Details

analyze1.2s (18.4%)

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)

sample1.7s (25.8%)

Results

1.1s	8256×	body	128	valid
518.0ms	3770×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify110.0ms (1.6%)

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

1.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.4b	(/.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	(*.f64 a (pow.f64 k m))
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series581.0ms (8.6%)

Counts

2 → 72

Calls

2 calls:

362.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
218.0ms	(*.f64 a (pow.f64 k m))

rewrite57.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
189×	`log-pow_binary64`
157×	`fma-def_binary64`

Counts

2 → 64

Calls

2 calls:

56.0ms	(*.f64 a (pow.f64 k m))
56.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	236	24
2	2986	24
3	5459	24
0	0	0
1	0	0

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-neg_binary64`
526×	`associate-r_binary64`
492×	`associate-l_binary64`
479×	`fma-def_binary64`
279×	`associate-/l*_binary64`

Counts

136 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1549
1	342	1460
2	1102	1240
3	3974	1236
4	5176	1236

prune213.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Error

1.4b

Counts

105 → 5

Alt Table

Status	Error	Program
	1.5b	(*.f64 (/.f64 (pow.f64 k m) (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)) (/.f64 a (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
▶	1.4b	(*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))
	1.4b	(*.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))))
	1.5b	(*.f64 (/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	1.5b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

Compiler

Compiled 2589 to 1470 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))
✓	3.6b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

series323.0ms (4.8%)

Counts

2 → 60

Calls

2 calls:

274.0ms	(*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))
49.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

rewrite60.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

559×	`log-prod_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
189×	`log-pow_binary64`
160×	`fma-def_binary64`

Counts

2 → 64

Calls

2 calls:

59.0ms	(*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))
59.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	236	28
2	2928	28
3	5275	28
0	0	0
1	0	0

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
542×	`associate-r_binary64`
466×	`associate-l_binary64`
440×	`fma-def_binary64`
328×	`cancel-sign-sub-inv_binary64`

Counts

124 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1657
1	389	1540
2	1229	1303
3	4211	1293
4	4950	1293

prune193.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Error

1.4b

Counts

115 → 5

Alt Table

Status	Error	Program
	26.7b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1))) 2) (pow.f64 k m))
	1.5b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
	1.4b	(*.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))))
▶	1.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	1.5b	(/.f64 (pow.f64 k m) (/.f64 (fma.f64 k (+.f64 k 10) 1) a))

Compiler

Compiled 2587 to 1532 computations (40.8% saved)

localize127.0ms (1.9%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	14.4b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series351.0ms (5.2%)

Counts

2 → 48

Calls

2 calls:

349.0ms	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite69.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
170×	`fma-def_binary64`
161×	`prod-diff_binary64`
139×	`add-sqr-sqrt_binary64`

Counts

2 → 74

Calls

2 calls:

67.0ms	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
67.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	280	27
2	3653	27
3	4887	27
0	0	0
1	0	0

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-neg_binary64`
532×	`associate-r_binary64`
439×	`associate-l_binary64`
436×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`

Counts

122 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1351
1	395	1260
2	1229	1040
3	4073	1035
4	4947	1035
5	4949	1035

prune214.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	199	5	204

Error

1.4b

Counts

204 → 5

Alt Table

Status	Error	Program
	26.7b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1))) 2) (pow.f64 k m))
	1.5b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
▶	1.4b	(*.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))))
✓	1.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	1.5b	(/.f64 (pow.f64 k m) (/.f64 (fma.f64 k (+.f64 k 10) 1) a))

Compiler

Compiled 5233 to 3135 computations (40.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))))
	14.4b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series336.0ms (5%)

Counts

2 → 60

Calls

2 calls:

284.0ms	(*.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))))
52.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))

rewrite131.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
226×	`fma-neg_binary64`
179×	`fma-def_binary64`
160×	`prod-diff_binary64`

Counts

2 → 83

Calls

2 calls:

129.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
129.0ms	(*.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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	283	33
2	3631	33
3	4972	33
4	4987	33
5	4983	33
0	0	0
1	0	0

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-neg_binary64`
634×	`fma-def_binary64`
355×	`cancel-sign-sub-inv_binary64`
286×	`associate-/l*_binary64`
274×	`times-frac_binary64`

Counts

143 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2131
1	479	1996
2	1534	1502
3	3808	1496
4	4921	1496
5	4955	1496

prune263.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	238	5	243

Error

1.4b

Counts

243 → 5

Alt Table

Status	Error	Program
	26.7b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1))) 2) (pow.f64 k m))
	1.5b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
✓	1.4b	(*.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))))
✓	1.4b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	1.5b	(/.f64 (pow.f64 k m) (/.f64 (fma.f64 k (+.f64 k 10) 1) a))

Compiler

Compiled 6309 to 3985 computations (36.8% saved)

regimes304.0ms (4.5%)

Accuracy

Total 0.1b remaining (3.8%)

Threshold costs 0.1b (3.8%)

Counts

85 → 1

Compiler

Compiled 6268 to 4338 computations (30.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	17	31
2	16	31

end104.0ms (1.5%)

Compiler: Compiled 146 to 103 computations (29.5% saved)

Details

analyze1.2s (18.4%)

sample1.7s (25.8%)

simplify110.0ms (1.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series581.0ms (8.6%)

rewrite57.0ms (0.8%)

simplify64.0ms (0.9%)

prune213.0ms (3.2%)

localize7.0ms (0.1%)

series323.0ms (4.8%)

rewrite60.0ms (0.9%)

simplify65.0ms (1%)

prune193.0ms (2.9%)

localize127.0ms (1.9%)

series351.0ms (5.2%)

rewrite69.0ms (1%)

simplify75.0ms (1.1%)

prune214.0ms (3.2%)

localize9.0ms (0.1%)

series336.0ms (5%)

rewrite131.0ms (1.9%)

simplify97.0ms (1.4%)

prune263.0ms (3.9%)

regimes304.0ms (4.5%)

simplify2.0ms (0%)

end104.0ms (1.5%)

Profiling