+.f64 m n))

rewrite39.0ms (0.4%)

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	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(-.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 (2%)

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

prune332.0ms (3.7%)

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

0.6b

Counts

255 → 3

Alt Table

Status	Error	Program
	15.9b	(.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))))
	15.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
▶	0.7b	(*.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 11197 to 5212 computations (53.5% saved)

localize20.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

prune75.0ms (0.8%)

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

0.6b

Counts

64 → 3

Alt Table

Status	Error	Program
▶	15.9b	(.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))))
	15.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (.f64 (cbrt.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))))
✓	0.7b	(*.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 1799 to 905 computations (49.7% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n)))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
✓	0.6b	(cbrt.f64 (+.f64 m n))
✓	35.7b	(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))

series88.0ms (1%)

Counts

4 → 132

Calls

4 calls:

30.0ms	(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))
27.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
23.0ms	(cbrt.f64 (+.f64 m n))
7.0ms	(.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n)))

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
47×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
34×	`associate-*r/_binary64`
34×	`flip-+_binary64`

Counts

4 → 159

Calls

4 calls:

18.0ms	(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))
16.0ms	(.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n)))
8.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
2.0ms	(cbrt.f64 (+.f64 m n))

simplify189.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-r_binary64`
579×	`associate-l_binary64`
435×	`times-frac_binary64`
356×	`*-commutative_binary64`
267×	`fma-neg_binary64`

Counts

291 → 305

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	568	8706
1	1236	7610
2	4230	7423
3	5304	7423

prune503.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	419	2	421
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	421	3	424

Error

0.6b

Counts

424 → 3

Alt Table

Status	Error	Program
✓	0.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	41.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 m n))) (cbrt.f64 (sqrt.f64 (+.f64 m n)))) (.f64 (cbrt.f64 (sqrt.f64 (+.f64 m n))) (cbrt.f64 (sqrt.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))))
▶	30.8b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m)))) (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))))

Compiler

Compiled 23942 to 10594 computations (55.8% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (+.f64 m n))
✓	0.9b	(.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m))))
✓	32.1b	(cbrt.f64 (*.f64 m m))
✓	37.4b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (.f64 m m)))) (cbrt.f64 (+.f64 m n))) 2) M))

series1.4s (15.6%)

Counts

3 → 96

Calls

3 calls:

804.0ms

(*.f64 K (fma.f64 2/3 (*.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m))))

576.0ms

(cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (fma.f64 2/3 (*.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m)))) (cbrt.f64 (+.f64 m n))) 2) M))

34.0ms

(cbrt.f64 (*.f64 m m))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

14.0ms

(cos.f64 (-.f64 (/.f64 (*.f64 (*.f64 K (fma.f64 2/3 (*.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m)))) (cbrt.f64 (+.f64 m n))) 2) M))

3.0ms

(*.f64 K (fma.f64 2/3 (*.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m))))

2.0ms

(cbrt.f64 (*.f64 m m))

simplify186.0ms (2%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary64`
307×	`*-commutative_binary64`
259×	`associate-+r+_binary64`
194×	`times-frac_binary64`
176×	`associate-+l+_binary64`

Counts

164 → 149

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	744	13797
1	1917	11627
2	5048	11627

prune427.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	207	3	210

Error

0.6b

Counts

210 → 3

Alt Table

Status	Error	Program
✓	0.7b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	30.8b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (.f64 m m))))) (cbrt.f64 (.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (.f64 m m)))))) (cbrt.f64 (.f64 K (fma.f64 2/3 (.f64 n (cbrt.f64 (/.f64 1 m))) (cbrt.f64 (*.f64 m m)))))) (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))))
	41.5b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 m n))) (cbrt.f64 (sqrt.f64 (+.f64 m n)))) (.f64 (cbrt.f64 (sqrt.f64 (+.f64 m n))) (cbrt.f64 (sqrt.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))))

Compiler

Compiled 20184 to 12076 computations (40.2% saved)

regimes476.0ms (5.2%)

Accuracy

Total 0.2b remaining (12.1%)

Threshold costs 0.2b (12.1%)

Counts

52 → 1

Compiler

Compiled 17216 to 10170 computations (40.9% 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

end6.0ms (0.1%)

Remove: (sort m n)
Compiler: Compiled 75 to 54 computations (28% saved)

sample1.8s (19.5%)

Algorithm

1×

intervals

Results

1.1s	7842×	body	128	valid
53.0ms	67×	body	1024	valid
50.0ms	74×	body	1024	invalid
36.0ms	272×	body	128	invalid
33.0ms	88×	body	512	invalid
29.0ms	66×	body	512	valid
20.0ms	21×	body	2048	invalid
11.0ms	38×	body	256	invalid
7.0ms	25×	body	256	valid

Compiler

Compiled 228 to 144 computations (36.8% saved)

Details

analyze2.9s (31.9%)

sample107.0ms (1.2%)

simplify63.0ms (0.7%)

prune4.0ms (0%)

localize20.0ms (0.2%)

series75.0ms (0.8%)

rewrite39.0ms (0.4%)

simplify179.0ms (2%)

prune332.0ms (3.7%)

localize20.0ms (0.2%)

prune75.0ms (0.8%)

localize27.0ms (0.3%)

series88.0ms (1%)

rewrite67.0ms (0.7%)

simplify189.0ms (2.1%)

prune503.0ms (5.5%)

localize29.0ms (0.3%)

series1.4s (15.6%)

rewrite81.0ms (0.9%)

simplify186.0ms (2%)

prune427.0ms (4.7%)

regimes476.0ms (5.2%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample1.8s (19.5%)

Profiling