Details

analyze348.0ms (5.2%)

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%	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 (47.5%)

Results

1.3s	8256×	body	128	valid
1.1s	1390×	body	1024	invalid
385.0ms	679×	body	512	invalid
170.0ms	1118×	body	128	invalid
117.0ms	350×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify21.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
257×	`associate-*l/_binary64`
214×	`unswap-sqr_binary64`
214×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	140	22
4	354	22
5	958	20
6	2187	20

Stop Event

1×	node limit

Counts

1 → 2

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(.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 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series476.0ms (7.1%)

Counts

3 → 48

Calls

3 calls:

262.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
212.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms	(*.f64 (PI.f64) n)

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
222×	`log-pow_binary64`
132×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	274	40
2	3319	40

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

51.0ms	(*.f64 (PI.f64) n)
51.0ms	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
51.0ms	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1144
1	183	984
2	587	828
3	3443	826

Stop Event

1×	node limit

Counts

130 → 99

prune120.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
	21.8b	(/.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	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
	0.4b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.5b	(/.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))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
▶	0.4b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))

Compiler

Compiled 2455 to 1676 computations (31.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series449.0ms (6.7%)

Counts

4 → 48

Calls

4 calls:

222.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
220.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
4.0ms	(sqrt.f64 (/.f64 1 k))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`log-prod_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
239×	`log-pow_binary64`
144×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	52
1	308	47
2	3513	47

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

55.0ms	(sqrt.f64 (/.f64 1 k))
55.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
55.0ms	(.f64 n (.f64 2 (PI.f64)))
55.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
433×	`associate-r_binary64`
373×	`associate-l_binary64`
176×	`distribute-rgt-in_binary64`
172×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1180
1	183	1020
2	587	864
3	3443	862

Stop Event

1×	node limit

Counts

141 → 111

prune135.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Error

0.0b

Counts

118 → 7

Alt Table

Status	Error	Program
	21.8b	(.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 (/.f64 1 k)))
	0.5b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 (/.f64 1 k)))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
▶	0.4b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.5b	(/.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))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2683 to 1985 computations (26% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series253.0ms (3.8%)

Counts

1 → 12

Calls

1 calls:

253.0ms

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

rewrite41.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
221×	`log-pow_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	274	21
2	3212	21

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

41.0ms

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

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

511×	`exp-sum_binary64`
353×	`unsub-neg_binary64`
342×	`exp-prod_binary64`
227×	`distribute-rgt-in_binary64`
224×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	372
1	72	372
2	162	276
3	571	276
4	2704	276

Stop Event

1×	node limit

Counts

30 → 22

prune94.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	21.8b	(.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 (/.f64 1 k)))
▶	0.5b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 (/.f64 1 k)))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
✓	0.4b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.5b	(/.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))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.9b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2046 to 1502 computations (26.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series63.0ms (0.9%)

Counts

3 → 12

Calls

3 calls:

52.0ms	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 (/.f64 1 k)))
9.0ms	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
3.0ms	(.f64 (PI.f64) (.f64 n 2))

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	332	40
2	3979	38

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

54.0ms	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 (/.f64 1 k)))
54.0ms	(.f64 (PI.f64) (.f64 n 2))
54.0ms	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	10	96
2	17	96
3	19	96

Stop Event

1×

saturated

Counts

71 → 61

prune142.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Error

Counts

118 → 8

Alt Table

Status	Error	Program
	21.8b	(.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 (/.f64 1 k)))
✓	0.5b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (sqrt.f64 (/.f64 1 k)))
	0.5b	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
✓	0.4b	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
	0.5b	(/.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))
	0.9b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	3.4b	(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))) (expm1.f64 (log1p.f64 (pow.f64 k -1/2))))
	0.9b	(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2759 to 2028 computations (26.5% saved)

regimes864.0ms (12.9%)

Accuracy

Total 0.4b remaining (90.9%)

Threshold costs 0.4b (90.9%)

Counts

181 → 1

Compiler

Compiled 16078 to 13002 computations (19.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	28	36

Stop Event

1×

saturated

end158.0ms (2.4%)

Compiler: Compiled 257 to 197 computations (23.3% saved)

Details

analyze348.0ms (5.2%)

sample3.2s (47.5%)

simplify21.0ms (0.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series476.0ms (7.1%)

rewrite53.0ms (0.8%)

simplify50.0ms (0.8%)

prune120.0ms (1.8%)

localize13.0ms (0.2%)

series449.0ms (6.7%)

rewrite57.0ms (0.8%)

simplify44.0ms (0.7%)

prune135.0ms (2%)

localize11.0ms (0.2%)

series253.0ms (3.8%)

rewrite41.0ms (0.6%)

simplify28.0ms (0.4%)

prune94.0ms (1.4%)

localize11.0ms (0.2%)

series63.0ms (0.9%)

rewrite55.0ms (0.8%)

simplify9.0ms (0.1%)

prune142.0ms (2.1%)

regimes864.0ms (12.9%)

simplify5.0ms (0.1%)

end158.0ms (2.4%)

Profiling