Details

analyze3.5s (32.2%)

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)

sample72.0ms (0.7%)

Algorithm

1×

intervals

Results

37.0ms	252×	body	128	valid
2.0ms	3×	body	1024	invalid
1.0ms	11×	body	128	invalid
1.0ms	3×	body	512	valid
1.0ms	3×	body	512	invalid
1.0ms	3×	body	256	invalid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	1024	valid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify65.0ms (0.6%)

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

12.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.2b	(.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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	32.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series67.0ms (0.6%)

Counts

4 → 168

Calls

4 calls:

27.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
19.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
15.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
6.0ms	(*.f64 K (+.f64 m n))

rewrite43.0ms (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:

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)
8.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
4.0ms	(*.f64 K (+.f64 m n))

simplify181.0ms (1.7%)

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

prune352.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	4	255

Error

0.8b

Counts

255 → 4

Alt Table

Status	Error	Program
	8.7b	(.f64 (-.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (*.f64 m (sin.f64 (neg.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.2b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.8b	(.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))))

Compiler

Compiled 11265 to 5272 computations (53.2% saved)

localize13.0ms (0.1%)

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)

series46.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

46.0ms

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

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-def_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
3×	`add-log-exp_binary64`

Counts

1 → 25

Calls

1 calls:

11.0ms

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

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

737×	`distribute-rgt-in_binary64`
733×	`fma-neg_binary64`
455×	`fma-def_binary64`
381×	`associate--l+_binary64`
377×	`associate-+l+_binary64`

Counts

73 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	1735
1	293	1532
2	742	1518
3	2610	1516
4	4954	1516
5	5359	1516

prune170.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	127	4	131

Error

0.8b

Counts

131 → 4

Alt Table

Status	Error	Program
▶	8.7b	(.f64 (-.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (*.f64 m (sin.f64 (neg.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.2b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.8b	(.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))))

Compiler

Compiled 3729 to 1851 computations (50.4% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (neg.f64 M))))))
✓	2.0b	(.f64 K (.f64 m (sin.f64 (neg.f64 M))))
✓	2.8b	(.f64 n (.f64 K (sin.f64 (neg.f64 M))))
✓	7.7b	(.f64 (-.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (*.f64 m (sin.f64 (neg.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

series560.0ms (5.2%)

Counts

4 → 102

Calls

4 calls:

465.0ms	(.f64 (-.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (*.f64 m (sin.f64 (neg.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
53.0ms	(+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (neg.f64 M))))))
21.0ms	(.f64 n (.f64 K (sin.f64 (neg.f64 M))))
20.0ms	(.f64 K (.f64 m (sin.f64 (neg.f64 M))))

rewrite78.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`associate-r_binary64`
42×	`add-sqr-sqrt_binary64`
41×	`exp-sum_binary64`
36×	`prod-diff_binary64`

Counts

4 → 127

Calls

4 calls:

39.0ms	(.f64 (-.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (*.f64 m (sin.f64 (neg.f64 M))))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
7.0ms	(+.f64 (.f64 1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/2 (.f64 K (.f64 m (sin.f64 (neg.f64 M))))))
4.0ms	(.f64 n (.f64 K (sin.f64 (neg.f64 M))))
4.0ms	(.f64 K (.f64 m (sin.f64 (neg.f64 M))))

simplify354.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

519×	`*-commutative_binary64`
430×	`associate-r_binary64`
210×	`+-commutative_binary64`
186×	`fma-def_binary64`
157×	`cancel-sign-sub-inv_binary64`

Counts

229 → 251

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	984	21378
1	3072	18334
2	4895	18334
3	5035	18334

prune458.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	251	4	255

Error

0.8b

Counts

255 → 4

Alt Table

Status	Error	Program
	39.5b	(.f64 (.f64 (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 (.f64 K (sin.f64 (neg.f64 M))) (+.f64 m n)))) (exp.f64 (-.f64 (-.f64 m n) (+.f64 l (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))) (exp.f64 (fma.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)) 1 (.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l) 1))))
▶	12.2b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.8b	(.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))))

Compiler

Compiled 26800 to 11858 computations (55.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))
✓	0.4b	(/.f64 K (sqrt.f64 2))
✓	0.4b	(/.f64 (+.f64 m n) (sqrt.f64 2))
✓	32.3b	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M)))

series122.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

54.0ms	(fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))
47.0ms	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M)))
14.0ms	(/.f64 (+.f64 m n) (sqrt.f64 2))
7.0ms	(/.f64 K (sqrt.f64 2))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
27×	`sqrt-prod_binary64`

Counts

4 → 111

Calls

4 calls:

5.0ms	(/.f64 (+.f64 m n) (sqrt.f64 2))
3.0ms	(/.f64 K (sqrt.f64 2))
1.0ms	(cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M)))
0.0ms	(fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-/l*_binary64`
297×	`fma-def_binary64`
256×	`associate-/r/_binary64`
157×	`associate-r_binary64`
151×	`associate-/l/_binary64`

Counts

231 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	4801
1	676	4507
2	2107	4029
3	5293	4029

prune255.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	180	5	185

Error

0.8b

Counts

185 → 5

Alt Table

Status	Error	Program
	47.3b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (log.f64 (exp.f64 (/.f64 (+.f64 m n) (sqrt.f64 2)))) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	0.9b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.2b	(.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 m n) (sqrt.f64 2))) (cbrt.f64 (/.f64 (+.f64 m n) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (+.f64 m n) (sqrt.f64 2)))) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
✓	12.2b	(*.f64 (cos.f64 (fma.f64 (/.f64 K (sqrt.f64 2)) (/.f64 (+.f64 m n) (sqrt.f64 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	27.8b	(.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))))

Compiler

Compiled 7851 to 4417 computations (43.7% saved)

regimes901.0ms (8.3%)

Accuracy

Total 0.2b remaining (15.4%)

Threshold costs 0.2b (15.4%)

Counts

89 → 1

Compiler

Compiled 21098 to 13980 computations (33.7% saved)

simplify5.0ms (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

end12.0ms (0.1%)

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

sample3.3s (30.5%)

Algorithm

1×

intervals

Results

2.0s	7864×	body	128	valid
106.0ms	87×	body	1024	invalid
71.0ms	98×	body	512	invalid
67.0ms	57×	body	1024	valid
66.0ms	278×	body	128	invalid
43.0ms	58×	body	512	valid
38.0ms	22×	body	2048	invalid
29.0ms	60×	body	256	invalid
11.0ms	21×	body	256	valid

Compiler

Compiled 255 to 180 computations (29.4% saved)

Details

analyze3.5s (32.2%)

sample72.0ms (0.7%)

simplify65.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.2%)

series67.0ms (0.6%)

rewrite43.0ms (0.4%)

simplify181.0ms (1.7%)

prune352.0ms (3.2%)

localize13.0ms (0.1%)

series46.0ms (0.4%)

rewrite16.0ms (0.1%)

simplify82.0ms (0.8%)

prune170.0ms (1.6%)

localize30.0ms (0.3%)

series560.0ms (5.2%)

rewrite78.0ms (0.7%)

simplify354.0ms (3.3%)

prune458.0ms (4.2%)

localize22.0ms (0.2%)

series122.0ms (1.1%)

rewrite15.0ms (0.1%)

simplify109.0ms (1%)

prune255.0ms (2.3%)

regimes901.0ms (8.3%)

simplify5.0ms (0%)

end12.0ms (0.1%)

sample3.3s (30.5%)

Profiling