Details

analyze1.3s (17.9%)

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 (24.7%)

Results

1.1s	8256×	body	128	valid
518.0ms	3826×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

627×	`rules-23-rev_binary64`
439×	`rules-6_binary64`
435×	`fma-neg_binary64`
229×	`rules-6-rev_binary64`
217×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	29	18
2	72	18
3	198	17
4	689	17
5	3213	17
6	4999	17
7	4502	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.5b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
▶	1.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 96 to 61 computations (36.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series421.0ms (5.9%)

Counts

2 → 72

Calls

2 calls:

238.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
183.0ms	(*.f64 a (pow.f64 k m))

rewrite73.0ms (1%)

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:

70.0ms	(*.f64 a (pow.f64 k m))
70.0ms	(/.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

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

687×	`rules-13_binary64`
581×	`rules-20_binary64`
529×	`fma-neg_binary64`
224×	`rules-21_binary64`
205×	`rules-14-rev_binary64`

Counts

215 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1683
1	412	1535
2	1863	1392
3	5215	1392

prune385.0ms (5.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	184	5	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	5	191

Error

1.2b

Counts

191 → 5

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))) 3)
	14.6b	(.f64 (sqrt.f64 (.f64 a (pow.f64 k m))) (/.f64 (sqrt.f64 (*.f64 a (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1)))
	1.6b	(.f64 (pow.f64 (cbrt.f64 (.f64 a (pow.f64 k m))) 2) (/.f64 (cbrt.f64 (*.f64 a (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1)))
▶	1.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	34.4b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (fma.f64 1/2 (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) (fma.f64 1/6 (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (pow.f64 (log.f64 k) 3) (pow.f64 m 3))) (.f64 (*.f64 (log.f64 k) m) (/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))))))

Compiler

Compiled 4712 to 2435 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	1.1b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series272.0ms (3.8%)

Counts

2 → 60

Calls

2 calls:

237.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
35.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite110.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

893×	`fma-neg_binary64`
395×	`prod-diff_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
158×	`egg-rr`

Counts

2 → 158

Calls

2 calls:

106.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
106.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	257	31
2	3153	31
3	5307	31
0	0	0
1	0	0

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

749×	`rules-20_binary64`
742×	`fma-neg_binary64`
341×	`rules-15-rev_binary64`
312×	`rules-14-rev_binary64`
277×	`rules-21_binary64`

Counts

218 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2180
1	541	1960
2	2489	1758
3	5211	1758

prune255.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	228	4	232

Error

1.2b

Counts

232 → 4

Alt Table

Status	Error	Program
	10.5b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
✓	1.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	1.5b	(/.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)))
▶	1.3b	(/.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 a))

Compiler

Compiled 6538 to 3868 computations (40.8% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	1.2b	(/.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 a))

series245.0ms (3.5%)

Counts

1 → 36

Calls

1 calls:

245.0ms

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

rewrite82.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

925×	`fma-neg_binary64`
391×	`prod-diff_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`

Counts

1 → 89

Calls

1 calls:

79.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	279	17
2	3414	17
3	5632	17
0	0	0
1	0	0

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
536×	`rules-20_binary64`
529×	`fma-neg_binary64`
438×	`rules-13_binary64`
172×	`rules-14-rev_binary64`

Counts

125 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1286
1	371	1158
2	1633	1011
3	4922	1011
4	4986	1011

prune198.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	192	4	196

Error

1.2b

Counts

196 → 4

Alt Table

Status	Error	Program
	10.5b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
✓	1.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
▶	1.5b	(/.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)))
✓	1.3b	(/.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 a))

Compiler

Compiled 5068 to 3124 computations (38.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	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)))
✓	13.1b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series491.0ms (6.9%)

Counts

3 → 84

Calls

3 calls:

245.0ms

(/.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)))

244.0ms

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

2.0ms

(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite79.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

482×	`prod-diff_binary64`
227×	`log1p-udef_binary64`
128×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`

Counts

3 → 101

Calls

3 calls:

77.0ms

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

77.0ms

(/.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)))

77.0ms

(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	300	46
2	3646	46
3	4948	46
0	0	0
1	0	0

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

897×	`rules-13_binary64`
386×	`rules-15-rev_binary64`
326×	`rules-21_binary64`
293×	`rules-14-rev_binary64`
211×	`fma-def_binary64`

Counts

185 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2785
1	657	2490
2	3093	2276
3	6676	2276

prune365.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	359	4	363

Error

1.2b

Counts

363 → 4

Alt Table

Status	Error	Program
	10.5b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
✓	1.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
✓	1.5b	(/.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)))
✓	1.3b	(/.f64 (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 a))

Compiler

Compiled 10393 to 6134 computations (41% saved)

regimes605.0ms (8.5%)

Accuracy

Total 0.1b remaining (4.5%)

Threshold costs 0.1b (4.5%)

Counts

148 → 1

Compiler

Compiled 12932 to 8710 computations (32.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	15	21
2	14	21

end78.0ms (1.1%)

Compiler: Compiled 108 to 76 computations (29.6% saved)

Details

analyze1.3s (17.9%)

sample1.8s (24.7%)

simplify62.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series421.0ms (5.9%)

rewrite73.0ms (1%)

simplify58.0ms (0.8%)

prune385.0ms (5.4%)

localize8.0ms (0.1%)

series272.0ms (3.8%)

rewrite110.0ms (1.5%)

simplify113.0ms (1.6%)

prune255.0ms (3.6%)

localize11.0ms (0.2%)

series245.0ms (3.5%)

rewrite82.0ms (1.1%)

simplify66.0ms (0.9%)

prune198.0ms (2.8%)

localize11.0ms (0.2%)

series491.0ms (6.9%)

rewrite79.0ms (1.1%)

simplify77.0ms (1.1%)

prune365.0ms (5.1%)

regimes605.0ms (8.5%)

simplify2.0ms (0%)

end78.0ms (1.1%)

Profiling