Details

analyze346.0ms (2.6%)

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)

sample3.1s (23.5%)

Results

1.3s	8256×	body	128	valid
1.0s	1325×	body	1024	invalid
360.0ms	626×	body	512	invalid
163.0ms	1100×	body	128	invalid
102.0ms	316×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
461×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
288×	`distribute-rgt-neg-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	129	22
4	280	22
5	634	20
6	1332	20
7	3121	20
8	4914	20
9	4550	20

prune10.0ms (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series503.0ms (3.8%)

Counts

3 → 48

Calls

3 calls:

270.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
230.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

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

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

405×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
243×	`fma-neg_binary64`
211×	`associate-/l*_binary64`
162×	`associate-l_binary64`

Counts

156 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4057
1	428	3712
2	1390	3636
3	4506	3636
4	4960	3636

prune217.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	23.3b	(/.f64 (-.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 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 4468 to 2822 computations (36.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series778.0ms (5.9%)

Counts

3 → 60

Calls

3 calls:

292.0ms

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

248.0ms

(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)))

238.0ms

(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

176×	`add-exp-log_binary64`
113×	`prod-exp_binary64`
63×	`pow-exp_binary64`
26×	`div-exp_binary64`
22×	`add-sqr-sqrt_binary64`

Counts

3 → 143

Calls

3 calls:

8.0ms

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

6.0ms

(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)))

5.0ms

(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))

simplify147.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

670×	`distribute-rgt-in_binary64`
322×	`fma-def_binary64`
315×	`fma-neg_binary64`
213×	`cancel-sign-sub-inv_binary64`
202×	`unswap-sqr_binary64`

Counts

203 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	255	5794
1	537	5172
2	1974	4578
3	4723	4577
4	5024	4577

prune487.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	325	7	332

Error

Counts

332 → 7

Alt Table

Status	Error	Program
	23.3b	(/.f64 (-.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 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))
▶	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 12037 to 8676 computations (27.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series265.0ms (2%)

Counts

1 → 12

Calls

1 calls:

264.0ms

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

rewrite97.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

382×	`sqrt-prod_binary64`
305×	`add-sqr-sqrt_binary64`
272×	`times-frac_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`

Counts

1 → 243

Calls

1 calls:

33.0ms

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

simplify279.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary64`
439×	`fma-def_binary64`
365×	`associate-/l*_binary64`
242×	`log-prod_binary64`
210×	`associate-l_binary64`

Counts

255 → 256

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	299	9436
1	463	8904
2	1598	8684
3	2585	8584
4	4107	8502
5	4969	8502

prune965.0ms (7.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	591	1	592
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	592	7	599

Error

Counts

599 → 7

Alt Table

Status	Error	Program
	9.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 2 (*.f64 k -1/2) 1)) k))
	23.3b	(/.f64 (-.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 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
▶	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 24460 to 15905 computations (35% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
✓	0.3b	(*.f64 n (PI.f64))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k)))
✓	0.6b	(cbrt.f64 k)

series277.0ms (2.1%)

Counts

4 → 36

Calls

4 calls:

158.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
87.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k)))
29.0ms	(cbrt.f64 k)
2.0ms	(*.f64 n (PI.f64))

rewrite87.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`add-sqr-sqrt_binary64`
200×	`times-frac_binary64`
95×	`sqrt-prod_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`

Counts

4 → 270

Calls

4 calls:

36.0ms	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
6.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k)))
3.0ms	(*.f64 n (PI.f64))
1.0ms	(cbrt.f64 k)

simplify296.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
362×	`associate-*r/_binary64`
351×	`associate-*l/_binary64`
315×	`associate-/l*_binary64`
302×	`*-commutative_binary64`

Counts

306 → 419

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	409	13133
1	1055	12105
2	2916	11578
3	4526	11572
4	5133	11572

prune635.0ms (4.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	459	0	459
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	459	7	466

Error

Counts

466 → 7

Alt Table

Status	Error	Program
	9.2b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 2 (*.f64 k -1/2) 1)) k))
	23.3b	(/.f64 (-.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 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (sqrt.f64 (sqrt.f64 k))))
✓	0.5b	(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
✓	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))

Compiler

Compiled 17486 to 9007 computations (48.5% saved)

regimes4.3s (32.3%)

Accuracy

Total 0.3b remaining (88.7%)

Threshold costs 0.3b (88.7%)

Counts

577 → 1

Compiler

Compiled 91779 to 67788 computations (26.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	18	31
2	18	31

end179.0ms (1.4%)

Compiler: Compiled 293 to 213 computations (27.3% saved)

Details

analyze346.0ms (2.6%)

sample3.1s (23.5%)

simplify45.0ms (0.3%)

prune10.0ms (0.1%)

localize9.0ms (0.1%)

series503.0ms (3.8%)

rewrite18.0ms (0.1%)

simplify124.0ms (0.9%)

prune217.0ms (1.6%)

localize13.0ms (0.1%)

series778.0ms (5.9%)

rewrite37.0ms (0.3%)

simplify147.0ms (1.1%)

prune487.0ms (3.7%)

localize12.0ms (0.1%)

series265.0ms (2%)

rewrite97.0ms (0.7%)

simplify279.0ms (2.1%)

prune965.0ms (7.3%)

localize12.0ms (0.1%)

series277.0ms (2.1%)

rewrite87.0ms (0.7%)

simplify296.0ms (2.2%)

prune635.0ms (4.8%)

regimes4.3s (32.3%)

simplify2.0ms (0%)

end179.0ms (1.4%)

Profiling