Details

analyze463.0ms (11.9%)

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)

sample2.3s (60.1%)

Results

1.3s	6146×	body	128	valid
349.0ms	714×	body	2048	valid
337.0ms	541×	body	4096	valid
194.0ms	474×	body	1024	valid
76.0ms	260×	body	512	valid
24.0ms	121×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% 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

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

11.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	39.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	11.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 85 to 61 computations (28.2% 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)
✓	0.8b	(+.f64 re (hypot.f64 re im))

series45.0ms (1.1%)

Counts

3 → 56

Calls

3 calls:

26.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
10.0ms	(hypot.f64 re im)
8.0ms	(+.f64 re (hypot.f64 re im))

rewrite45.0ms (1.1%)

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

Calls

3 calls:

44.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
43.0ms	(hypot.f64 re im)
43.0ms	(+.f64 re (hypot.f64 re im))

simplify34.0ms (0.9%)

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

prune95.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	146	7	153

Error

4.5b

Counts

153 → 7

Alt Table

Status	Error	Program
▶	39.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	43.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	43.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	11.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 3122 to 2115 computations (32.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 re re) (.f64 im im))
✓	0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
✓	0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
✓	31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series51.0ms (1.3%)

Counts

4 → 80

Calls

4 calls:

27.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

540×	`fma-def_binary64`
265×	`fma-neg_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
161×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	246	30
2	3342	30

Stop Event

1×	node limit

Counts

4 → 161

Calls

4 calls:

51.0ms	(+.f64 (.f64 re re) (.f64 im im))
51.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
51.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
51.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
410×	`associate-r_binary64`
334×	`associate-l_binary64`
287×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1552
1	418	1448
2	1367	1384

Stop Event

1×	node limit

Counts

241 → 238

prune132.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Error

4.5b

Counts

245 → 7

Alt Table

Status	Error	Program
✓	39.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	43.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	43.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	11.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 4725 to 3144 computations (33.5% saved)

localize4.0ms (0.1%)

prune5.0ms (0.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Error

4.5b

Counts

7 → 7

Alt Table

Status	Error	Program
✓	39.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	43.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	43.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	11.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 129 to 106 computations (17.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

series6.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite29.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`log1p-expm1-u_binary64`
450×	`expm1-log1p-u_binary64`
351×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`
158×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	121	6
2	1299	6

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

29.0ms

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

17 → 17

prune12.0ms (0.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	3	3
Picked	0	1	1
Done	1	2	3
Total	16	8	24

Error

4.5b

Counts

24 → 8

Alt Table

Status	Error	Program
✓	39.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	52.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
	43.1b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 2 im) 1/4) 2))
✓	43.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	44.5b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 im)))))
✓	11.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 260 to 224 computations (13.8% saved)

regimes322.0ms (8.3%)

Accuracy

Total 5.9b remaining (50.1%)

Threshold costs 0b (0%)

Counts

36 → 2

Compiler

Compiled 3438 to 2791 computations (18.8% saved)

bsearch67.0ms (1.7%)

Steps

Iters	Range		Point
9	-8.328351343210212e+171	-6.001052788937208e+166	-7.671150916840835e+166

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	28	39

Stop Event

1×

saturated

end109.0ms (2.8%)

Compiler: Compiled 152 to 121 computations (20.4% saved)

Details

analyze463.0ms (11.9%)

sample2.3s (60.1%)

simplify7.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series45.0ms (1.1%)

rewrite45.0ms (1.1%)

simplify34.0ms (0.9%)

prune95.0ms (2.4%)

localize9.0ms (0.2%)

series51.0ms (1.3%)

rewrite54.0ms (1.4%)

simplify42.0ms (1.1%)

prune132.0ms (3.4%)

localize4.0ms (0.1%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite29.0ms (0.8%)

simplify6.0ms (0.1%)

prune12.0ms (0.3%)

regimes322.0ms (8.3%)

bsearch67.0ms (1.7%)

simplify2.0ms (0.1%)

end109.0ms (2.8%)

Profiling