Details

analyze1.3s (19.9%)

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)

sample1.8s (27.1%)

Results

1.2s	8256×	body	128	valid
569.0ms	3960×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify42.0ms (0.6%)

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

1.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series423.0ms (6.3%)

Counts

2 → 72

Calls

2 calls:

236.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
187.0ms	(*.f64 a (pow.f64 k m))

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	24
1	236	24
2	3128	24

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

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

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-r_binary64`
483×	`associate-l_binary64`
474×	`fma-def_binary64`
279×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1549
1	368	1460
2	1184	1240

Stop Event

1×	node limit

Counts

136 → 104

prune102.0ms (1.5%)

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

0.0b

Counts

105 → 5

Alt Table

Status	Error	Program
	23.9b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 a (/.f64 (.f64 k k) (pow.f64 k m))) (-.f64 (/.f64 99 (*.f64 k k)) (/.f64 10 k))))
▶	1.7b	(neg.f64 (/.f64 (*.f64 a (pow.f64 k m)) (neg.f64 (fma.f64 k (+.f64 k 10) 1))))
	1.8b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
	19.5b	(.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) 1) (/.f64 (sqrt.f64 (*.f64 a (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1)))
	29.2b	(fma.f64 (/.f64 a (fma.f64 k k (fma.f64 k 10 1))) (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k k (fma.f64 k 10 1))))

Compiler

Compiled 2606 to 1492 computations (42.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	1.7b	(/.f64 (*.f64 a (pow.f64 k m)) (neg.f64 (fma.f64 k (+.f64 k 10) 1)))

series234.0ms (3.5%)

Counts

1 → 36

Calls

1 calls:

234.0ms

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

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
189×	`log-pow_binary64`
167×	`fma-def_binary64`
130×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	258	17
2	3558	17

Stop Event

1×	node limit

Counts

1 → 50

Calls

1 calls:

45.0ms

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

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-r_binary64`
417×	`associate-l_binary64`
387×	`fma-def_binary64`
283×	`associate-/l*_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1290
1	377	1195
2	1226	931

Stop Event

1×	node limit

Counts

86 → 80

prune97.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
✓	1.7b	(neg.f64 (/.f64 (*.f64 a (pow.f64 k m)) (neg.f64 (fma.f64 k (+.f64 k 10) 1))))
▶	1.8b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
	17.0b	(neg.f64 (*.f64 (/.f64 a k) (neg.f64 (/.f64 (pow.f64 k m) k))))
	19.5b	(.f64 (/.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) 1) (/.f64 (sqrt.f64 (*.f64 a (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1)))
	29.2b	(fma.f64 (/.f64 a (fma.f64 k k (fma.f64 k 10 1))) (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k k (fma.f64 k 10 1))))

Compiler

Compiled 2687 to 1615 computations (39.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))
✓	0.2b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
✓	3.1b	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

series587.0ms (8.8%)

Counts

3 → 96

Calls

3 calls:

329.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
242.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))
16.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

rewrite62.0ms (0.9%)

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

Calls

3 calls:

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

simplify74.0ms (1.1%)

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

prune256.0ms (3.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	3	0	3
Picked	1	0	1
Done	1	0	1
Total	197	4	201

Error

Counts

201 → 4

Alt Table

Status	Error	Program
	17.0b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
▶	1.7b	(/.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))
	18.0b	(pow.f64 (+.f64 (fma.f64 10 (/.f64 (/.f64 k a) (pow.f64 k m)) (/.f64 1 (.f64 a (pow.f64 k m)))) (.f64 (/.f64 k a) (/.f64 k (pow.f64 k m)))) -1)
	1.7b	(*.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) a)

Compiler

Compiled 6694 to 4011 computations (40.1% saved)

localize10.0ms (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 (neg.f64 m)))
✓	3.1b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

series406.0ms (6.1%)

Counts

2 → 60

Calls

2 calls:

362.0ms	(/.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))
44.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
174×	`fma-def_binary64`
144×	`prod-diff_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	266	28
2	3760	28

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

51.0ms	(/.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))
51.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

306×	`cancel-sign-sub-inv_binary64`
235×	`times-frac_binary64`
189×	`associate-r_binary64`
176×	`associate-+r+_binary64`
164×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3004
1	728	2748
2	3242	2633

Stop Event

1×	node limit

Counts

134 → 121

prune121.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
	17.0b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
✓	1.7b	(/.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))
	18.0b	(pow.f64 (+.f64 (fma.f64 10 (/.f64 (/.f64 k a) (pow.f64 k m)) (/.f64 1 (.f64 a (pow.f64 k m)))) (.f64 (/.f64 k a) (/.f64 k (pow.f64 k m)))) -1)
	1.7b	(*.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) a)

Compiler

Compiled 4549 to 2746 computations (39.6% saved)

regimes708.0ms (10.6%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

141 → 2

Compiler

Compiled 10560 to 7282 computations (31% saved)

bsearch29.0ms (0.4%)

Steps

Iters	Range		Point
7	4.0917409456465584e+128	4.2947958697398283e+132	3.9990722708710586e+132

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	41
1	30	41
2	32	41
3	33	41

Stop Event

1×

saturated

end75.0ms (1.1%)

Compiler: Compiled 136 to 84 computations (38.2% saved)

Details

analyze1.3s (19.9%)

sample1.8s (27.1%)

simplify42.0ms (0.6%)

prune3.0ms (0%)

localize11.0ms (0.2%)

series423.0ms (6.3%)

rewrite54.0ms (0.8%)

simplify37.0ms (0.6%)

prune102.0ms (1.5%)

localize9.0ms (0.1%)

series234.0ms (3.5%)

rewrite46.0ms (0.7%)

simplify31.0ms (0.5%)

prune97.0ms (1.4%)

localize8.0ms (0.1%)

series587.0ms (8.8%)

rewrite62.0ms (0.9%)

simplify74.0ms (1.1%)

prune256.0ms (3.8%)

localize10.0ms (0.1%)

series406.0ms (6.1%)

rewrite53.0ms (0.8%)

simplify58.0ms (0.9%)

prune121.0ms (1.8%)

regimes708.0ms (10.6%)

bsearch29.0ms (0.4%)

simplify2.0ms (0%)

end75.0ms (1.1%)

Profiling