Details

analyze596.0ms (7.2%)

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%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample104.0ms (1.3%)

Algorithm

1×

intervals

Results

32.0ms	53×	body	1024	nan
26.0ms	256×	body	128	valid
16.0ms	70×	body	128	overflowed
8.0ms	21×	body	512	nan
2.0ms	32×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify49.0ms (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

0.3b

Counts

3 → 2

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)))
▶	0.4b	(/.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)

localize10.0ms (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))
✓	0.2b	(/.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)

series529.0ms (6.4%)

Counts

3 → 48

Calls

3 calls:

277.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
248.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite22.0ms (0.3%)

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:

6.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify128.0ms (1.5%)

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

prune212.0ms (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
	0.5b	(.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))))
	0.4b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (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 (.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))))
	18.4b	(/.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 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (sqrt.f64 k))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
	0.6b	(/.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))))

Compiler

Compiled 4344 to 2746 computations (36.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
✓	0.2b	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
✓	0.3b	(*.f64 n (PI.f64))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))

series148.0ms (1.8%)

Counts

4 → 0

Calls

4 calls:

87.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
47.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
12.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
2.0ms	(*.f64 n (PI.f64))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
43×	`sqrt-prod_binary64`
39×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`

Counts

4 → 145

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
12.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
3.0ms	(*.f64 n (PI.f64))
3.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

simplify176.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-def_binary64`
457×	`associate-/l*_binary64`
326×	`*-commutative_binary64`
314×	`associate-*r/_binary64`
282×	`associate-*l/_binary64`

Counts

145 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3965
1	343	3724
2	1166	3696
3	3309	3696
4	4467	3696
5	4991	3696
6	4973	3696

prune253.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	198	7	205

Error

Counts

205 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (PI.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))))
	18.4b	(/.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 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64)))))) (sqrt.f64 k))
	0.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k)))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	10.5b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))

Compiler

Compiled 5964 to 3232 computations (45.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series85.0ms (1%)

Counts

2 → 0

Calls

2 calls:

48.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
37.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64`
108×	`*-un-lft-identity_binary64`
108×	`add-sqr-sqrt_binary64`
108×	`add-cube-cbrt_binary64`
94×	`sqrt-prod_binary64`

Counts

2 → 187

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
6.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))

simplify329.0ms (4%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-neg_binary64`
426×	`div-sub_binary64`
402×	`unswap-sqr_binary64`
356×	`*-commutative_binary64`
295×	`distribute-rgt-in_binary64`

Counts

187 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	5375
1	234	4957
2	578	4849
3	1688	4849
4	1831	4849
5	1920	4849
6	2407	4849
7	3234	4849
8	3880	4849
9	4989	4849
10	4651	4849

prune328.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	271	6	277

Error

Counts

277 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (PI.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	10.5b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
▶	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))

Compiler

Compiled 8680 to 4951 computations (43% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))))
✓	0.4b	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
✓	0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))

series123.0ms (1.5%)

Counts

3 → 0

Calls

3 calls:

64.0ms

(/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))

46.0ms

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

13.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 129

Calls

3 calls:

8.0ms

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

7.0ms

(/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))

6.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))

simplify167.0ms (2%)

Algorithm

1×	egg-herbie

Rules

937×	`times-frac_binary64`
894×	`div-sub_binary64`
412×	`associate-/l*_binary64`
392×	`associate-/r*_binary64`
284×	`associate-r_binary64`

Counts

129 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2936
1	233	2549
2	796	2495
3	3404	2495
4	3555	2495
5	3806	2495
6	4761	2495
7	6052	2495

prune241.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (PI.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))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
	10.5b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
✓	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))))

Compiler

Compiled 5585 to 3055 computations (45.3% saved)

regimes1.4s (17.4%)

Accuracy

Total 0.3b remaining (75.9%)

Threshold costs 0.3b (75.9%)

Counts

250 → 1

Compiler

Compiled 28782 to 21009 computations (27% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	21	37
2	21	37

end1.0ms (0%)

Compiler: Compiled 25 to 18 computations (28% saved)

sample3.2s (38.6%)

Algorithm

1×

intervals

Results

874.0ms	8000×	body	128	valid
849.0ms	1385×	body	1024	nan
439.0ms	2375×	body	128	overflowed
284.0ms	670×	body	512	nan
77.0ms	310×	body	256	nan
75.0ms	978×	body	128	nan
39.0ms	298×	body	128	invalid

Compiler

Compiled 191 to 142 computations (25.7% saved)

Details

analyze596.0ms (7.2%)

sample104.0ms (1.3%)

simplify49.0ms (0.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series529.0ms (6.4%)

rewrite22.0ms (0.3%)

simplify128.0ms (1.5%)

prune212.0ms (2.6%)

localize10.0ms (0.1%)

series148.0ms (1.8%)

rewrite43.0ms (0.5%)

simplify176.0ms (2.1%)

prune253.0ms (3.1%)

localize11.0ms (0.1%)

series85.0ms (1%)

rewrite35.0ms (0.4%)

simplify329.0ms (4%)

prune328.0ms (4%)

localize15.0ms (0.2%)

series123.0ms (1.5%)

rewrite29.0ms (0.4%)

simplify167.0ms (2%)

prune241.0ms (2.9%)

regimes1.4s (17.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.2s (38.6%)

Profiling