Details

analyze662.0ms (11%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample27.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

prune3.0ms (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

23.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.8b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
▶	23.8b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

Compiler

Compiled 104 to 54 computations (48.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	23.3b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

series100.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

90.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
9.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
0.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-def_binary64`
413×	`associate-/l/_binary64`
364×	`fma-neg_binary64`
246×	`distribute-rgt-neg-in_binary64`
245×	`distribute-lft-neg-in_binary64`

Counts

135 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	2544
1	202	2411
2	606	2327
3	2192	2279
4	5101	2279

prune79.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Error

2.1b

Counts

97 → 9

Alt Table

Status	Error	Program
	23.7b	(/.f64 (/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (sqrt.f64 (fma.f64 y.re y.re (.f64 y.im y.im)))) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
	36.8b	(/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (.f64 y.re y.re)))
▶	15.7b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))
	37.4b	(/.f64 x.re y.re)
	35.8b	(+.f64 (/.f64 x.im y.im) (.f64 (/.f64 y.re (.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
	37.6b	(.f64 (/.f64 (sqrt.f64 (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
	37.5b	(/.f64 x.im y.im)
	16.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 y.im x.im (.f64 y.re x.re))) (cbrt.f64 (fma.f64 y.im x.im (.f64 y.re x.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
	21.0b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))

Compiler

Compiled 2346 to 514 computations (78.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y.im y.re)
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))
✓	0.5b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	14.8b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series240.0ms (4%)

Counts

4 → 168

Calls

4 calls:

112.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))
105.0ms	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
13.0ms	(hypot.f64 y.im y.re)
9.0ms	(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))
2.0ms	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
0.0ms	(fma.f64 y.im x.im (*.f64 y.re x.re))
0.0ms	(hypot.f64 y.im y.re)

simplify148.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

868×	`times-frac_binary64`
516×	`fma-neg_binary64`
377×	`fma-def_binary64`
306×	`cancel-sign-sub-inv_binary64`
282×	`distribute-rgt-in_binary64`

Counts

275 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	5947
1	619	5325
2	2094	5152
3	4840	5152
4	5143	5152

prune277.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	300	5	305
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	307	7	314

Error

0.1b

Counts

314 → 7

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	23.8b	(/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
	42.8b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
▶	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
	21.0b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))

Compiler

Compiled 7837 to 2421 computations (69.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
✓	0.3b	(/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
✓	14.8b	(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series561.0ms (9.3%)

Counts

4 → 136

Calls

4 calls:

245.0ms	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
180.0ms	(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
112.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
23.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))

rewrite102.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

368×	`times-frac_binary64`
276×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`
186×	`add-cube-cbrt_binary64`
122×	`sqrt-prod_binary64`

Counts

4 → 351

Calls

4 calls:

32.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
7.0ms	(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
3.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))
2.0ms	(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

simplify448.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
302×	`associate-/l*_binary64`
301×	`associate-*l/_binary64`
294×	`associate-r_binary64`
290×	`associate-/l/_binary64`

Counts

487 → 576

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	18201
1	1263	15336
2	4062	15143
3	4966	15143
4	4996	15143
5	4957	15143

prune332.0ms (5.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	576	0	576
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	576	7	583

Error

0.1b

Counts

583 → 7

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
	23.8b	(/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
	42.8b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
✓	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
▶	21.0b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))

Compiler

Compiled 20947 to 4512 computations (78.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.im y.im (*.f64 y.re y.re))
✓	1.3b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
✓	16.2b	(/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (.f64 y.re y.re)))
✓	16.4b	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))

series254.0ms (4.2%)

Counts

4 → 132

Calls

4 calls:

147.0ms	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
80.0ms	(/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (.f64 y.re y.re)))
20.0ms	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))
7.0ms	(fma.f64 y.im y.im (*.f64 y.re y.re))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 72

Calls

4 calls:

3.0ms	(/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (.f64 y.re y.re)))
2.0ms	(/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re)))
0.0ms	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
0.0ms	(fma.f64 y.im y.im (*.f64 y.re y.re))

simplify125.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l*_binary64`
792×	`times-frac_binary64`
348×	`fma-neg_binary64`
266×	`associate-/l/_binary64`
249×	`associate-/r/_binary64`

Counts

204 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	4352
1	420	4073
2	1367	3968
3	4690	3968
4	4966	3968

prune113.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	165	7	172

Error

0.0b

Counts

172 → 7

Alt Table

Status	Error	Program
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	23.8b	(+.f64 (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (.f64 y.re y.re))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (.f64 y.re y.re))))
	33.2b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
✓	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
	9.9b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (.f64 y.re y.re))) (.f64 (/.f64 y.re (hypot.f64 y.im y.re)) (/.f64 x.re (hypot.f64 y.im y.re))))
	21.0b	(fma.f64 x.im (.f64 y.im (/.f64 1 (fma.f64 y.im y.im (.f64 y.re y.re)))) (/.f64 (.f64 y.re x.re) (fma.f64 y.im y.im (.f64 y.re y.re))))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)))

Compiler

Compiled 4445 to 986 computations (77.8% saved)

regimes1.4s (24%)

Accuracy

Total 6.3b remaining (99%)

Threshold costs 0b (0%)

Counts

137 → 3

Compiler

Compiled 14603 to 7954 computations (45.5% saved)

bsearch28.0ms (0.5%)

Steps

Iters	Range		Point
8	1.9798221448362845e+146	9.863307307441638e+148	9.773934898556053e+148
3	-2.0632768866689627e+102	-1.5579177129281398e+102	-2.0316919383101615e+102

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	75
1	38	75
2	45	73
3	53	73
4	56	73
5	57	73
6	55	73

end1.0ms (0%)

Compiler: Compiled 55 to 26 computations (52.7% saved)

sample896.0ms (14.9%)

Algorithm

1×

intervals

Results

422.0ms	8000×	body	128	valid
30.0ms	477×	body	128	invalid

Compiler

Compiled 229 to 117 computations (48.9% saved)

Details

analyze662.0ms (11%)

sample27.0ms (0.4%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series100.0ms (1.7%)

rewrite6.0ms (0.1%)

simplify80.0ms (1.3%)

prune79.0ms (1.3%)

localize9.0ms (0.2%)

series240.0ms (4%)

rewrite21.0ms (0.3%)

simplify148.0ms (2.5%)

prune277.0ms (4.6%)

localize11.0ms (0.2%)

series561.0ms (9.3%)

rewrite102.0ms (1.7%)

simplify448.0ms (7.5%)

prune332.0ms (5.5%)

localize10.0ms (0.2%)

series254.0ms (4.2%)

rewrite11.0ms (0.2%)

simplify125.0ms (2.1%)

prune113.0ms (1.9%)

regimes1.4s (24%)

bsearch28.0ms (0.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample896.0ms (14.9%)

Profiling