Details

analyze1.3s (18.7%)

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 (26.3%)

Results

1.2s	8256×	body	128	valid
542.0ms	3739×	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

2.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series447.0ms (6.6%)

Counts

2 → 72

Calls

2 calls:

256.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
192.0ms	(*.f64 a (pow.f64 k m))

rewrite49.0ms (0.7%)

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:

47.0ms	(*.f64 a (pow.f64 k m))
47.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

simplify35.0ms (0.5%)

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

prune106.0ms (1.6%)

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
	26.6b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 a 3) (pow.f64 (pow.f64 k m) 3))) (fma.f64 k (+.f64 k 10) 1))
	27.4b	(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))))
▶	2.1b	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
	2.6b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 3)
	2.2b	(*.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))))

Compiler

Compiled 2598 to 1502 computations (42.2% 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)
✓	3.8b	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

series537.0ms (8%)

Counts

3 → 96

Calls

3 calls:

308.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
218.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))
11.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

rewrite61.0ms (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:

57.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m))
57.0ms	(pow.f64 (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (pow.f64 k m)) -1)
57.0ms	(/.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

prune213.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Error

0.0b

Counts

201 → 4

Alt Table

Status	Error	Program
▶	2.1b	(*.f64 (pow.f64 k m) (/.f64 a (fma.f64 k (+.f64 k 10) 1)))
	3.5b	(pow.f64 (/.f64 (+.f64 (/.f64 k (/.f64 a k)) (fma.f64 10 (/.f64 k a) (/.f64 1 a))) (pow.f64 k m)) -1)
	2.1b	(/.f64 (sqrt.f64 (pow.f64 k m)) (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m))))
	22.6b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 6688 to 4011 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 k m) (/.f64 a (fma.f64 k (+.f64 k 10) 1)))
✓	4.0b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

series282.0ms (4.2%)

Counts

2 → 60

Calls

2 calls:

242.0ms	(*.f64 (pow.f64 k m) (/.f64 a (fma.f64 k (+.f64 k 10) 1)))
40.0ms	(/.f64 a (fma.f64 k (+.f64 k 10) 1))

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	236	28
2	3069	28

Stop Event

1×	node limit

Counts

2 → 63

Calls

2 calls:

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

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

536×	`associate-r_binary64`
459×	`associate-l_binary64`
439×	`fma-def_binary64`
328×	`cancel-sign-sub-inv_binary64`
267×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1657
1	413	1540
2	1337	1303

Stop Event

1×	node limit

Counts

123 → 109

prune99.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Error

0.0b

Counts

113 → 4

Alt Table

Status	Error	Program
✓	2.1b	(*.f64 (pow.f64 k m) (/.f64 a (fma.f64 k (+.f64 k 10) 1)))
	3.5b	(pow.f64 (/.f64 (+.f64 (/.f64 k (/.f64 a k)) (fma.f64 10 (/.f64 k a) (/.f64 1 a))) (pow.f64 k m)) -1)
▶	2.1b	(/.f64 (sqrt.f64 (pow.f64 k m)) (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m))))
	22.6b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 2510 to 1470 computations (41.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (pow.f64 k m))
✓	0.0b	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m)))
✓	0.2b	(/.f64 (sqrt.f64 (pow.f64 k m)) (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m))))
	3.8b	(/.f64 (fma.f64 k (+.f64 k 10) 1) a)

series522.0ms (7.7%)

Counts

3 → 96

Calls

3 calls:

249.0ms	(/.f64 (sqrt.f64 (pow.f64 k m)) (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m))))
241.0ms	(/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m)))
31.0ms	(sqrt.f64 (pow.f64 k m))

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
150×	`prod-diff_binary64`
143×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	287	42
2	4002	42

Stop Event

1×	node limit

Counts

3 → 111

Calls

3 calls:

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

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
302×	`cancel-sign-sub-inv_binary64`
225×	`associate-/r/_binary64`
210×	`times-frac_binary64`
162×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2792
1	647	2539
2	2195	2263

Stop Event

1×	node limit

Counts

207 → 178

prune230.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	262	4	266

Error

0.0b

Counts

266 → 4

Alt Table

Status	Error	Program
✓	2.1b	(*.f64 (pow.f64 k m) (/.f64 a (fma.f64 k (+.f64 k 10) 1)))
	3.5b	(pow.f64 (/.f64 (+.f64 (/.f64 k (/.f64 a k)) (fma.f64 10 (/.f64 k a) (/.f64 1 a))) (pow.f64 k m)) -1)
✓	2.1b	(/.f64 (sqrt.f64 (pow.f64 k m)) (/.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) a) (sqrt.f64 (pow.f64 k m))))
	22.6b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))

Compiler

Compiled 6960 to 3550 computations (49% saved)

regimes662.0ms (9.8%)

Accuracy

Total 0.0b remaining (70.5%)

Threshold costs 0.0b (70.5%)

Counts

131 → 2

Compiler

Compiled 9564 to 6494 computations (32.1% saved)

bsearch29.0ms (0.4%)

Steps

Iters	Range		Point
8	7.094438506513813e+137	5.2027954957715214e+141	4.516851269647946e+141

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

end76.0ms (1.1%)

Compiler: Compiled 127 to 76 computations (40.2% saved)

Details

analyze1.3s (18.7%)

sample1.8s (26.3%)

simplify42.0ms (0.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series447.0ms (6.6%)

rewrite49.0ms (0.7%)

simplify35.0ms (0.5%)

prune106.0ms (1.6%)

localize8.0ms (0.1%)

series537.0ms (8%)

rewrite61.0ms (0.9%)

simplify74.0ms (1.1%)

prune213.0ms (3.2%)

localize8.0ms (0.1%)

series282.0ms (4.2%)

rewrite52.0ms (0.8%)

simplify41.0ms (0.6%)

prune99.0ms (1.5%)

localize9.0ms (0.1%)

series522.0ms (7.7%)

rewrite62.0ms (0.9%)

simplify54.0ms (0.8%)

prune230.0ms (3.4%)

regimes662.0ms (9.8%)

bsearch29.0ms (0.4%)

simplify2.0ms (0%)

end76.0ms (1.1%)

Profiling