Details

analyze630.0ms (5.4%)

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)

sample5.7s (49.4%)

Results

2.4s	8256×	body	128	valid
2.0s	1321×	body	1024	invalid
751.0ms	706×	body	512	invalid
341.0ms	1146×	body	128	invalid
211.0ms	352×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify88.0ms (0.8%)

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

prune8.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(.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)

localize18.0ms (0.2%)

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))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series819.0ms (7.1%)

Counts

3 → 48

Calls

3 calls:

468.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
348.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite20.0ms (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	(.f64 (.f64 2 (PI.f64)) n)
4.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

simplify138.0ms (1.2%)

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 (1.9%)

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

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.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))))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
▶	0.6b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(.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)))
	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	22.5b	(/.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))

Compiler

Compiled 4283 to 2780 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series303.0ms (2.6%)

Counts

3 → 24

Calls

3 calls:

251.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))
39.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
13.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

9.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (*.f64 k -1/2))
6.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

411×	`associate-l_binary64`
399×	`associate-r_binary64`
362×	`distribute-rgt-in_binary64`
357×	`distribute-lft-in_binary64`
345×	`exp-prod_binary64`

Counts

106 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2242
1	303	2093
2	855	2081
3	4547	2077
4	5184	2077

prune175.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

Counts

138 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	10.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
▶	0.6b	(/.f64 (exp.f64 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(.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)))
	22.5b	(/.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))

Compiler

Compiled 3769 to 2466 computations (34.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
✓	0.4b	(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
	0.4b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	1.0b	(log.f64 (*.f64 2 (PI.f64)))

series251.0ms (2.2%)

Counts

2 → 8

Calls

2 calls:

251.0ms	(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
0.0ms	(log.f64 (*.f64 2 (PI.f64)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
10×	`log-pow_binary64`
9×	`*-un-lft-identity_binary64`
6×	`distribute-lft-out_binary64`
5×	`add-exp-log_binary64`

Counts

2 → 41

Calls

2 calls:

5.0ms	(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
2.0ms	(log.f64 (*.f64 2 (PI.f64)))

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

795×	`unsub-neg_binary64`
652×	`fma-neg_binary64`
623×	`fma-def_binary64`
428×	`associate-+l+_binary64`
413×	`associate-+r+_binary64`

Counts

49 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	611
1	123	556
2	283	556
3	964	556
4	3302	556
5	4982	556
6	4915	556
7	4976	556
8	4992	556
9	4916	556

prune134.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	111	7	118

Error

Counts

118 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	10.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
✓	0.6b	(/.f64 (exp.f64 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
▶	0.6b	(.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)))
	22.5b	(/.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))

Compiler

Compiled 3574 to 2319 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))

series437.0ms (3.8%)

Counts

4 → 44

Calls

4 calls:

343.0ms	(.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)))
59.0ms	(/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
31.0ms	(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 (0.4%)

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:

17.0ms	(.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))
3.0ms	(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
2.0ms	(pow.f64 n (fma.f64 k -1/2 1/2))

simplify210.0ms (1.8%)

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

prune383.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	289	7	296

Error

Counts

296 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	10.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (/.f64 k (.f64 n (*.f64 2 (PI.f64))))))
	0.7b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
✓	0.6b	(/.f64 (exp.f64 (.f64 -1/2 (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	0.6b	(.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)))
	22.5b	(/.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))

Compiler

Compiled 8647 to 5639 computations (34.8% saved)

regimes1.6s (13.6%)

Accuracy

Total 0.5b remaining (95.2%)

Threshold costs 0.5b (95.2%)

Counts

288 → 1

Compiler

Compiled 33962 to 26057 computations (23.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	21	31
2	21	31

end136.0ms (1.2%)

Compiler: Compiled 225 to 167 computations (25.8% saved)

Details

analyze630.0ms (5.4%)

sample5.7s (49.4%)

simplify88.0ms (0.8%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

series819.0ms (7.1%)

rewrite20.0ms (0.2%)

simplify138.0ms (1.2%)

prune217.0ms (1.9%)

localize11.0ms (0.1%)

series303.0ms (2.6%)

rewrite22.0ms (0.2%)

simplify94.0ms (0.8%)

prune175.0ms (1.5%)

localize16.0ms (0.1%)

series251.0ms (2.2%)

rewrite8.0ms (0.1%)

simplify118.0ms (1%)

prune134.0ms (1.2%)

localize11.0ms (0.1%)

series437.0ms (3.8%)

rewrite48.0ms (0.4%)

simplify210.0ms (1.8%)

prune383.0ms (3.3%)

regimes1.6s (13.6%)

simplify2.0ms (0%)

end136.0ms (1.2%)

Profiling