Details

analyze561.0ms (16.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
37.5%	62.4%	0.1%	7
42.1%	57.8%	0.1%	8
54.6%	45.3%	0.1%	9
57.4%	42.5%	0.1%	10
64.4%	35.5%	0.1%	11
65.9%	34%	0.1%	12
69.6%	30.3%	0.1%	13
70.3%	29.6%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.7s (48.5%)

Results

754.0ms	6279×	body	128	valid
354.0ms	655×	body	2048	valid
307.0ms	523×	body	4096	valid
166.0ms	450×	body	1024	valid
67.0ms	223×	body	512	valid
25.0ms	126×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess16.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

10×	`fma-def_binary64`
7×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`
4×	`distribute-rgt-in_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	45	30
2	55	30
3	59	30
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	34	15
3	36	15

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

13.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.1b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.3b	(+.f64 re (hypot.f64 re im))

series54.0ms (1.6%)

Counts

3 → 56

Calls

18 calls:

10.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	re	-inf
6.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	0
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	-inf
4.0ms	(hypot.f64 re im)	re	-inf

rewrite44.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`expm1-log1p-u_binary64`
589×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
85×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	178	23
2	2341	23

Stop Event

1×	node limit

Counts

3 → 79

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
411×	`associate-r_binary64`
333×	`associate-l_binary64`
287×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1348
1	416	1280
2	1361	1216

Stop Event

1×	node limit

Counts

135 → 151

prune94.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	6	152

Error

6.9b

Counts

152 → 6

Alt Table

Status	Error	Program
▶	13.6b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	47.5b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 3096 to 2096 computations (32.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.1b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
	0.3b	(+.f64 re (hypot.f64 re im))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))

series51.0ms (1.5%)

Counts

2 → 16

Calls

12 calls:

8.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))	re	-inf
6.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))	im	0
6.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))	im	0
5.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))	im	-inf
5.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))	im	inf

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

856×	`log1p-expm1-u_binary64`
856×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	192	21
2	2361	21

Stop Event

1×	node limit

Counts

2 → 43

simplify32.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-def_binary64`
435×	`associate-r_binary64`
359×	`associate-l_binary64`
310×	`cancel-sign-sub-inv_binary64`
282×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	800
1	349	731
2	1189	664

Stop Event

1×	node limit

Counts

59 → 72

prune111.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Error

6.9b

Counts

189 → 7

Alt Table

Status	Error	Program
✓	13.6b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	47.5b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	28.6b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)))
✓	13.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 4038 to 2805 computations (30.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))
	0.3b	(+.f64 re (hypot.f64 re im))
✓	0.4b	(pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)
✓	14.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3))

series128.0ms (3.7%)

Counts

3 → 24

Calls

18 calls:

16.0ms	(pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)	im	inf
16.0ms	(pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)	im	-inf
13.0ms	(pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)	re	-inf
13.0ms	(pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)	im	0
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 3))	im	0

rewrite50.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`prod-diff_binary64`
450×	`log-prod_binary64`
203×	`fma-def_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	232	37
2	2625	37

Stop Event

1×	node limit

Counts

3 → 98

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
601×	`fma-neg_binary64`
377×	`*-commutative_binary64`
247×	`cancel-sign-sub-inv_binary64`
213×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1310
1	393	1138
2	1413	964
3	4533	964

Stop Event

1×	node limit

Counts

122 → 99

prune114.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	162	9	171

Error

6.9b

Counts

171 → 9

Alt Table

Status	Error	Program
	52.0b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 im 2)) 3)))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	52.2b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (neg.f64 im) 2)) 3)))
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	52.0b	(.f64 1/2 (cbrt.f64 (.f64 (*.f64 (sqrt.f64 2) 2) (pow.f64 im 3/2))))
✓	13.6b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
▶	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	28.6b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)))

Compiler

Compiled 3891 to 2714 computations (30.2% saved)

localize7.0ms (0.2%)

prune4.0ms (0.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	3	3
Total	9	9

Error

6.9b

Counts

9 → 9

Alt Table

Status	Error	Program
	52.0b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 im 2)) 3)))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	52.2b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (neg.f64 im) 2)) 3)))
	56.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	52.0b	(.f64 1/2 (cbrt.f64 (.f64 (*.f64 (sqrt.f64 2) 2) (pow.f64 im 3/2))))
✓	13.6b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
✓	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	28.6b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 3)))

Compiler

Compiled 113 to 95 computations (15.9% saved)

regimes234.0ms (6.7%)

Accuracy

Total 3.9b remaining (40.4%)

Threshold costs 0b (0%)

Counts

28 → 2

Compiler

Compiled 2721 to 2211 computations (18.7% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(sqrt.f64 (*.f64 2 (+.f64 (sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im))) re)))

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	1.9961721129825474e-145	]

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	38	58

Stop Event

1×

saturated

end121.0ms (3.5%)

Stop Event

1×

fuel

Compiler

Compiled 193 to 153 computations (20.7% saved)

Details

analyze561.0ms (16.1%)

sample1.7s (48.5%)

preprocess16.0ms (0.4%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series54.0ms (1.6%)

rewrite44.0ms (1.3%)

simplify41.0ms (1.2%)

prune94.0ms (2.7%)

localize7.0ms (0.2%)

series51.0ms (1.5%)

rewrite42.0ms (1.2%)

simplify32.0ms (0.9%)

prune111.0ms (3.2%)

localize8.0ms (0.2%)

series128.0ms (3.7%)

rewrite50.0ms (1.4%)

simplify49.0ms (1.4%)

prune114.0ms (3.3%)

localize7.0ms (0.2%)

prune4.0ms (0.1%)

regimes234.0ms (6.7%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end121.0ms (3.5%)

Profiling