Details

analyze514.0ms (13.4%)

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)

sample49.0ms (1.3%)

Algorithm

1×

intervals

Results

19.0ms	197×	body	128	valid
9.0ms	21×	body	2048	valid
5.0ms	13×	body	4096	valid
4.0ms	16×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify7.0ms (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

prune5.0ms (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

13.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	36.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize9.0ms (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)
✓	1.2b	(+.f64 re (hypot.f64 re im))

series79.0ms (2.1%)

Counts

3 → 56

Calls

3 calls:

51.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
15.0ms	(hypot.f64 re im)
14.0ms	(+.f64 re (hypot.f64 re im))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 42

Calls

3 calls:

4.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
3.0ms	(+.f64 re (hypot.f64 re im))
2.0ms	(hypot.f64 re im)

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
531×	`fma-neg_binary64`
460×	`associate-r_binary64`
385×	`associate-l_binary64`
294×	`cancel-sign-sub-inv_binary64`

Counts

98 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1829
1	514	1737
2	1465	1673
3	4990	1673
4	5308	1673

prune87.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	114	6	120

Error

6.6b

Counts

120 → 6

Alt Table

Status	Error	Program
	16.5b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
▶	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 2633 to 1800 computations (31.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
✓	9.0b	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

series82.0ms (2.1%)

Counts

3 → 56

Calls

3 calls:

53.0ms

(sqrt.f64 (*.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))

15.0ms

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

13.0ms

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

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
19×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

5.0ms

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

3.0ms

(sqrt.f64 (*.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))

2.0ms

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

simplify97.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-neg_binary64`
680×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
255×	`associate-/l*_binary64`
239×	`times-frac_binary64`

Counts

140 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2236
1	567	2078
2	1681	1994
3	4673	1994
4	5330	1994

prune166.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	259	6	265

Error

6.6b

Counts

265 → 6

Alt Table

Status	Error	Program
	16.5b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
▶	15.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 6309 to 3570 computations (43.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	0.6b	(cbrt.f64 re)
✓	15.0b	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

series111.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

40.0ms	(cbrt.f64 re)
40.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
30.0ms	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

7.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
1.0ms	(cbrt.f64 re)
1.0ms	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
474×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
393×	`distribute-neg-frac_binary64`
315×	`fma-def_binary64`

Counts

113 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1156
1	269	1039
2	864	983
3	3732	968
4	4770	956
5	4915	956

prune181.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	252	6	258

Error

6.6b

Counts

258 → 6

Alt Table

Status	Error	Program
	16.5b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 6633 to 2655 computations (60% saved)

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.6b	(cbrt.f64 re)
	15.0b	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

prune514.0ms (13.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	755	1	756
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	756	6	762

Error

6.6b

Counts

762 → 6

Alt Table

Status	Error	Program
	16.5b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 48854 to 8879 computations (81.8% saved)

regimes281.0ms (7.3%)

Accuracy

Total 4.3b remaining (36.2%)

Threshold costs 0b (0%)

Counts

22 → 2

Compiler

Compiled 3581 to 2029 computations (43.3% saved)

bsearch37.0ms (1%)

Steps

Iters	Range		Point
7	-4.2354348912974205e+144	-2.7453559540601653e+142	-5.435225094155723e+142

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

end1.0ms (0%)

Compiler: Compiled 28 to 22 computations (21.4% saved)

sample1.4s (35.6%)

Algorithm

1×

intervals

Results

417.0ms	6093×	body	128	valid
221.0ms	647×	body	2048	valid
216.0ms	522×	body	4096	valid
103.0ms	400×	body	1024	valid
48.0ms	225×	body	512	valid
14.0ms	113×	body	256	valid

Compiler

Compiled 207 to 102 computations (50.7% saved)

Details

analyze514.0ms (13.4%)

sample49.0ms (1.3%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

series79.0ms (2.1%)

rewrite10.0ms (0.3%)

simplify81.0ms (2.1%)

prune87.0ms (2.3%)

localize9.0ms (0.2%)

series82.0ms (2.1%)

rewrite16.0ms (0.4%)

simplify97.0ms (2.5%)

prune166.0ms (4.3%)

localize14.0ms (0.4%)

series111.0ms (2.9%)

rewrite11.0ms (0.3%)

simplify86.0ms (2.2%)

prune181.0ms (4.7%)

localize27.0ms (0.7%)

prune514.0ms (13.3%)

regimes281.0ms (7.3%)

bsearch37.0ms (1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.4s (35.6%)

Profiling