Details

analyze370.0ms (5%)

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 (42.4%)

Results

1.3s	8256×	body	128	valid
1.1s	1375×	body	1024	invalid
387.0ms	667×	body	512	invalid
174.0ms	1160×	body	128	invalid
121.0ms	370×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify47.0ms (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 (0.1%)

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

0.7b

Counts

3 → 2

Alt Table

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

series521.0ms (7%)

Counts

3 → 48

Calls

3 calls:

269.0ms	(/.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)

rewrite20.0ms (0.3%)

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

simplify120.0ms (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

prune207.0ms (2.8%)

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
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (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)))
	1.5b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
	1.1b	(.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))))
	0.9b	(.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))))
	0.8b	(/.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))))))

Compiler

Compiled 4237 to 2746 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
✓	0.5b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

series507.0ms (6.9%)

Counts

4 → 48

Calls

4 calls:

265.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
234.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
5.0ms	(sqrt.f64 (/.f64 1 k))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
27×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`

Counts

4 → 119

Calls

4 calls:

8.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
4.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 n (.f64 2 (PI.f64)))
2.0ms	(sqrt.f64 (/.f64 1 k))

simplify152.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

498×	`*-commutative_binary64`
487×	`distribute-rgt-in_binary64`
481×	`distribute-lft-in_binary64`
259×	`times-frac_binary64`
231×	`fma-neg_binary64`

Counts

167 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	3470
1	391	3090
2	1278	3062
3	3634	3062
4	4927	3062
5	4999	3062
6	4930	3062

prune175.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
▶	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (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)))
	1.5b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
	1.1b	(.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))))
	0.9b	(.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))))
	0.8b	(/.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))))))

Compiler

Compiled 3761 to 2757 computations (26.7% saved)

localize10.0ms (0.1%)

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))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 k))
✓	0.6b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

series320.0ms (4.3%)

Counts

3 → 24

Calls

3 calls:

230.0ms

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

77.0ms

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

13.0ms

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

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
15×	`pow1_binary64`
11×	`prod-exp_binary64`
8×	`add-cbrt-cube_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 66

Calls

3 calls:

9.0ms

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

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

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
689×	`associate-/l*_binary64`
259×	`distribute-rgt-in_binary64`
254×	`distribute-lft-in_binary64`
246×	`associate-/r*_binary64`

Counts

90 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2252
1	321	1968
2	1044	1956
3	4708	1954
4	5368	1954

prune174.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	141	7	148

Error

Counts

148 → 7

Alt Table

Status	Error	Program
	1.2b	(/.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (sqrt.f64 (cbrt.f64 k)))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
✓	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
▶	0.7b	(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k) -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.9b	(.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))))

Compiler

Compiled 3921 to 2550 computations (35% saved)

localize11.0ms (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))) k)
✓	0.2b	(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k) -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.6b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

series326.0ms (4.4%)

Counts

2 → 24

Calls

2 calls:

227.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) k)
99.0ms	(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k) -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
13×	`prod-exp_binary64`
11×	`pow-exp_binary64`
8×	`div-exp_binary64`
8×	`pow1_binary64`

Counts

2 → 56

Calls

2 calls:

9.0ms	(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k) -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
4.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) k)

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
233×	`associate-/r*_binary64`
221×	`associate-/l/_binary64`
213×	`associate-*l/_binary64`
212×	`distribute-rgt-in_binary64`

Counts

80 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2060
1	307	1790
2	1041	1788
3	4611	1788
4	4969	1788
5	4981	1788

prune162.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Error

Counts

142 → 7

Alt Table

Status	Error	Program
	1.2b	(/.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (sqrt.f64 (cbrt.f64 k)))
	0.8b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.8b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (cbrt.f64 k))))
	0.8b	(/.f64 1 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))))
✓	0.7b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
✓	0.7b	(/.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k) -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
	0.9b	(.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))))

Compiler

Compiled 3606 to 2327 computations (35.5% saved)

regimes732.0ms (9.9%)

Accuracy

Total 0.6b remaining (93.7%)

Threshold costs 0.6b (93.7%)

Counts

152 → 1

Compiler

Compiled 14242 to 11086 computations (22.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	21	30
2	20	30

end132.0ms (1.8%)

Compiler: Compiled 207 to 158 computations (23.7% saved)

Details

analyze370.0ms (5%)

sample3.1s (42.4%)

simplify47.0ms (0.6%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series521.0ms (7%)

rewrite20.0ms (0.3%)

simplify120.0ms (1.6%)

prune207.0ms (2.8%)

localize11.0ms (0.1%)

series507.0ms (6.9%)

rewrite26.0ms (0.3%)

simplify152.0ms (2.1%)

prune175.0ms (2.4%)

localize10.0ms (0.1%)

series320.0ms (4.3%)

rewrite20.0ms (0.3%)

simplify83.0ms (1.1%)

prune174.0ms (2.3%)

localize11.0ms (0.2%)

series326.0ms (4.4%)

rewrite23.0ms (0.3%)

simplify98.0ms (1.3%)

prune162.0ms (2.2%)

regimes732.0ms (9.9%)

simplify2.0ms (0%)

end132.0ms (1.8%)

Profiling