Details

analyze1.3s (10.6%)

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 (15%)

Symmetry

(sort a k m)

Results

1.2s	8256×	body	128	valid
546.0ms	3860×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1210×	`rules-43_binary64`
1204×	`rules-42_binary64`
578×	`fma-neg_binary64`
368×	`fma-def_binary64`
309×	`rules-11_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	81	18
2	259	18
3	1135	17
4	3638	17
5	30	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

34.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.3b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.5b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series500.0ms (4.1%)

Counts

2 → 72

Calls

2 calls:

288.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
212.0ms	(*.f64 a (pow.f64 k m))

rewrite74.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

856×	`fma-neg_binary64`
372×	`prod-diff_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
143×	`egg-rr`

Counts

2 → 143

Calls

2 calls:

71.0ms	(*.f64 a (pow.f64 k m))
71.0ms	(/.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	255	24
2	3094	24
3	5142	24
0	0	0
1	0	0

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

473×	`rules-21_binary64`
291×	`fma-neg_binary64`
238×	`fma-def_binary64`
226×	`rules-20_binary64`
215×	`rules-40_binary64`

Counts

215 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1635
1	844	1497
2	4244	1374
3	4975	1374
4	4887	1374

prune159.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	180	8	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	8	189

Error

26.4b

Counts

189 → 8

Alt Table

Status	Error	Program
▶	34.3b	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))
	38.2b	(fabs.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))
	58.9b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) (fma.f64 1/2 (.f64 a (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) a)) (fma.f64 k (+.f64 k 10) 1))
	51.7b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
	57.3b	(fma.f64 a (/.f64 (*.f64 (log.f64 k) m) (fma.f64 k 10 (fma.f64 k k 1))) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))))
	34.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
	50.8b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))
	58.8b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (fma.f64 1/2 (.f64 (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (fma.f64 1/6 (.f64 (.f64 (pow.f64 (log.f64 k) 3) (pow.f64 m 3)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (.f64 (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))))))

Compiler

Compiled 4800 to 2480 computations (48.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (pow.f64 k m))
✓	0.0b	(fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0)
✓	0.0b	(*.f64 (sqrt.f64 (pow.f64 k m)) a)
✓	2.5b	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))

series1.3s (10.4%)

Counts

4 → 132

Calls

4 calls:

509.0ms	(fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0)
468.0ms	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))
256.0ms	(*.f64 (sqrt.f64 (pow.f64 k m)) a)
30.0ms	(sqrt.f64 (pow.f64 k m))

rewrite85.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

373×	`prod-diff_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
179×	`egg-rr`
131×	`add-sqr-sqrt_binary64`

Counts

4 → 179

Calls

4 calls:

81.0ms	(sqrt.f64 (pow.f64 k m))
81.0ms	(fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0)
81.0ms	(*.f64 (sqrt.f64 (pow.f64 k m)) a)
81.0ms	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	317	39
2	3639	39
3	5027	39
0	0	0
1	0	0

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

387×	`fma-def_binary64`
348×	`fma-neg_binary64`
282×	`rules-20_binary64`
263×	`rules-7-rev_binary64`
260×	`rules-40_binary64`

Counts

311 → 250

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	140	2439
1	1047	2266
2	4919	2266

prune219.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	301	8	309

Error

26.4b

Counts

309 → 8

Alt Table

Status	Error	Program
✓	34.3b	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))
	38.2b	(fabs.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))
	58.9b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) (fma.f64 1/2 (.f64 a (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) a)) (fma.f64 k (+.f64 k 10) 1))
	51.7b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
	57.3b	(fma.f64 a (/.f64 (*.f64 (log.f64 k) m) (fma.f64 k 10 (fma.f64 k k 1))) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))))
▶	34.7b	(/.f64 (log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
	50.8b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))
	58.8b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (fma.f64 1/2 (.f64 (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (fma.f64 1/6 (.f64 (.f64 (pow.f64 (log.f64 k) 3) (pow.f64 m 3)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (.f64 (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))))))

Compiler

Compiled 8337 to 4109 computations (50.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (exp.f64 a) (pow.f64 k m))
✓	0.6b	(log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m)))
✓	1.4b	(/.f64 (log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))

series4.8s (39.5%)

Counts

3 → 108

Calls

3 calls:

2.5s	(log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m)))
1.7s	(/.f64 (log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
664.0ms	(pow.f64 (exp.f64 a) (pow.f64 k m))

rewrite86.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

949×	`fma-neg_binary64`
358×	`prod-diff_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
187×	`egg-rr`

Counts

3 → 187

Calls

3 calls:

