Details

analyze343.0ms (3.7%)

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 (34.3%)

Symmetry

(sort k n)

Results

1.3s	8256×	body	128	valid
1.1s	1414×	body	1024	invalid
377.0ms	673×	body	512	invalid
191.0ms	1220×	body	128	invalid
120.0ms	362×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

205×	`fma-neg_binary64`
136×	`rules-40_binary64`
136×	`rules-41_binary64`
136×	`rules-42_binary64`
136×	`rules-43_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	75	22
2	188	22
3	557	22
4	410	22

prune4.0ms (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

8.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	8.7b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 100 to 80 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series502.0ms (5.4%)

Counts

3 → 48

Calls

3 calls:

275.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
222.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite77.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

429×	`prod-diff_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
131×	`egg-rr`
127×	`add-sqr-sqrt_binary64`

Counts

3 → 131

Calls

3 calls:

74.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
74.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
74.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	298	47
2	3558	47
3	5057	47
0	0	0
1	0	0

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
381×	`rules-40_binary64`
381×	`rules-42_binary64`
380×	`rules-41_binary64`
380×	`rules-43_binary64`

Counts

179 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1204
1	471	1030
2	1669	992
3	4730	992
4	4886	992

prune222.0ms (2.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	134	16	150
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	136	16	152

Error

8.5b

Counts

152 → 16

Alt Table

Status	Error	Program
	8.7b	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	29.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (sqrt.f64 k))
	29.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) 3) 1/3)
	11.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
	9.1b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) 2))
	8.9b	(/.f64 (pow.f64 (+.f64 (fma.f64 (cbrt.f64 n) (.f64 (.f64 2 (PI.f64)) (pow.f64 (cbrt.f64 n) 2)) (neg.f64 (.f64 0 n))) (fma.f64 0 n (.f64 0 n))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	8.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
	28.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	11.3b	(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))))
	41.5b	(/.f64 (pow.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	40.1b	(/.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
	32.9b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 k 3/2)))
	8.8b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) 2)
	10.8b	(/.f64 (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (sqrt.f64 k))
	20.6b	(/.f64 (pow.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 2 (PI.f64)) n))) 1) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
▶	8.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))

Compiler

Compiled 4273 to 3078 computations (28% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series512.0ms (5.5%)

Counts

4 → 28

Calls

4 calls:

263.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
242.0ms	(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
5.0ms	(sqrt.f64 (/.f64 1 k))
2.0ms	(*.f64 n (PI.f64))

rewrite103.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

536×	`prod-diff_binary64`
210×	`egg-rr`
140×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Counts

4 → 210

Calls

4 calls:

96.0ms	(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))
96.0ms	(sqrt.f64 (/.f64 1 k))
96.0ms	(*.f64 n (PI.f64))
96.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	333	46
2	4086	46
3	5117	46
0	0	0
1	0	0

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

553×	`rules-40_binary64`
553×	`rules-42_binary64`
548×	`rules-41_binary64`
548×	`rules-43_binary64`
399×	`rules-20_binary64`

Counts

238 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	986
1	544	908
2	2176	842
3	4839	842
4	4918	842

prune390.0ms (4.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	218	9	227
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	225	18	243

Error

8.4b

Counts

243 → 18

Alt Table

Status	Error	Program
	29.3b	(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) 3) 1/3)
	32.9b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 k 3/2)))
	8.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
	8.7b	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	26.2b	(.f64 (pow.f64 (pow.f64 (/.f64 1 k) 3/2) 1/3) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	11.3b	(exp.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))))
	11.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))
	9.1b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) 2))
	8.9b	(/.f64 (pow.f64 (+.f64 (fma.f64 (cbrt.f64 n) (.f64 (.f64 2 (PI.f64)) (pow.f64 (cbrt.f64 n) 2)) (neg.f64 (.f64 0 n))) (fma.f64 0 n (.f64 0 n))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	8.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
	28.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	21.8b	(sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	41.5b	(/.f64 (pow.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	40.1b	(/.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
	41.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (-.f64 1 k))))
	20.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)) (-.f64 1 k))))
	11.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
▶	8.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))

Compiler

Compiled 6738 to 4713 computations (30.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series93.0ms (1%)

Counts

2 → 0

Calls

2 calls:

80.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
13.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

rewrite93.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

516×	`prod-diff_binary64`
143×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`
135×	`expm1-log1p-u_binary64`
134×	`add-log-exp_binary64`

Counts

2 → 120

Calls

2 calls:

