Details

analyze468.0ms (13.3%)

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)

sample1.8s (52.1%)

Results

819.0ms	6230×	body	128	valid
367.0ms	582×	body	4096	valid
342.0ms	634×	body	2048	valid
172.0ms	425×	body	1024	valid
83.0ms	265×	body	512	valid
26.0ms	120×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

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

12.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.0b	(.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 2 expressions with local error:

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

series21.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(+.f64 re (hypot.f64 re im))
9.0ms	(hypot.f64 re im)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

979×	`fma-neg_binary64`
303×	`fma-def_binary64`
267×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`
242×	`distribute-neg-frac_binary64`

Counts

75 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1182
1	320	1139
2	820	1115
3	3018	1115
4	4899	1115
5	5044	1115

prune54.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Error

6.7b

Counts

88 → 4

Alt Table

Status	Error	Program
▶	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 1759 to 1189 computations (32.4% saved)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

6.7b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 65 to 55 computations (15.4% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

6.7b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 57 to 48 computations (15.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
✓	0.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	5.9b	(/.f64 (pow.f64 im 2) re)
✓	17.8b	(sqrt.f64 (.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))

series55.0ms (1.6%)

Counts

4 → 48

Calls

4 calls:

19.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
13.0ms	(sqrt.f64 (.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))
12.0ms	(/.f64 (pow.f64 im 2) re)
11.0ms	(.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 113

Calls

4 calls:

8.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
7.0ms	(.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
5.0ms	(sqrt.f64 (.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))
5.0ms	(/.f64 (pow.f64 im 2) re)

simplify117.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-*l/_binary64`
415×	`associate-*r/_binary64`
307×	`unswap-sqr_binary64`
274×	`associate-/l*_binary64`
238×	`*-commutative_binary64`

Counts

161 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2147
1	312	1862
2	897	1861
3	3287	1861
4	4390	1861
5	4885	1861
6	4898	1861

prune97.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	0	0	0
Picked	0	1	1
Done	2	1	3
Total	177	5	182

Error

0.2b

Counts

182 → 5

Alt Table

Status	Error	Program
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.5b	(.f64 -1/2 (.f64 im (sqrt.f64 (/.f64 -1 re))))
✓	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	53.5b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 -1 re)) im))
	52.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 -1/2 (.f64 (/.f64 (pow.f64 (*.f64 (cbrt.f64 im) (cbrt.f64 im)) 2) 1) (/.f64 (pow.f64 (cbrt.f64 im) 2) re))))))

Compiler

Compiled 3247 to 2249 computations (30.7% saved)

regimes501.0ms (14.2%)

Accuracy

Total 12.0b remaining (98.2%)

Threshold costs 0b (0%)

Counts

44 → 4

Compiler

Compiled 5237 to 3983 computations (23.9% saved)

bsearch126.0ms (3.6%)

Steps

Iters	Range	Point
10	-5.105613356017411e+48	-2.3988213188738563e+35	-1.0966303163833297e+42
3	-3.190891745981019e+101	-2.365937419251058e+101	-2.719946185401384e+101
6	-3.7927732202685575e+193	-3.294839493150124e+192	-1.1586911918034763e+193

Iters

Range

Point

-5.105613356017411e+48

-2.3988213188738563e+35

-1.0966303163833297e+42

-3.190891745981019e+101

-2.365937419251058e+101

-2.719946185401384e+101

-3.7927732202685575e+193

-3.294839493150124e+192

-1.1586911918034763e+193

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	88
1	45	88
2	45	88

end96.0ms (2.7%)

Compiler: Compiled 191 to 140 computations (26.7% saved)

Details

analyze468.0ms (13.3%)

sample1.8s (52.1%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify75.0ms (2.1%)

prune54.0ms (1.5%)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series55.0ms (1.6%)

rewrite32.0ms (0.9%)

simplify117.0ms (3.3%)

prune97.0ms (2.8%)

regimes501.0ms (14.2%)

bsearch126.0ms (3.6%)

simplify3.0ms (0.1%)

end96.0ms (2.7%)

Profiling