82.0ms	(pow.f64 (exp.f64 a) (pow.f64 k m))
82.0ms	(log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m)))
82.0ms	(/.f64 (log.f64 (pow.f64 (exp.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	293	33
2	3490	33
3	5746	33
0	0	0
1	0	0

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

457×	`fma-def_binary64`
421×	`fma-neg_binary64`
348×	`rules-20_binary64`
322×	`rules-13_binary64`
306×	`rules-40_binary64`

Counts

295 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	161	2329
1	1230	2139
2	5325	2139

prune166.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	252	9	261

Error

16.9b

Counts

261 → 9

Alt Table

Status	Error	Program
✓	34.3b	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))
	38.2b	(fabs.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))
	58.9b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) (fma.f64 1/2 (.f64 a (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) a)) (fma.f64 k (+.f64 k 10) 1))
	51.7b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
	53.7b	(/.f64 (log.f64 (fma.f64 a (.f64 (log.f64 k) (.f64 m (exp.f64 a))) (exp.f64 a))) (fma.f64 k (+.f64 k 10) 1))
	57.3b	(fma.f64 a (/.f64 (*.f64 (log.f64 k) m) (fma.f64 k 10 (fma.f64 k k 1))) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))))
▶	23.4b	(/.f64 (log.f64 1) (fma.f64 k (+.f64 k 10) 1))
	50.8b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))
	58.8b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (fma.f64 1/2 (.f64 (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (fma.f64 1/6 (.f64 (.f64 (pow.f64 (log.f64 k) 3) (pow.f64 m 3)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (.f64 (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))))))

Compiler

Compiled 6434 to 3322 computations (48.4% saved)

localize5.0ms (0%)

prune8.0ms (0.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	1	1
Total	9	9

Error

16.9b

Counts

9 → 9

Alt Table

Status	Error	Program
✓	34.3b	(/.f64 (fma.f64 (sqrt.f64 (pow.f64 k m)) (*.f64 (sqrt.f64 (pow.f64 k m)) a) 0) (fma.f64 k (+.f64 k 10) 1))
	38.2b	(fabs.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1)))
	58.9b	(/.f64 (fma.f64 a (.f64 (log.f64 k) m) (fma.f64 1/2 (.f64 a (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) a)) (fma.f64 k (+.f64 k 10) 1))
	51.7b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 k k))
	53.7b	(/.f64 (log.f64 (fma.f64 a (.f64 (log.f64 k) (.f64 m (exp.f64 a))) (exp.f64 a))) (fma.f64 k (+.f64 k 10) 1))
	57.3b	(fma.f64 a (/.f64 (*.f64 (log.f64 k) m) (fma.f64 k 10 (fma.f64 k k 1))) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))))
✓	23.4b	(/.f64 (log.f64 1) (fma.f64 k (+.f64 k 10) 1))
	50.8b	(/.f64 a (fma.f64 k (+.f64 k 10) 1))
	58.8b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (fma.f64 1/2 (.f64 (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (fma.f64 1/6 (.f64 (.f64 (pow.f64 (log.f64 k) 3) (pow.f64 m 3)) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))) (.f64 (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))))))

Compiler

Compiled 217 to 139 computations (35.9% saved)

regimes765.0ms (6.3%)

Accuracy

Total 12.8b remaining (86.8%)

Threshold costs 0b (0%)

Counts

99 → 3

Compiler

Compiled 8220 to 5566 computations (32.3% saved)

bsearch427.0ms (3.5%)

Steps

Iters	Range		Point
8	220.00588302081806	108892.73409744595	222.24157684555098
11	3.6260711123666066e-267	4.3994181849560203e-246	3.6592210806688855e-267

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	22	46
2	20	46

end168.0ms (1.4%)

Remove: (sort a k m)
Compiler: Compiled 361 to 243 computations (32.7% saved)

Details

analyze1.3s (10.6%)

sample1.8s (15%)

simplify55.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series500.0ms (4.1%)

rewrite74.0ms (0.6%)

simplify100.0ms (0.8%)

prune159.0ms (1.3%)

localize11.0ms (0.1%)

series1.3s (10.4%)

rewrite85.0ms (0.7%)

simplify86.0ms (0.7%)

prune219.0ms (1.8%)

localize12.0ms (0.1%)

series4.8s (39.5%)

rewrite86.0ms (0.7%)

simplify60.0ms (0.5%)

prune166.0ms (1.4%)

localize5.0ms (0%)

prune8.0ms (0.1%)

regimes765.0ms (6.3%)

bsearch427.0ms (3.5%)

simplify2.0ms (0%)

end168.0ms (1.4%)

Profiling