Details

analyze1.4s (20%)

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
6.2%	93.6%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
19.5%	79.6%	0.9%	9
23.8%	66.9%	9.3%	10
27.3%	63.1%	9.6%	11
30%	56.3%	13.7%	12
31.4%	43.4%	25.2%	13
33.1%	41.3%	25.6%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.8s (25.7%)

Results

1.1s	8256×	body	128	valid
612.0ms	4143×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess50.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

549×	`associate-l_binary64`
388×	`associate-r_binary64`
288×	`unswap-sqr_binary64`
269×	`associate-/l*_binary64`
260×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	71	72
2	171	68
3	369	68
4	1018	68
5	3458	68
6	4263	68
7	4441	68
8	4731	68
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-l_binary64`
401×	`*-commutative_binary64`
393×	`associate-*r/_binary64`
357×	`unswap-sqr_binary64`
261×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	56	17
3	111	17
4	279	17
5	877	17
6	2831	17
7	4305	17
8	4397	17
9	4562	17
10	4781	17

Stop Event

1×	node limit

Counts

1 → 2

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

series269.0ms (3.9%)

Counts

2 → 48

Calls

12 calls:

88.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	0
65.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	inf
62.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	-inf
16.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	m	-inf
15.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	k	-inf

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	236	25
2	3128	25

Stop Event

1×	node limit

Counts

2 → 72

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

510×	`associate-r_binary64`
419×	`associate-l_binary64`
341×	`fma-def_binary64`
251×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1332
1	347	1231
2	1110	979

Stop Event

1×	node limit

Counts

120 → 112

prune109.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
	17.2b	(.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (/.f64 1 (fma.f64 k (+.f64 k 10) 1))))
	21.8b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	1.5b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
	13.4b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)

Compiler

Compiled 2578 to 1486 computations (42.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))
✓	0.4b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
✓	2.9b	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

series560.0ms (8.2%)

Counts

3 → 96

Calls

24 calls:

91.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)	a	-inf
81.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)	a	0
68.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)	a	inf
67.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))	a	0
56.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))	a	-inf

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

245×	`expm1-udef_binary64`
245×	`log1p-udef_binary64`
162×	`fma-def_binary64`
141×	`add-sqr-sqrt_binary64`
138×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	283	45
2	3767	45

Stop Event

1×	node limit

Counts

3 → 124

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	4169
1	892	3922
2	3881	3667

Stop Event

1×	node limit

Counts

220 → 196

prune242.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	231	5	236

Error

0.0b

Counts

236 → 5

Alt Table

Status	Error	Program
	18.6b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2))
✓	1.5b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	13.4b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)
	21.8b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 7303 to 4412 computations (39.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.1b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)
✓	3.1b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))
✓	6.8b	(sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m)))

series205.0ms (3%)

Counts

3 → 72

Calls

24 calls:

22.0ms	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)	m	inf
18.0ms	(sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m)))	m	inf
17.0ms	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)	m	-inf
14.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))	a	inf
14.0ms	(sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m)))	m	-inf

rewrite69.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
214×	`log-pow_binary64`
171×	`fma-def_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	300	47
2	3493	47

Stop Event

1×	node limit

Counts

3 → 106

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

548×	`cancel-sign-sub-inv_binary64`
344×	`times-frac_binary64`
336×	`associate-/l*_binary64`
236×	`fma-neg_binary64`
218×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2624
1	644	2244
2	2211	1798

Stop Event

1×	node limit

Counts

178 → 185

prune197.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	220	5	225

Error

0.0b

Counts

225 → 5

Alt Table

Status	Error	Program
▶	18.6b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2))
✓	1.5b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	13.4b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)
	21.8b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 5409 to 3346 computations (38.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 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))) -2)
✓	1.2b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))
✓	13.3b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2))

series832.0ms (12.1%)

Counts

3 → 108

Calls

27 calls:

84.0ms	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2)	a	0
82.0ms	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2)	a	-inf
79.0ms	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2))	a	0
74.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))	a	0
73.0ms	(pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2)	a	inf

rewrite66.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
172×	`fma-def_binary64`
147×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	301	54
2	3819	54

Stop Event

1×	node limit

Counts

3 → 116

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

392×	`associate-r_binary64`
317×	`times-frac_binary64`
296×	`associate-/l*_binary64`
280×	`fma-def_binary64`
242×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	359	5764
1	1237	5323

Stop Event

1×	node limit

Counts

224 → 217

prune259.0ms (3.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	252	5	257

Error

0.0b

Counts

257 → 5

Alt Table

Status	Error	Program
✓	18.6b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))) -2))
✓	1.5b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
✓	1.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	13.4b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)
	21.8b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 9207 to 5734 computations (37.7% saved)

regimes293.0ms (4.3%)

Accuracy

Total 0.0b remaining (48.2%)

Threshold costs 0.0b (48.2%)

Counts

72 → 2

Compiler

Compiled 4528 to 3154 computations (30.3% saved)

bsearch24.0ms (0.3%)

Algorithm

1×	binary-search

Calls

1 calls:

22.0ms

Steps

Iters	Point		Range
1.0742694774859784e+149	∈ [	8.352298993010659e+147	,	1.3466706418126133e+149	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	23	36

Stop Event

1×

saturated

end86.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 136 to 87 computations (36% saved)

Details

analyze1.4s (20%)

sample1.8s (25.7%)

preprocess50.0ms (0.7%)

simplify45.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series269.0ms (3.9%)

rewrite54.0ms (0.8%)

simplify33.0ms (0.5%)

prune109.0ms (1.6%)

localize8.0ms (0.1%)

series560.0ms (8.2%)

rewrite73.0ms (1.1%)

simplify82.0ms (1.2%)

prune242.0ms (3.5%)

localize10.0ms (0.1%)

series205.0ms (3%)

rewrite69.0ms (1%)

simplify59.0ms (0.9%)

prune197.0ms (2.9%)

localize9.0ms (0.1%)

series832.0ms (12.1%)

rewrite66.0ms (1%)

simplify75.0ms (1.1%)

prune259.0ms (3.8%)

regimes293.0ms (4.3%)

bsearch24.0ms (0.3%)

simplify2.0ms (0%)

end86.0ms (1.3%)

Profiling