Details

analyze346.0ms (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)

sample3.2s (47.3%)

Results

1.4s	8256×	body	128	valid
1.1s	1318×	body	1024	invalid
367.0ms	659×	body	512	invalid
203.0ms	1204×	body	128	invalid
124.0ms	355×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify46.0ms (0.7%)

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

0.3b

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))
	0.4b	(.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)

series527.0ms (7.7%)

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))
247.0ms	(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 (0.3%)

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

simplify125.0ms (1.8%)

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

prune228.0ms (3.3%)

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
▶	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (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))))
	0.5b	(.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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	0.7b	(/.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))
	0.8b	(.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)))
	26.0b	(/.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 (.f64 1/2 (.f64 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/48 (.f64 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))

Compiler

Compiled 4318 to 2718 computations (37.1% saved)

localize12.0ms (0.2%)

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

series140.0ms (2%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
41.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
12.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
3.0ms	(*.f64 n (PI.f64))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
18×	`pow1_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`prod-exp_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 98

Calls

4 calls:

10.0ms	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 k))
7.0ms	(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
3.0ms	(*.f64 n (PI.f64))
3.0ms	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-def_binary64`
334×	`distribute-rgt-in_binary64`
332×	`distribute-lft-in_binary64`
280×	`associate-/r*_binary64`
269×	`associate-*l/_binary64`

Counts

110 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2985
1	365	2651
2	1373	2611
3	4679	2603
4	5478	2603

prune218.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Error

Counts

172 → 6

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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	11.7b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 n (PI.f64)) 2))) 3)) (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))))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))))) (sqrt.f64 k))

Compiler

Compiled 4686 to 2607 computations (44.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series113.0ms (1.6%)

Counts

3 → 0

Calls

3 calls:

87.0ms

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

14.0ms

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

12.0ms

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

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
13×	`pow1_binary64`

Counts

3 → 81

Calls

3 calls:

11.0ms

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

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
477×	`associate-/r*_binary64`
329×	`associate-*l/_binary64`
294×	`*-commutative_binary64`
262×	`associate-/l/_binary64`

Counts

81 → 92

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	132	2167
1	254	1881
2	1012	1881
3	3531	1881
4	4797	1881
5	5183	1881

prune160.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Error

Counts

142 → 6

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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
▶	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (sqrt.f64 n) (*.f64 (PI.f64) (sqrt.f64 n)))))) (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))))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))))) (sqrt.f64 k))

Compiler

Compiled 3855 to 2036 computations (47.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(*.f64 (PI.f64) (sqrt.f64 n))
✓	0.4b	(.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))
✓	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (sqrt.f64 n) (*.f64 (PI.f64) (sqrt.f64 n)))))

series28.0ms (0.4%)

Counts

3 → 8

Calls

3 calls:

15.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (sqrt.f64 n) (*.f64 (PI.f64) (sqrt.f64 n)))))
8.0ms	(*.f64 (PI.f64) (sqrt.f64 n))
5.0ms	(.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
12×	`sqrt-prod_binary64`
12×	`add-cbrt-cube_binary64`

Counts

3 → 77

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (sqrt.f64 n) (*.f64 (PI.f64) (sqrt.f64 n)))))
5.0ms	(.f64 (sqrt.f64 n) (.f64 (PI.f64) (sqrt.f64 n)))
3.0ms	(*.f64 (PI.f64) (sqrt.f64 n))

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

577×	`times-frac_binary64`
510×	`associate-/r*_binary64`
405×	`log-div_binary64`
275×	`log-prod_binary64`
243×	`*-commutative_binary64`

Counts

85 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	95	1273
1	183	881
2	505	881
3	661	881
4	833	881
5	1106	881
6	2107	881
7	4318	881
8	4956	881

prune141.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

Counts

131 → 6

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 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (sqrt.f64 n) (*.f64 (PI.f64) (sqrt.f64 n)))))) (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))))
✓	0.3b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 k))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))))) (sqrt.f64 k))

Compiler

Compiled 3726 to 1779 computations (52.3% saved)

regimes978.0ms (14.3%)

Accuracy

Total 0.2b remaining (68.1%)

Threshold costs 0.2b (68.1%)

Counts

197 → 1

Compiler

Compiled 21720 to 16017 computations (26.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	23	32
2	21	32

end117.0ms (1.7%)

Compiler: Compiled 186 to 137 computations (26.3% saved)

Details

analyze346.0ms (5%)

sample3.2s (47.3%)

simplify46.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series527.0ms (7.7%)

rewrite21.0ms (0.3%)

simplify125.0ms (1.8%)

prune228.0ms (3.3%)

localize12.0ms (0.2%)

series140.0ms (2%)

rewrite28.0ms (0.4%)

simplify103.0ms (1.5%)

prune218.0ms (3.2%)

localize13.0ms (0.2%)

series113.0ms (1.6%)

rewrite25.0ms (0.4%)

simplify97.0ms (1.4%)

prune160.0ms (2.3%)

localize17.0ms (0.2%)

series28.0ms (0.4%)

rewrite22.0ms (0.3%)

simplify95.0ms (1.4%)

prune141.0ms (2.1%)

regimes978.0ms (14.3%)

simplify2.0ms (0%)

end117.0ms (1.7%)

Profiling