90.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
90.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	349	31
2	4237	31
3	5238	31
0	0	0
1	0	0

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune582.0ms (6.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	282	18	300

Error

8.4b

Counts

300 → 18

Alt Table

Status	Error	Program
	29.3b	(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) 3) 1/3)
	32.9b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 k 3/2)))
	8.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
▶	8.7b	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	26.2b	(.f64 (pow.f64 (pow.f64 (/.f64 1 k) 3/2) 1/3) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	11.3b	(exp.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))))
✓	8.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
	9.1b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))) 0)
	8.9b	(/.f64 (pow.f64 (+.f64 (fma.f64 (cbrt.f64 n) (.f64 (.f64 2 (PI.f64)) (pow.f64 (cbrt.f64 n) 2)) (neg.f64 (.f64 0 n))) (fma.f64 0 n (.f64 0 n))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	8.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
	28.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	21.8b	(sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	41.5b	(/.f64 (pow.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	40.1b	(/.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
	41.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (-.f64 1 k))))
	20.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)) (-.f64 1 k))))
	11.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	11.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))

Compiler

Compiled 8973 to 5876 computations (34.5% saved)

localize59.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2))
✓	0.2b	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
✓	0.4b	(/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n))

series643.0ms (6.9%)

Counts

3 → 48

Calls

3 calls:

369.0ms	(pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2))
272.0ms	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
3.0ms	(/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n))

rewrite134.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

475×	`prod-diff_binary64`
240×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
129×	`log1p-expm1-u_binary64`
129×	`expm1-log1p-u_binary64`

Counts

3 → 124

Calls

3 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	321	47
2	3838	47
3	5148	47
0	0	0
1	0	0

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
381×	`rules-40_binary64`
381×	`rules-42_binary64`
380×	`rules-41_binary64`
380×	`rules-43_binary64`

Counts

172 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1204
1	471	1030
2	1669	992
3	4730	992
4	4886	992

prune212.0ms (2.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	15	16
Picked	0	1	1
Done	0	1	1
Total	142	18	160

Error

8.4b

Counts

160 → 18

Alt Table

Status	Error	Program
	29.3b	(pow.f64 (pow.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) 3) 1/3)
	32.9b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) 3) (pow.f64 k 3/2)))
	8.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
✓	8.7b	(/.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 1 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	26.2b	(.f64 (pow.f64 (pow.f64 (/.f64 1 k) 3/2) 1/3) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	11.3b	(exp.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))))
✓	8.6b	(.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
	9.1b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))) 2) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))) 0)
	8.9b	(/.f64 (pow.f64 (+.f64 (fma.f64 (cbrt.f64 n) (.f64 (.f64 2 (PI.f64)) (pow.f64 (cbrt.f64 n) 2)) (neg.f64 (.f64 0 n))) (fma.f64 0 n (.f64 0 n))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	8.8b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
	28.3b	(/.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	21.8b	(sqrt.f64 (.f64 (/.f64 1 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	41.5b	(/.f64 (pow.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 2) (PI.f64)) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	41.6b	(/.f64 (pow.f64 (log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	40.1b	(/.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 k))
	20.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)) (-.f64 1 k))))
	11.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
	11.0b	(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))))

Compiler

Compiled 3501 to 2474 computations (29.3% saved)

regimes1.5s (15.5%)

Accuracy

Total 0.5b remaining (91.7%)

Threshold costs 0.5b (91.7%)

Counts

230 → 1

Compiler

Compiled 21999 to 17683 computations (19.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	17	33
2	16	33

end425.0ms (4.5%)

Remove: (sort k n)
Compiler: Compiled 461 to 368 computations (20.2% saved)

Details

analyze343.0ms (3.7%)

sample3.2s (34.3%)

simplify18.0ms (0.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series502.0ms (5.4%)

rewrite77.0ms (0.8%)

simplify78.0ms (0.8%)

prune222.0ms (2.4%)

localize12.0ms (0.1%)

series512.0ms (5.5%)

rewrite103.0ms (1.1%)

simplify80.0ms (0.9%)

prune390.0ms (4.2%)

localize11.0ms (0.1%)

series93.0ms (1%)

rewrite93.0ms (1%)

simplify12.0ms (0.1%)

prune582.0ms (6.2%)

localize59.0ms (0.6%)

series643.0ms (6.9%)

rewrite134.0ms (1.4%)

simplify79.0ms (0.8%)

prune212.0ms (2.3%)

regimes1.5s (15.5%)

simplify2.0ms (0%)

end425.0ms (4.5%)

Profiling