Details

analyze384.0ms (5.4%)

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)

sample3.4s (47.7%)

Results

1.4s	8256×	body	128	valid
1.2s	1428×	body	1024	invalid
408.0ms	733×	body	512	invalid
236.0ms	1217×	body	128	invalid
119.0ms	359×	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

0.2b

Counts

3 → 2

Alt Table

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

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)

series450.0ms (6.4%)

Counts

3 → 48

Calls

3 calls:

227.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
217.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite62.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 85

Calls

3 calls:

60.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
60.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
60.0ms	(.f64 (.f64 2 (PI.f64)) n)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	273	43
2	3155	43
3	5471	43
0	0	0
1	0	0

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
455×	`distribute-rgt-neg-in_binary64`
454×	`distribute-lft-neg-in_binary64`
435×	`associate-r_binary64`
375×	`associate-l_binary64`

Counts

133 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1180
1	181	1020
2	524	864
3	2685	862
4	5113	862

prune161.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Error

0.0b

Counts

104 → 7

Alt Table

Status	Error	Program
	9.7b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k))
	0.6b	(/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	0.9b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
	0.5b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2472 to 1727 computations (30.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series433.0ms (6.1%)

Counts

4 → 28

Calls

4 calls:

222.0ms	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
204.0ms	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
4.0ms	(sqrt.f64 (/.f64 1 k))
2.0ms	(*.f64 n (PI.f64))

rewrite66.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 95

Calls

4 calls:

64.0ms	(sqrt.f64 (/.f64 1 k))
64.0ms	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
64.0ms	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
64.0ms	(*.f64 n (PI.f64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	307	44
2	3283	44
3	5477	44
0	0	0
1	0	0

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
455×	`distribute-rgt-neg-in_binary64`
454×	`distribute-lft-neg-in_binary64`
434×	`associate-r_binary64`
374×	`associate-l_binary64`

Counts

123 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	900
1	174	820
2	515	648
3	2667	646
4	5080	646

prune149.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	110	7	117

Error

Counts

117 → 7

Alt Table

Status	Error	Program
	9.7b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k))
	0.6b	(/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
▶	0.3b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
	0.4b	(.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2600 to 1815 computations (30.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series257.0ms (3.6%)

Counts

2 → 12

Calls

2 calls:

245.0ms	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
12.0ms	(/.f64 1 (sqrt.f64 k))

rewrite59.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

696×	`log-prod_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
239×	`log-pow_binary64`
145×	`add-sqr-sqrt_binary64`

Counts

2 → 57

Calls

2 calls:

58.0ms	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
58.0ms	(/.f64 1 (sqrt.f64 k))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	309	24
2	3335	24
3	5640	24
0	0	0
1	0	0

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

884×	`exp-prod_binary64`
511×	`exp-sum_binary64`
353×	`unsub-neg_binary64`
252×	`exp-neg_binary64`
237×	`exp-diff_binary64`

Counts

69 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	372
1	72	372
2	139	276
3	484	276
4	1884	276
5	4240	276
6	4805	276
7	4937	276

prune139.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	116	7	123

Error

Counts

123 → 7

Alt Table

Status	Error	Program
	9.7b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k))
	0.6b	(/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
▶	0.4b	(.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2699 to 1813 computations (32.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series63.0ms (0.9%)

Counts

2 → 0

Calls

2 calls:

51.0ms	(.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (/.f64 1 k)))
12.0ms	(sqrt.f64 (.f64 (.f64 n (PI.f64)) 2))

rewrite62.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

281×	`log-pow_binary64`
272×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Counts

2 → 44

Calls

2 calls:

61.0ms	(.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (/.f64 1 k)))
61.0ms	(sqrt.f64 (.f64 (.f64 n (PI.f64)) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	330	32
2	3720	30
3	4904	30
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune127.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Error

Counts

121 → 7

Alt Table

Status	Error	Program
	9.7b	(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) 2) k))
	0.6b	(/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) n)) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) n)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n))) (sqrt.f64 k))
✓	0.4b	(.f64 (.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) 2) (.f64 k -1/2)) (sqrt.f64 (.f64 (*.f64 n (PI.f64)) 2))) (sqrt.f64 (/.f64 1 k)))
	0.6b	(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))

Compiler

Compiled 2815 to 1815 computations (35.5% saved)

regimes881.0ms (12.5%)

Accuracy

Total 0.4b remaining (89%)

Threshold costs 0.4b (89%)

Counts

184 → 1

Compiler

Compiled 16306 to 13231 computations (18.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	17	23
2	17	23

end132.0ms (1.9%)

Compiler: Compiled 188 to 150 computations (20.2% saved)

Details

analyze384.0ms (5.4%)

sample3.4s (47.7%)

simplify46.0ms (0.7%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series450.0ms (6.4%)

rewrite62.0ms (0.9%)

simplify50.0ms (0.7%)

prune161.0ms (2.3%)

localize10.0ms (0.1%)

series433.0ms (6.1%)

rewrite66.0ms (0.9%)

simplify51.0ms (0.7%)

prune149.0ms (2.1%)

localize10.0ms (0.1%)

series257.0ms (3.6%)

rewrite59.0ms (0.8%)

simplify66.0ms (0.9%)

prune139.0ms (2%)

localize10.0ms (0.1%)

series63.0ms (0.9%)

rewrite62.0ms (0.9%)

simplify7.0ms (0.1%)

prune127.0ms (1.8%)

regimes881.0ms (12.5%)

simplify2.0ms (0%)

end132.0ms (1.9%)

Profiling