Details

analyze448.0ms (15.3%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.7s (56.7%)

Results

742.0ms	6266×	body	128	valid
338.0ms	693×	body	2048	valid
292.0ms	499×	body	4096	valid
173.0ms	444×	body	1024	valid
70.0ms	238×	body	512	valid
24.0ms	116×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess17.0ms (0.6%)

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)

simplify7.0ms (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

13.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series49.0ms (1.7%)

Counts

3 → 56

Calls

18 calls:

7.0ms	(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))))	re	-inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	-inf
3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	re	inf

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`log1p-expm1-u_binary64`
844×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
88×	`pow1_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	178	23
2	2361	23

Stop Event

1×	node limit

Counts

3 → 79

simplify37.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
410×	`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

prune88.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Error

7.2b

Counts

152 → 5

Alt Table

Status	Error	Program
	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	56.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	47.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 3070 to 2075 computations (32.4% saved)

localize4.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

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

Error

7.2b

Counts

5 → 5

Alt Table

Status	Error	Program
▶	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	56.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	47.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 94 to 78 computations (17% saved)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

7.2b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	56.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	47.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 85 to 70 computations (17.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 im re) im)
✓	0.2b	(.f64 (.f64 (/.f64 im re) im) -1/2)
✓	0.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	18.4b	(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 im re) im) -1/2)))

series53.0ms (1.8%)

Counts

4 → 72

Calls

24 calls:

5.0ms	(*.f64 (/.f64 im re) im)	im	-inf
3.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))	im	-inf
3.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))	re	inf
3.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))	re	0
2.0ms	(sqrt.f64 (.f64 2 (.f64 (*.f64 (/.f64 im re) im) -1/2)))	re	inf

rewrite53.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`log-prod_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
176×	`log-pow_binary64`
121×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	251	44
2	2985	44

Stop Event

1×	node limit

Counts

4 → 94

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

304×	`*-commutative_binary64`
303×	`fma-neg_binary64`
281×	`associate-l_binary64`
259×	`associate-*l/_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	668
1	35	668
2	74	668
3	143	668
4	365	668
5	1210	668
6	2497	668
7	3678	668
8	4206	668

Stop Event

1×	node limit

Counts

166 → 105

prune46.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	1	0	1
Picked	0	1	1
Done	2	1	3
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
✓	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	57.3b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 -1 re)) im))
	53.1b	(.f64 -1/2 (.f64 im (sqrt.f64 (/.f64 -1 re))))
	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (*.f64 im -1/2) (/.f64 re im)))))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	56.2b	(.f64 1/2 (pow.f64 (.f64 (/.f64 (*.f64 im im) re) -1) 1/2))

Compiler

Compiled 1640 to 1042 computations (36.5% saved)

regimes242.0ms (8.3%)

Accuracy

Total 10.4b remaining (98.2%)

Threshold costs 0b (0%)

Counts

23 → 2

Compiler

Compiled 2188 to 1722 computations (21.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

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

Steps

Iters	Point		Range
0.0	∈ [	0.0	,	1.4036192788020722e-241	]

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	47
1	32	47

Stop Event

1×

saturated

end84.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 139 to 103 computations (25.9% saved)

Details

analyze448.0ms (15.3%)

sample1.7s (56.7%)

preprocess17.0ms (0.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series49.0ms (1.7%)

rewrite47.0ms (1.6%)

simplify37.0ms (1.3%)

prune88.0ms (3%)

localize4.0ms (0.1%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series53.0ms (1.8%)

rewrite53.0ms (1.8%)

simplify57.0ms (1.9%)

prune46.0ms (1.6%)

regimes242.0ms (8.3%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end84.0ms (2.9%)

Profiling