Details

analyze365.0ms (4.2%)

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)

sample3.4s (38.6%)

Results

1.4s	8256×	body	128	valid
1.2s	1402×	body	1024	invalid
394.0ms	654×	body	512	invalid
188.0ms	1172×	body	128	invalid
112.0ms	301×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify50.0ms (0.6%)

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

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	0.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

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	(.f64 (.f64 2 (PI.f64)) n)
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.4b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series547.0ms (6.3%)

Counts

3 → 48

Calls

3 calls:

290.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
253.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

simplify135.0ms (1.6%)

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

prune230.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

Counts

170 → 8

Alt Table

Status	Error	Program
	0.9b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.5b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
	23.4b	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) k)) (.f64 1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.5b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
▶	0.5b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
	0.7b	(.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))))

Compiler

Compiled 4335 to 2832 computations (34.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series323.0ms (3.7%)

Counts

4 → 36

Calls

4 calls:

227.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
79.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
14.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
23×	`sqrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
4.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 k -1/2))
4.0ms	(.f64 n (.f64 2 (PI.f64)))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

452×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
212×	`fma-neg_binary64`
203×	`times-frac_binary64`
192×	`associate-/l*_binary64`

Counts

138 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2559
1	364	2368
2	1145	2356
3	4762	2352
4	4949	2352

prune193.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	8.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.9b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(.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))))

Compiler

Compiled 4137 to 2685 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 n (fma.f64 k -1/2 1/2))
✓	0.2b	(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
✓	0.6b	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

series442.0ms (5.1%)

Counts

4 → 44

Calls

4 calls:

347.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
61.0ms	(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
29.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))
5.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
57×	`sqrt-prod_binary64`

Counts

4 → 219

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
5.0ms	(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
2.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
1.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))

simplify197.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
474×	`times-frac_binary64`
289×	`unswap-sqr_binary64`
267×	`associate-l_binary64`
260×	`associate-r_binary64`

Counts

263 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	7120
1	664	6701
2	2470	6684
3	4388	6684
4	4963	6684

prune370.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	290	6	296

Error

Counts

296 → 6

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	8.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
	0.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
▶	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.9b	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

Compiler

Compiled 8698 to 5682 computations (34.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series557.0ms (6.4%)

Counts

3 → 36

Calls

3 calls:

299.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
252.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
6.0ms	(sqrt.f64 (/.f64 1 k))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64`

Counts

3 → 99

Calls

3 calls:

11.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
6.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
3.0ms	(sqrt.f64 (/.f64 1 k))

simplify137.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
323×	`*-commutative_binary64`
267×	`exp-prod_binary64`
240×	`distribute-rgt-in_binary64`
235×	`fma-neg_binary64`

Counts

135 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	3139
1	333	2801
2	935	2773
3	2619	2765
4	4537	2765
5	5024	2765

prune188.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	153	6	159

Error

Counts

159 → 6

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	8.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k)))
	0.9b	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (fabs.f64 (cbrt.f64 k))) (sqrt.f64 (cbrt.f64 k))))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 1)) (sqrt.f64 k))
✓	0.6b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.9b	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

Compiler

Compiled 3694 to 2720 computations (26.4% saved)

regimes1.2s (14%)

Accuracy

Total 0.5b remaining (95%)

Threshold costs 0.5b (95%)

Counts

199 → 1

Compiler

Compiled 20228 to 15513 computations (23.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	17	34
2	17	34

end122.0ms (1.4%)

Compiler: Compiled 168 to 133 computations (20.8% saved)

Details

analyze365.0ms (4.2%)

sample3.4s (38.6%)

simplify50.0ms (0.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series547.0ms (6.3%)

rewrite21.0ms (0.2%)

simplify135.0ms (1.6%)

prune230.0ms (2.6%)

localize19.0ms (0.2%)

series323.0ms (3.7%)

rewrite22.0ms (0.3%)

simplify93.0ms (1.1%)

prune193.0ms (2.2%)

localize11.0ms (0.1%)

series442.0ms (5.1%)

rewrite48.0ms (0.5%)

simplify197.0ms (2.3%)

prune370.0ms (4.3%)

localize12.0ms (0.1%)

series557.0ms (6.4%)

rewrite28.0ms (0.3%)

simplify137.0ms (1.6%)

prune188.0ms (2.2%)

regimes1.2s (14%)

simplify3.0ms (0%)

end122.0ms (1.4%)

Profiling