Details

analyze3.0s (35%)

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)

sample122.0ms (1.4%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

38.0ms	251×	body	128	valid
3.0ms	4×	body	1024	valid
2.0ms	4×	body	512	invalid
1.0ms	11×	body	128	invalid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify78.0ms (0.9%)

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 (0.1%)

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

13.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.9b	(.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 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	33.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series108.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

49.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
32.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
20.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(*.f64 K (+.f64 m n))

rewrite47.0ms (0.6%)

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:

12.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
5.0ms	(*.f64 K (+.f64 m n))

simplify165.0ms (2%)

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

prune324.0ms (3.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	232	4	236

Error

0.9b

Counts

236 → 4

Alt Table

Status	Error	Program
	13.9b	(.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))))
	14.0b	(.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))))
	13.9b	(.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))))
▶	1.1b	(*.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 10493 to 4991 computations (52.4% saved)

localize14.0ms (0.2%)

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)

prune161.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	113	4	117

Error

0.9b

Counts

117 → 4

Alt Table

Status	Error	Program
	13.9b	(.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))))
	14.0b	(.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))))
▶	13.9b	(.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))))
✓	1.1b	(*.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 3475 to 1725 computations (50.4% saved)

localize23.0ms (0.3%)

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	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))
✓	0.6b	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
✓	33.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))

series238.0ms (2.8%)

Counts

3 → 144

Calls

3 calls:

180.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
29.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
28.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M))
7.0ms	(pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 n m)) 2) M)) 3))

simplify254.0ms (3%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-l_binary64`
417×	`fma-def_binary64`
410×	`*-commutative_binary64`
382×	`fma-neg_binary64`
244×	`sub-neg_binary64`

Counts

227 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	542	8711
1	1274	7517
2	4122	7499
3	4910	7499
4	4988	7499

prune413.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	213	4	217

Error

0.9b

Counts

217 → 4

Alt Table

Status	Error	Program
	33.3b	(.f64 (cbrt.f64 (exp.f64 (.f64 (log.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))))
▶	13.9b	(.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))))
	14.0b	(.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))))
✓	1.1b	(*.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 12492 to 6550 computations (47.6% saved)

localize23.0ms (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))
✓	33.4b	(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))

series97.0ms (1.1%)

Counts

4 → 132

Calls

4 calls:

33.0ms	(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))
32.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
23.0ms	(cbrt.f64 (+.f64 m n))
8.0ms	(.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n)))

rewrite79.0ms (0.9%)

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)))
15.0ms	(*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))
2.0ms	(cbrt.f64 (+.f64 m n))

simplify190.0ms (2.2%)

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

prune653.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	420	1	421
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	422	3	425

Error

0.9b

Counts

425 → 3

Alt Table

Status	Error	Program
	13.8b	(.f64 (-.f64 (.f64 (cos.f64 (fma.f64 (/.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 2)) (neg.f64 (.f64 M 1)))) (cos.f64 (fma.f64 (neg.f64 M) 1 (.f64 M 1)))) (.f64 (sin.f64 (fma.f64 (/.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 2)) (neg.f64 (.f64 M 1)))) (sin.f64 (fma.f64 (neg.f64 M) 1 (*.f64 M 1))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	1.1b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	13.9b	(.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))))

Compiler

Compiled 23878 to 10561 computations (55.8% saved)

regimes518.0ms (6.1%)

Accuracy

Total 0.2b remaining (12.4%)

Threshold costs 0.2b (12.4%)

Counts

64 → 1

Compiler

Compiled 16040 to 9732 computations (39.3% 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)

sample2.0s (23%)

Algorithm

1×

intervals

Results

1.1s	7850×	body	128	valid
63.0ms	301×	body	128	invalid
58.0ms	83×	body	1024	invalid
55.0ms	95×	body	512	invalid
44.0ms	67×	body	1024	valid
24.0ms	58×	body	512	valid
11.0ms	42×	body	256	invalid
10.0ms	12×	body	2048	invalid
7.0ms	24×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 236 to 152 computations (35.6% saved)

Details

analyze3.0s (35%)

sample122.0ms (1.4%)

simplify78.0ms (0.9%)

prune4.0ms (0.1%)

localize19.0ms (0.2%)

series108.0ms (1.3%)

rewrite47.0ms (0.6%)

simplify165.0ms (2%)

prune324.0ms (3.8%)

localize14.0ms (0.2%)

prune161.0ms (1.9%)

localize23.0ms (0.3%)

series238.0ms (2.8%)

rewrite25.0ms (0.3%)

simplify254.0ms (3%)

prune413.0ms (4.9%)

localize23.0ms (0.3%)

series97.0ms (1.1%)

rewrite79.0ms (0.9%)

simplify190.0ms (2.2%)

prune653.0ms (7.7%)

regimes518.0ms (6.1%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample2.0s (23%)

Profiling