Details

analyze1.4s (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.9s (27.3%)

Results

1.3s	8256×	body	128	valid
551.0ms	3787×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune3.0ms (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

0.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.9b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series297.0ms (4.2%)

Counts

2 → 48

Calls

2 calls:

295.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
2.0ms	(fma.f64 k (+.f64 k 10) 1)

rewrite57.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

72× egg-rr

Counts

2 → 72

Calls

2 calls:

55.0ms	((/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)) (fma.f64 k (+.f64 k 10) 1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	236	25
2	2986	25
3	5459	25
0	0	0
1	0	0

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-r_binary64`
426×	`associate-l_binary64`
348×	`fma-def_binary64`
251×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`

Counts

120 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1332
1	322	1231
2	1031	979
3	3766	979
4	4838	979
5	4944	979

prune89.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	3	113

Error

0.9b

Counts

113 → 3

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
	1.0b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
▶	1.0b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

Compiler

Compiled 2535 to 1429 computations (43.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
✓	0.9b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

series462.0ms (6.5%)

Counts

3 → 84

Calls

3 calls:

385.0ms	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
43.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
34.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))

rewrite67.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

99× egg-rr

Counts

3 → 99

Calls

2 calls:

65.0ms	((*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	265	45
2	3271	45
3	4903	45
0	0	0
1	0	0

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

618×	`cancel-sign-sub-inv_binary64`
572×	`fma-neg_binary64`
324×	`unswap-sqr_binary64`
289×	`times-frac_binary64`
222×	`sub-neg_binary64`

Counts

183 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	2832
1	637	2542
2	2160	2148
3	3785	2132
4	5239	2132

prune192.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Error

0.9b

Counts

222 → 3

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
▶	1.0b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	1.0b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

Compiler

Compiled 5215 to 3172 computations (39.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	11.6b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series407.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

292.0ms	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
60.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
53.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite137.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

139× egg-rr

Counts

4 → 139

Calls

2 calls:

134.0ms

((sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	283	56
2	3631	56
3	4972	56
4	4987	56
5	4983	56
0	0	0
1	0	0

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-neg_binary64`
521×	`cancel-sign-sub-inv_binary64`
305×	`associate-/l*_binary64`
295×	`times-frac_binary64`
262×	`associate-/r*_binary64`

Counts

235 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	2713
1	645	2536
2	2008	2038
3	3981	2016
4	4946	2016

prune253.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	294	3	297

Error

0.0b

Counts

297 → 3

Alt Table

Status	Error	Program
▶	1.0b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
✓	1.0b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
	30.1b	(fma.f64 (/.f64 (pow.f64 k m) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 7787 to 4893 computations (37.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.1b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
✓	0.9b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series680.0ms (9.6%)

Counts

2 → 72

Calls

2 calls:

415.0ms	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
264.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite63.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

91× egg-rr

Counts

2 → 91

Calls

2 calls:

61.0ms	((/.f64 (fma.f64 k (+.f64 k 10) 1) (.f64 a (pow.f64 k m))) (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (.f64 a (pow.f64 k m))) -1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	277	34
2	3351	34
3	4939	34
0	0	0
1	0	0

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

376×	`cancel-sign-sub-inv_binary64`
270×	`times-frac_binary64`
264×	`associate-r_binary64`
223×	`associate-/l*_binary64`
222×	`associate-+r+_binary64`

Counts

163 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3702
1	853	3451
2	3706	3289
3	4743	3289
4	4953	3289

prune166.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	182	3	185

Error

0.0b

Counts

185 → 3

Alt Table

Status	Error	Program
✓	1.0b	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -1)
✓	1.0b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
	30.1b	(fma.f64 (/.f64 (pow.f64 k m) k) (/.f64 a k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 6249 to 3677 computations (41.2% saved)

regimes223.0ms (3.1%)

Accuracy

Total 1.9b remaining (97.8%)

Threshold costs 0b (0%)

Counts

64 → 1

Compiler

Compiled 3960 to 2726 computations (31.2% saved)

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	18	19
2	17	19

end152.0ms (2.1%)

Compiler: Compiled 89 to 59 computations (33.7% saved)

Details

analyze1.4s (19.3%)

sample1.9s (27.3%)

simplify102.0ms (1.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series297.0ms (4.2%)

rewrite57.0ms (0.8%)

simplify75.0ms (1.1%)

prune89.0ms (1.2%)

localize12.0ms (0.2%)

series462.0ms (6.5%)

rewrite67.0ms (0.9%)

simplify93.0ms (1.3%)

prune192.0ms (2.7%)

localize9.0ms (0.1%)

series407.0ms (5.7%)

rewrite137.0ms (1.9%)

simplify90.0ms (1.3%)

prune253.0ms (3.6%)

localize8.0ms (0.1%)

series680.0ms (9.6%)

rewrite63.0ms (0.9%)

simplify105.0ms (1.5%)

prune166.0ms (2.3%)

regimes223.0ms (3.1%)

simplify40.0ms (0.6%)

end152.0ms (2.1%)

Profiling