Details

analyze351.0ms (4.8%)

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 (43%)

Results

1.3s	8256×	body	128	valid
1.1s	1422×	body	1024	invalid
413.0ms	712×	body	512	invalid
177.0ms	1147×	body	128	invalid
118.0ms	362×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify48.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.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 (.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))
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series437.0ms (5.9%)

Counts

3 → 48

Calls

3 calls:

225.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
209.0ms	(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×	`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:

7.0ms	(/.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)

simplify124.0ms (1.7%)

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

prune206.0ms (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
▶	0.2b	(/.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))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
	0.4b	(.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))))
	0.5b	(.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 (.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))))
	0.7b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
	0.6b	(.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))))

Compiler

Compiled 4247 to 2764 computations (34.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series98.0ms (1.3%)

Counts

4 → 24

Calls

4 calls:

55.0ms	(/.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))
31.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
9.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
3.0ms	(.f64 n (.f64 2 (PI.f64)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
21×	`pow1_binary64`
19×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`

Counts

4 → 98

Calls

4 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))
9.0ms	(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
4.0ms	(.f64 n (.f64 2 (PI.f64)))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

436×	`distribute-rgt-in_binary64`
434×	`distribute-lft-in_binary64`
257×	`associate-/l/_binary64`
199×	`associate-l_binary64`
198×	`associate-r_binary64`

Counts

122 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	3143
1	388	2789
2	1552	2749
3	4698	2749
4	5000	2749
5	4978	2749

prune262.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
✓	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	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
▶	0.5b	(.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 (.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))))
	0.7b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
	0.6b	(.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))))

Compiler

Compiled 5129 to 3228 computations (37.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series439.0ms (6%)

Counts

3 → 36

Calls

3 calls:

224.0ms	(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
201.0ms	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
14.0ms	(sqrt.f64 (/.f64 1 k))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
32×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64`

Counts

3 → 99

Calls

3 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))
2.0ms	(sqrt.f64 (/.f64 1 k))

simplify118.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
323×	`*-commutative_binary64`
267×	`exp-prod_binary64`
240×	`distribute-rgt-in_binary64`
235×	`fma-neg_binary64`

Counts

135 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	3139
1	333	2801
2	935	2773
3	2619	2765
4	4537	2765
5	5024	2765

prune210.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	161	7	168

Error

Counts

168 → 7

Alt Table

Status	Error	Program
✓	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	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
✓	0.5b	(.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 (.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))))
	0.7b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
	0.6b	(.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))))

Compiler

Compiled 4039 to 2964 computations (26.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))
✓	0.4b	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
✓	0.5b	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
✓	0.6b	(cbrt.f64 n)

series131.0ms (1.8%)

Counts

4 → 48

Calls

4 calls:

43.0ms	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
39.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
31.0ms	(cbrt.f64 n)
19.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64))))
5.0ms	(*.f64 (cbrt.f64 n) (cbrt.f64 n))
4.0ms	(.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))
1.0ms	(cbrt.f64 n)

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
519×	`*-commutative_binary64`
326×	`sqr-pow_binary64`
310×	`log-prod_binary64`
268×	`exp-prod_binary64`

Counts

156 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1587
1	248	1348
2	986	1310
3	1663	1296
4	3002	1202
5	4604	1202
6	4881	1202

prune203.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
✓	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	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (cbrt.f64 n) (.f64 2 (PI.f64)))))) (sqrt.f64 k))
	0.7b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
✓	0.5b	(.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 (.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))))
	0.7b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
	0.6b	(.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))))

Compiler

Compiled 5662 to 3000 computations (47% saved)

regimes1.1s (14.4%)

Accuracy

Total 0.4b remaining (89.7%)

Threshold costs 0.4b (89.7%)

Counts

213 → 1

Compiler

Compiled 21658 to 16762 computations (22.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	23	34
2	22	34

end136.0ms (1.8%)

Compiler: Compiled 219 to 167 computations (23.7% saved)

Details

analyze351.0ms (4.8%)

sample3.2s (43%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series437.0ms (5.9%)

rewrite21.0ms (0.3%)

simplify124.0ms (1.7%)

prune206.0ms (2.8%)

localize9.0ms (0.1%)

series98.0ms (1.3%)

rewrite29.0ms (0.4%)

simplify126.0ms (1.7%)

prune262.0ms (3.6%)

localize10.0ms (0.1%)

series439.0ms (6%)

rewrite23.0ms (0.3%)

simplify118.0ms (1.6%)

prune210.0ms (2.9%)

localize15.0ms (0.2%)

series131.0ms (1.8%)

rewrite26.0ms (0.4%)

simplify102.0ms (1.4%)

prune203.0ms (2.7%)

regimes1.1s (14.4%)

simplify2.0ms (0%)

end136.0ms (1.8%)

Profiling