Details

analyze732.0ms (7.8%)

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)

sample1.3s (13.6%)

Results

1.2s	8256×	body	128	valid
63.0ms	489×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (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%)

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

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(/.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 66 to 32 computations (51.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.2b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	26.3b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))

series95.0ms (1%)

Counts

3 → 120

Calls

3 calls:

80.0ms	(/.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))
6.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

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

simplify86.0ms (0.9%)

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

169 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2836
1	205	2674
2	613	2590
3	2201	2542
4	5123	2542

prune95.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	9	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Error

2.1b

Counts

120 → 9

Alt Table

Status	Error	Program
	37.4b	(/.f64 x.im y.im)
	19.5b	(.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)))
▶	18.9b	(.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)))
	38.5b	(/.f64 x.re y.re)
	38.0b	(-.f64 (fma.f64 y.re (/.f64 x.re (.f64 y.im y.im)) (/.f64 x.im y.im)) (.f64 (/.f64 (*.f64 y.re y.re) (pow.f64 y.im 3)) (+.f64 x.im (/.f64 x.re (/.f64 y.im 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))))
	26.6b	(/.f64 (/.f64 (fma.f64 y.im x.im (.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (.f64 y.im y.im))))
	27.1b	(/.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im)))) (/.f64 (fma.f64 y.re y.re (.f64 y.im y.im)) (cbrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)))))
	26.0b	(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 2769 to 604 computations (78.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (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))
✓	17.8b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series228.0ms (2.4%)

Counts

4 → 168

Calls

4 calls:

103.0ms	(.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)))
97.0ms	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
19.0ms	(/.f64 1 (hypot.f64 y.im y.re))
9.0ms	(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 130

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 1 (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))

simplify161.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

872×	`times-frac_binary64`
508×	`fma-neg_binary64`
381×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
274×	`distribute-rgt-in_binary64`

Counts

298 → 285

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	6511
1	629	5720
2	2135	5547
3	4879	5539
4	5183	5539

prune202.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	278	7	285
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	285	9	294

Error

0.0b

Counts

294 → 9

Alt Table

Status	Error	Program
	45.3b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
	19.5b	(.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)))
	26.0b	(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))))
	26.9b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
▶	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.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))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	38.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (/.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	31.9b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))

Compiler

Compiled 7458 to 2237 computations (70% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.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)))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.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))
	17.8b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series368.0ms (3.9%)

Counts

2 → 80

Calls

2 calls:

247.0ms

(*.f64 (sqrt.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)))

121.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
32×	`sqrt-prod_binary64`
32×	`associate-l_binary64`
27×	`*-un-lft-identity_binary64`

Counts

2 → 97

Calls

2 calls:

11.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))

9.0ms

(*.f64 (sqrt.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)))

simplify154.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
313×	`fma-def_binary64`
291×	`cancel-sign-sub-inv_binary64`
236×	`associate-r_binary64`
208×	`distribute-rgt-in_binary64`

Counts

177 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	6085
1	534	5171
2	1893	5061
3	4563	5061
4	5001	5061

prune223.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	306	9	315

Error

0.0b

Counts

315 → 9

Alt Table

Status	Error	Program
	26.0b	(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))))
	26.9b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
✓	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.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))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	45.4b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im))))
▶	19.5b	(.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)))
	38.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (/.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	31.9b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))

Compiler

Compiled 10268 to 3995 computations (61.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.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))))
	0.5b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	5.8b	(/.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))
✓	18.3b	(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

series340.0ms (3.6%)

Counts

3 → 144

Calls

3 calls:

160.0ms

(/.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))

108.0ms

(*.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))))

72.0ms

(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms

(*.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))))

4.0ms

(/.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))

1.0ms

(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

simplify195.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

873×	`associate-/l*_binary64`
508×	`fma-def_binary64`
330×	`*-commutative_binary64`
279×	`cancel-sign-sub-inv_binary64`
178×	`sub-neg_binary64`

Counts

222 → 377

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	829	13980
1	2878	12671
2	5673	12671

prune551.0ms (5.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	638	0	638
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	638	9	647

Error

0.0b

Counts

647 → 9

Alt Table

Status	Error	Program
	26.0b	(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))))
	26.9b	(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (.f64 y.re y.re))) y.re (/.f64 (.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
✓	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.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))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
	45.4b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im))))
✓	19.5b	(.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)))
	38.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (/.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	31.2b	(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
	31.9b	(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))

Compiler

Compiled 38003 to 15044 computations (60.4% saved)

regimes4.3s (45.6%)

Accuracy

Total 9.8b remaining (98.6%)

Threshold costs 0b (0%)

Counts

204 → 5

Compiler

Compiled 22193 to 12284 computations (44.6% saved)

bsearch102.0ms (1.1%)

Steps

Iters	Range		Point
9	7.060439802304055e+93	7.718541126311962e+98	5.209498248710266e+98
7	1.2640662547794736e-100	1.6017282220243597e-98	1.544901258368836e-100
10	-1.7678441460080387e-125	-1.5461171796053897e-136	-1.0098211784491114e-135
9	-6.481809507013464e+133	-6.924095184360179e+127	-2.558733259505715e+128

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	38	117
1	49	117
2	56	115
3	63	115
4	66	115
5	67	115
6	65	115

end141.0ms (1.5%)

Compiler: Compiled 377 to 181 computations (52% saved)

Details

analyze732.0ms (7.8%)

sample1.3s (13.6%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series95.0ms (1%)

rewrite5.0ms (0.1%)

simplify86.0ms (0.9%)

prune95.0ms (1%)

localize9.0ms (0.1%)

series228.0ms (2.4%)

rewrite22.0ms (0.2%)

simplify161.0ms (1.7%)

prune202.0ms (2.2%)

localize11.0ms (0.1%)

series368.0ms (3.9%)

rewrite31.0ms (0.3%)

simplify154.0ms (1.6%)

prune223.0ms (2.4%)

localize13.0ms (0.1%)

series340.0ms (3.6%)

rewrite18.0ms (0.2%)

simplify195.0ms (2.1%)

prune551.0ms (5.9%)

regimes4.3s (45.6%)

bsearch102.0ms (1.1%)

simplify5.0ms (0.1%)

end141.0ms (1.5%)

Profiling