Details

analyze3.0s (33.2%)

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)

sample111.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort m n)

Results

33.0ms	248×	body	128	valid
3.0ms	4×	body	1024	valid
2.0ms	3×	body	1024	invalid
2.0ms	4×	body	512	valid
1.0ms	10×	body	128	invalid
1.0ms	3×	body	512	invalid
1.0ms	1×	body	2048	invalid
1.0ms	2×	body	256	invalid

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify62.0ms (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

12.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.4b	(.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)

localize18.0ms (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)
✓	34.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series74.0ms (0.8%)

Counts

4 → 168

Calls

4 calls:

28.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
17.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(*.f64 K (+.f64 m n))

rewrite40.0ms (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:

9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
6.0ms	(*.f64 K (+.f64 m n))

simplify177.0ms (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

prune523.0ms (5.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	248	6	254
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	6	255

Error

1.5b

Counts

255 → 6

Alt Table

Status	Error	Program
	27.6b	(.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))))
▶	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	12.4b	(*.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))))
	12.3b	(.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	8.9b	(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	6.5b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 11393 to 5358 computations (53% saved)

localize14.0ms (0.2%)

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)

series54.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

54.0ms

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

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
26×	`fabs-mul_binary64`
21×	`add-cube-cbrt_binary64`

Counts

1 → 73

Calls

1 calls:

19.0ms

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

simplify130.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-neg_binary64`
479×	`distribute-rgt-in_binary64`
424×	`distribute-lft-in_binary64`
346×	`cancel-sign-sub-inv_binary64`
269×	`sub-neg_binary64`

Counts

121 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	6040
1	583	4533
2	1860	3642
3	4530	3634
4	4954	3634

prune275.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	179	6	185

Error

1.5b

Counts

185 → 6

Alt Table

Status	Error	Program
	27.6b	(.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))))
▶	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (-.f64 (-.f64 m n) (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) l)))
	12.4b	(*.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))))
	12.3b	(.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	8.9b	(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	6.5b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 7356 to 3752 computations (49% saved)

localize16.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

17.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
3×	`pow-unpow_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

11.0ms

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

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-neg_binary64`
510×	`cancel-sign-sub-inv_binary64`
416×	`unswap-sqr_binary64`
402×	`distribute-rgt-in_binary64`
281×	`fma-def_binary64`

Counts

59 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1345
1	225	1225
2	570	1176
3	1953	1170
4	4214	1170
5	4820	1170
6	4968	1170

prune105.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	61	6	67

Error

1.5b

Counts

67 → 6

Alt Table

Status	Error	Program
	27.6b	(.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))))
✓	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (-.f64 (-.f64 m n) (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) l)))
	12.4b	(*.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))))
	12.3b	(.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	8.9b	(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
▶	6.5b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 1922 to 1053 computations (45.2% saved)

localize17.0ms (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 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.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)
✓	26.9b	(cos.f64 (.f64 1/2 (.f64 K m)))

series286.0ms (3.2%)

Counts

2 → 68

Calls

2 calls:

277.0ms	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
9.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
44×	`associate-r_binary64`
41×	`exp-sum_binary64`
36×	`prod-diff_binary64`
36×	`add-sqr-sqrt_binary64`

Counts

2 → 71

Calls

2 calls:

44.0ms	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
2.0ms	(cos.f64 (.f64 1/2 (.f64 K m)))

simplify197.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

801×	`associate-r_binary64`
611×	`associate-l_binary64`
464×	`fma-neg_binary64`
463×	`fma-def_binary64`
204×	`*-commutative_binary64`

Counts

139 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	460	10062
1	1301	9043
2	4985	9041
3	5411	9041

prune638.0ms (7.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	314	7	321

Error

1.5b

Counts

321 → 7

Alt Table

Status	Error	Program
	27.6b	(.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))))
✓	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (-.f64 (-.f64 m n) (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) l)))
	6.5b	(.f64 (cos.f64 (.f64 1/2 (*.f64 K m))) (exp.f64 (-.f64 (-.f64 (-.f64 m n) (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) l)))
	12.4b	(*.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))))
	12.3b	(.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2)) (cbrt.f64 (/.f64 (.f64 K (+.f64 m n)) 2))) (cbrt.f64 (/.f64 (*.f64 K (+.f64 m n)) 2)) (neg.f64 M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	8.9b	(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))
	6.5b	(.f64 (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (*.f64 K m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))))

Compiler

Compiled 19827 to 10344 computations (47.8% saved)

regimes901.0ms (10%)

Accuracy

Total 0.3b remaining (21.2%)

Threshold costs 0.3b (21.2%)

Counts

105 → 1

Compiler

Compiled 27482 to 17136 computations (37.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	42	29
3	54	29
4	61	29
5	63	29
6	63	29

end6.0ms (0.1%)

Compiler: Compiled 72 to 51 computations (29.2% saved)

sample2.2s (24.1%)

Algorithm

1×

intervals

Results

1.2s	7835×	body	128	valid
54.0ms	81×	body	1024	invalid
48.0ms	70×	body	1024	valid
45.0ms	96×	body	512	invalid
45.0ms	301×	body	128	invalid
29.0ms	65×	body	512	valid
22.0ms	21×	body	2048	invalid
14.0ms	46×	body	256	invalid
9.0ms	30×	body	256	valid

Compiler

Compiled 300 to 208 computations (30.7% saved)

Details

analyze3.0s (33.2%)

sample111.0ms (1.2%)

simplify62.0ms (0.7%)

prune4.0ms (0%)

localize18.0ms (0.2%)

series74.0ms (0.8%)

rewrite40.0ms (0.4%)

simplify177.0ms (2%)

prune523.0ms (5.8%)

localize14.0ms (0.2%)

series54.0ms (0.6%)

rewrite30.0ms (0.3%)

simplify130.0ms (1.4%)

prune275.0ms (3%)

localize16.0ms (0.2%)

series18.0ms (0.2%)

rewrite12.0ms (0.1%)

simplify92.0ms (1%)

prune105.0ms (1.2%)

localize17.0ms (0.2%)

series286.0ms (3.2%)

rewrite60.0ms (0.7%)

simplify197.0ms (2.2%)

prune638.0ms (7.1%)

regimes901.0ms (10%)

simplify3.0ms (0%)

end6.0ms (0.1%)

sample2.2s (24.1%)

Profiling