Details

analyze335.0ms (4.7%)

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)

sample3.1s (44.1%)

Results

1.3s	8256×	body	128	valid
1.1s	1361×	body	1024	invalid
377.0ms	723×	body	512	invalid
182.0ms	1207×	body	128	invalid
124.0ms	370×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify55.0ms (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

prune5.0ms (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))
	0.5b	(.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)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series520.0ms (7.3%)

Counts

3 → 48

Calls

3 calls:

274.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
243.0ms	(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:

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)

simplify112.0ms (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

prune222.0ms (3.1%)

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

0.0b

Counts

170 → 8

Alt Table

Status	Error	Program
▶	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)))
	0.4b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	22.7b	(/.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))
	0.8b	(.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 (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))))
	0.5b	(/.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)))
	0.5b	(/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)))))

Compiler

Compiled 4328 to 2730 computations (36.9% saved)

localize9.0ms (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)))
✓	0.1b	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
✓	0.2b	(*.f64 n (PI.f64))
✓	0.4b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))

series141.0ms (2%)

Counts

4 → 0

Calls

4 calls:

80.0ms	(.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))
11.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
2.0ms	(*.f64 n (PI.f64))

rewrite35.0ms (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:

11.0ms	(.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)))
8.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
3.0ms	(*.f64 n (PI.f64))
2.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

simplify159.0ms (2.2%)

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

prune272.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	192	5	197
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	197	8	205

Error

Counts

205 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))
▶	0.3b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2))) (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/4 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	10.8b	(.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 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k)))
	0.5b	(/.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)))

Compiler

Compiled 5950 to 3220 computations (45.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/4 k)))
	0.1b	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
	0.2b	(*.f64 n (PI.f64))
	0.4b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))

series80.0ms (1.1%)

Counts

1 → 0

Calls

1 calls:

80.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/4 k)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
30×	`add-exp-log_binary64`
28×	`associate-l_binary64`
28×	`times-frac_binary64`
20×	`sqrt-prod_binary64`

Counts

1 → 62

Calls

1 calls:

11.0ms

(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 -1/4 k)))

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
642×	`associate-l_binary64`
573×	`associate-r_binary64`
294×	`associate-/l*_binary64`
257×	`associate-*l/_binary64`

Counts

62 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2400
1	239	2247
2	736	2219
3	3317	2219
4	4727	2219
5	5346	2219

prune328.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	224	8	232

Error

Counts

232 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2))) (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/4 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	10.8b	(.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 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k)))
	0.5b	(/.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)))

Compiler

Compiled 9058 to 5090 computations (43.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series69.0ms (1%)

Counts

3 → 0

Calls

3 calls:

46.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
15.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
9.0ms	(sqrt.f64 (*.f64 n (PI.f64)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
12×	`sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
6.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
2.0ms	(sqrt.f64 (*.f64 n (PI.f64)))

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

943×	`div-sub_binary64`
533×	`times-frac_binary64`
518×	`associate-/l*_binary64`
234×	`associate-l_binary64`
202×	`associate-/l/_binary64`

Counts

72 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	1211
1	179	1088
2	617	1088
3	2795	1088
4	2855	1088
5	3065	1088
6	3688	1088
7	4313	1088
8	4865	1088

prune149.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	8	129

Error

Counts

129 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))))
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2))) (.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 -1/4 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))))
	0.4b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	10.8b	(.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 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k)))
	0.5b	(/.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)))

Compiler

Compiled 3233 to 1680 computations (48% saved)

regimes1.0s (14.5%)

Accuracy

Total 0.3b remaining (80.4%)

Threshold costs 0.3b (80.4%)

Counts

209 → 1

Compiler

Compiled 22624 to 16662 computations (26.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	23	31
2	22	31

end137.0ms (1.9%)

Compiler: Compiled 235 to 167 computations (28.9% saved)

Details

analyze335.0ms (4.7%)

sample3.1s (44.1%)

simplify55.0ms (0.8%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series520.0ms (7.3%)

rewrite22.0ms (0.3%)

simplify112.0ms (1.6%)

prune222.0ms (3.1%)

localize9.0ms (0.1%)

series141.0ms (2%)

rewrite35.0ms (0.5%)

simplify159.0ms (2.2%)

prune272.0ms (3.8%)

localize13.0ms (0.2%)

series80.0ms (1.1%)

rewrite20.0ms (0.3%)

simplify103.0ms (1.5%)

prune328.0ms (4.6%)

localize11.0ms (0.2%)

series69.0ms (1%)

rewrite17.0ms (0.2%)

simplify113.0ms (1.6%)

prune149.0ms (2.1%)

regimes1.0s (14.5%)

simplify2.0ms (0%)

end137.0ms (1.9%)

Profiling