Details

analyze1.8s (36.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.8s (36.8%)

Results

810.0ms	6288×	body	128	valid
353.0ms	555×	body	4096	valid
332.0ms	645×	body	2048	valid
168.0ms	422×	body	1024	valid
67.0ms	215×	body	512	valid
27.0ms	131×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify7.0ms (0.1%)

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

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

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	1.7b	(+.f64 re (hypot.f64 re im))

series25.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(+.f64 re (hypot.f64 re im))
11.0ms	(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)

simplify74.0ms (1.5%)

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

prune62.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Error

9.0b

Counts

88 → 5

Alt Table

Status	Error	Program
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (.f64 (/.f64 (.f64 im im) re) -1/2)))))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 1841 to 1253 computations (31.9% saved)

localize4.0ms (0.1%)

prune5.0ms (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

9.0b

Counts

5 → 5

Alt Table

Status	Error	Program
▶	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (.f64 (/.f64 (.f64 im im) re) -1/2)))))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 147 to 119 computations (19% saved)

localize4.0ms (0.1%)

prune5.0ms (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

9.0b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	48.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (.f64 (/.f64 (.f64 im im) re) -1/2)))))))
▶	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 139 to 112 computations (19.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	0.0b	(.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
✓	7.6b	(/.f64 (pow.f64 im 2) re)
✓	20.3b	(sqrt.f64 (.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))

series64.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

23.0ms	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
16.0ms	(sqrt.f64 (.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re))))
12.0ms	(.f64 2 (.f64 -1/2 (/.f64 (pow.f64 im 2) re)))
12.0ms	(/.f64 (pow.f64 im 2) re)

rewrite30.0ms (0.6%)

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)))))
8.0ms	(.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))))
3.0ms	(/.f64 (pow.f64 im 2) re)

simplify126.0ms (2.6%)

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

prune112.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	5	178
Fresh	0	1	1
Picked	1	0	1
Done	2	1	3
Total	176	7	183

Error

0.0b

Counts

183 → 7

Alt Table

Status	Error	Program
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 1 (/.f64 re (pow.f64 im 2)))))))
	57.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 5/128 (/.f64 (pow.f64 im 8) (pow.f64 re 7)) (fma.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16 (.f64 (/.f64 (.f64 im im) re) -1/2)))))))
	53.2b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 -1 re)) im))
✓	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 im (/.f64 re im))))))
	51.5b	(.f64 -1/2 (.f64 im (sqrt.f64 (/.f64 -1 re))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 -1/2 (.f64 im (/.f64 im re))))))

Compiler

Compiled 3293 to 2286 computations (30.6% saved)

regimes620.0ms (12.8%)

Accuracy

Total 10.9b remaining (98.6%)

Threshold costs 0b (0%)

Counts

62 → 2

Compiler

Compiled 7726 to 6028 computations (22% saved)

bsearch41.0ms (0.8%)

Steps

Iters	Range		Point
8	-0.0001842406890998269	-3.544636178674044e-8	-0.00017542879764735815

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	27	39
2	27	39

end109.0ms (2.2%)

Compiler: Compiled 173 to 135 computations (22% saved)

Details

analyze1.8s (36.2%)

sample1.8s (36.8%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series25.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify74.0ms (1.5%)

prune62.0ms (1.3%)

localize4.0ms (0.1%)

prune5.0ms (0.1%)

localize4.0ms (0.1%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

series64.0ms (1.3%)

rewrite30.0ms (0.6%)

simplify126.0ms (2.6%)

prune112.0ms (2.3%)

regimes620.0ms (12.8%)

bsearch41.0ms (0.8%)

simplify3.0ms (0.1%)

end109.0ms (2.2%)

Profiling