Details

analyze446.0ms (14%)

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 (53.5%)

Results

779.0ms	6336×	body	128	valid
347.0ms	552×	body	4096	valid
310.0ms	630×	body	2048	valid
169.0ms	417×	body	1024	valid
67.0ms	230×	body	512	valid
18.0ms	91×	body	256	valid

Compiler

Compiled 36 to 26 computations (27.8% saved)

preprocess16.0ms (0.5%)

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

prune4.0ms (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

12.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.5b	(+.f64 re (hypot.f64 re im))

series42.0ms (1.3%)

Counts

2 → 32

Calls

12 calls:

7.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	inf
7.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	0
6.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	re	-inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	re	inf
5.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))	im	-inf

rewrite41.0ms (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	19
1	178	19
2	2341	19

Stop Event

1×	node limit

Counts

2 → 60

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
387×	`associate-r_binary64`
306×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`
223×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	860
1	345	810
2	1133	762

Stop Event

1×	node limit

Counts

92 → 105

prune68.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	5	106

Error

6.1b

Counts

106 → 5

Alt Table

Status	Error	Program
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
▶	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 2179 to 1465 computations (32.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.4b	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)
	0.5b	(+.f64 re (hypot.f64 re im))

series90.0ms (2.8%)

Counts

3 → 24

Calls

18 calls:

10.0ms	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)	re	inf
7.0ms	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)	im	inf
7.0ms	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))	im	-inf
7.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))	im	0
7.0ms	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))	im	0

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`egg-rr`
91×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	215	28
2	2425	28

Stop Event

1×	node limit

Counts

3 → 92

simplify32.0ms (1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
413×	`times-frac_binary64`
395×	`associate-l_binary64`
389×	`associate-/l*_binary64`
361×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	957
1	419	866
2	1447	795

Stop Event

1×	node limit

Counts

116 → 136

prune123.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	200	6	206

Error

6.1b

Counts

206 → 6

Alt Table

Status	Error	Program
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))

Compiler

Compiled 4443 to 2942 computations (33.8% saved)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

6.1b

Counts

6 → 6

Alt Table

Status	Error	Program
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))

Compiler

Compiled 103 to 86 computations (16.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.3%)

Counts

1 → 0

Calls

3 calls:

6.0ms	(pow.f64 (sqrt.f64 im) 2)	im	0
2.0ms	(pow.f64 (sqrt.f64 im) 2)	im	inf
2.0ms	(pow.f64 (sqrt.f64 im) 2)	im	-inf

rewrite27.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

302×	`log1p-expm1-u_binary64`
302×	`expm1-log1p-u_binary64`
272×	`add-cbrt-cube_binary64`
266×	`add-log-exp_binary64`
265×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	103	1
2	893	1

Stop Event

1×	node limit

Counts

1 → 28

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

28 → 28

prune18.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	2	2
Picked	1	0	1
Done	1	2	3
Total	28	6	34

Error

6.1b

Counts

34 → 6

Alt Table

Status	Error	Program
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (/.f64 im re) im) -1/2))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
✓	12.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (*.f64 (log.f64 (cbrt.f64 im)) 3)))))
	46.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 im 5/6) (pow.f64 im 1/6)))))

Compiler

Compiled 397 to 312 computations (21.4% saved)

regimes279.0ms (8.8%)

Accuracy

Total 4.7b remaining (44.8%)

Threshold costs 0b (0%)

Counts

32 → 2

Compiler

Compiled 3116 to 2557 computations (17.9% saved)

bsearch81.0ms (2.5%)

Algorithm

1×	binary-search

Calls

1 calls:

80.0ms

re

Steps

Iters	Point		Range
-1.4619441467110438e+169	∈ [	-5.9481663784466175e+190	,	-8.605072274841426e+168	]

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

end89.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 133 to 106 computations (20.3% saved)

Details

analyze446.0ms (14%)

sample1.7s (53.5%)

preprocess16.0ms (0.5%)

simplify7.0ms (0.2%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series42.0ms (1.3%)

rewrite41.0ms (1.3%)

simplify28.0ms (0.9%)

prune68.0ms (2.1%)

localize8.0ms (0.2%)

series90.0ms (2.8%)

rewrite46.0ms (1.4%)

simplify32.0ms (1%)

prune123.0ms (3.9%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite27.0ms (0.9%)

simplify6.0ms (0.2%)

prune18.0ms (0.6%)

regimes279.0ms (8.8%)

bsearch81.0ms (2.5%)

simplify2.0ms (0.1%)

end89.0ms (2.8%)

Profiling