Details

analyze346.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	25%	57.9%	7
18%	20.3%	61.8%	8
18.3%	16.4%	65.3%	9
18.5%	13.7%	67.8%	10
18.6%	11.5%	69.9%	11
18.7%	10%	71.3%	12
18.7%	8.9%	72.4%	13
18.7%	8.2%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.2s (43.5%)

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

1.3s	8256×	body	128	valid
1.1s	1349×	body	1024	invalid
408.0ms	665×	body	512	invalid
176.0ms	1148×	body	128	invalid
118.0ms	365×	body	256	invalid

Compiler

Compiled 92 to 77 computations (16.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series427.0ms (5.8%)

Counts

4 → 48

Calls

4 calls:

215.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
199.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
10.0ms	(/.f64 1 (sqrt.f64 k))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite128.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
191×	`prod-diff_binary64`
150×	`fma-def_binary64`
149×	`add-sqr-sqrt_binary64`

Counts

4 → 87

Calls

4 calls:

126.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
126.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
126.0ms	(/.f64 1 (sqrt.f64 k))
126.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	306	51
2	3697	51
3	4924	51
0	0	0
1	0	0

prune143.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	9	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Error

0.0b

Counts

136 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	23.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k 1/2))))
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 3144 to 2287 computations (27.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series440.0ms (5.9%)

Counts

3 → 48

Calls

3 calls:

231.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
206.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite97.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

247×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
227×	`prod-diff_binary64`
207×	`fma-udef_binary64`
151×	`fma-def_binary64`

Counts

3 → 73

Calls

3 calls:

94.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
94.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
94.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	285	47
2	3560	47
3	4959	47
4	4898	47
0	0	0
1	0	0

prune137.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	121	9	130

Error

0.0b

Counts

130 → 9

Alt Table

Status	Error	Program
	23.2b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4))))
	0.5b	(.f64 (.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k 1/2))))
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 2762 to 1968 computations (28.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series429.0ms (5.8%)

Counts

4 → 48

Calls

4 calls:

220.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
200.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 (PI.f64)) n)
4.0ms	(sqrt.f64 (/.f64 1 k))

rewrite134.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
184×	`fma-neg_binary64`
152×	`fma-def_binary64`
148×	`add-sqr-sqrt_binary64`

Counts

4 → 81

Calls

4 calls:

132.0ms	(sqrt.f64 (/.f64 1 k))
132.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
132.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
132.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	305	51
2	3630	49
3	4917	49
4	4992	49
5	4982	49
0	0	0
1	0	0

prune144.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	131	7	138

Error

0.0b

Counts

138 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (pow.f64 (pow.f64 k 1/4) -1) (pow.f64 (pow.f64 k 1/4) -1)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k 1/2))))
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
	12.5b	(sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))
▶	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 1 k) 2))))

Compiler

Compiled 2834 to 2133 computations (24.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))
✓	0.2b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

series797.0ms (10.8%)

Counts

4 → 72

Calls

4 calls:

379.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))
213.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
202.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite84.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

286×	`log1p-udef_binary64`
261×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`

Counts

4 → 113

Calls

4 calls:

81.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4))
81.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
81.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
81.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	338	70
2	4239	70
3	5136	70
0	0	0
1	0	0

prune203.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	185	7	192

Error

0.0b

Counts

192 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (.f64 (pow.f64 k -1/4) (pow.f64 k -1/4)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k 1/2))))
	0.8b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
	12.5b	(sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1 k))))
✓	0.5b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 4))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) n) (/.f64 (-.f64 1 k) 2))))

Compiler

Compiled 4776 to 3559 computations (25.5% saved)

regimes504.0ms (6.8%)

Accuracy

Total 0.4b remaining (86.8%)

Threshold costs 0.4b (86.8%)

Counts

119 → 1

Compiler

Compiled 10210 to 8438 computations (17.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	19	21
2	23	21
3	25	21
4	26	21
5	25	21

end124.0ms (1.7%)

Compiler: Compiled 183 to 147 computations (19.7% saved)

Details

analyze346.0ms (4.7%)

sample3.2s (43.5%)

localize11.0ms (0.1%)

series427.0ms (5.8%)

rewrite128.0ms (1.7%)

prune143.0ms (1.9%)

localize9.0ms (0.1%)

series440.0ms (5.9%)

rewrite97.0ms (1.3%)

prune137.0ms (1.9%)

localize10.0ms (0.1%)

series429.0ms (5.8%)

rewrite134.0ms (1.8%)

prune144.0ms (1.9%)

localize13.0ms (0.2%)

series797.0ms (10.8%)

rewrite84.0ms (1.1%)

prune203.0ms (2.7%)

regimes504.0ms (6.8%)

simplify2.0ms (0%)

end124.0ms (1.7%)

Profiling