Details

analyze715.0ms (12.8%)

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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify9.0ms (0.2%)

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	14	26
1	20	26
2	24	26
3	24	26

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

25.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.9b	(/.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)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y.re y.re (*.f64 y.im y.im))
✓	0.5b	(fma.f64 x.re y.re (*.f64 x.im y.im))
✓	25.4b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (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 x.re y.re (*.f64 x.im y.im))
0.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

series146.0ms (2.6%)

Counts

3 → 120

Calls

3 calls:

93.0ms	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
33.0ms	(fma.f64 x.re y.re (*.f64 x.im y.im))
19.0ms	(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify134.0ms (2.4%)

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 → 314

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	3814
1	207	3601
2	615	3517
3	2203	3469
4	5125	3469

prune78.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	307	7	314
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	307	8	315

Error

1.9b

Counts

315 → 8

Alt Table

Status	Error	Program
✓	25.9b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	24.1b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	37.5b	(/.f64 x.re y.re)
	45.3b	(/.f64 (sqrt.f64 (fma.f64 x.re y.re (.f64 x.im y.im))) (/.f64 (fma.f64 y.re y.re (.f64 y.im y.im)) (sqrt.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)))))
	39.0b	(/.f64 x.im y.im)
▶	15.9b	(.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)))
	40.9b	(/.f64 (.f64 y.im x.im) (fma.f64 y.re y.re (.f64 y.im y.im)))
	34.7b	(fma.f64 x.im (/.f64 y.im (pow.f64 y.re 2)) (/.f64 x.re y.re))

Compiler

Compiled 2591 to 726 computations (72% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 y.im y.re))
✓	0.3b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	0.3b	(.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)))
✓	14.8b	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

rewrite22.0ms (0.4%)

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:

10.0ms	(.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))
2.0ms	(/.f64 1 (hypot.f64 y.im y.re))
0.0ms	(fma.f64 y.im x.im (*.f64 y.re x.re))

series295.0ms (5.3%)

Counts

4 → 168

Calls

4 calls:

121.0ms	(.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)))
119.0ms	(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
32.0ms	(fma.f64 y.im x.im (*.f64 y.re x.re))
23.0ms	(/.f64 1 (hypot.f64 y.im y.re))

simplify241.0ms (4.3%)

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 → 545

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	8379
1	631	7498
2	2137	7307
3	4881	7299
4	5185	7299

prune204.0ms (3.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	537	8	545
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	541	12	553

Error

0.0b

Counts

553 → 12

Alt Table

Status	Error	Program
	16.6b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im)))) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	50.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 -1/2 (fma.f64 (/.f64 (pow.f64 y.im 3) (pow.f64 y.re 3)) x.im (/.f64 (.f64 x.re (pow.f64 y.im 2)) (pow.f64 y.re 2))) (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	25.9b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	24.1b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	47.3b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (+.f64 x.re (/.f64 (.f64 y.im x.im) y.re)))
✓	15.9b	(.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)))
	34.7b	(fma.f64 (/.f64 x.re (pow.f64 y.im 2)) y.re (/.f64 x.im y.im))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
	45.4b	(*.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 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))
	45.0b	(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
	34.7b	(fma.f64 x.im (/.f64 y.im (pow.f64 y.re 2)) (/.f64 x.re y.re))

Compiler

Compiled 7485 to 2414 computations (67.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (hypot.f64 y.im y.re))
✓	0.1b	(/.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))
	0.3b	(fma.f64 y.im x.im (*.f64 y.re x.re))
✓	14.9b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

2 → 67

Calls

2 calls:

5.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re)))
5.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))

series211.0ms (3.8%)

Counts

2 → 96

Calls

2 calls:

106.0ms	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re)))
105.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))

simplify197.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-/r*_binary64`
413×	`fma-neg_binary64`
396×	`associate-/l/_binary64`
377×	`associate-*l/_binary64`
272×	`associate-/r/_binary64`

Counts

163 → 309

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	167	5481
1	449	4692
2	1583	4506
3	4315	4506
4	4789	4494
5	4977	4494

prune164.0ms (2.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	500	4	504
Fresh	6	3	9
Picked	0	1	1
Done	0	2	2
Total	506	10	516

Error

0.0b

Counts

516 → 10

Alt Table

Status	Error	Program
▶	16.6b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im)))) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	50.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 -1/2 (fma.f64 (/.f64 (pow.f64 y.im 3) (pow.f64 y.re 3)) x.im (/.f64 (.f64 x.re (pow.f64 y.im 2)) (pow.f64 y.re 2))) (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	25.9b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	24.1b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	45.3b	(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
✓	15.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))
	45.0b	(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
	46.8b	(/.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re) (hypot.f64 y.im y.re))
✓	15.9b	(.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)))
	42.8b	(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))

Compiler

Compiled 6018 to 2226 computations (63% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im)))) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im))) (hypot.f64 y.im y.re)))
	15.4b	(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))
	15.4b	(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))
✓	15.4b	(cbrt.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`associate-r_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

11.0ms

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

1.0ms

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

series227.0ms (4.1%)

Counts

2 → 96

Calls

2 calls:

160.0ms

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

67.0ms

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

simplify146.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
444×	`associate-r_binary64`
375×	`associate-/l*_binary64`
339×	`associate-l_binary64`
318×	`associate-/r*_binary64`

Counts

156 → 274

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	387	7721
1	1304	7054
2	5252	7054

prune326.0ms (5.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	595	0	595
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	595	10	605

Error

0.0b

Counts

605 → 10

Alt Table

Status	Error	Program
✓	16.6b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (.f64 (.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im)))) (/.f64 (cbrt.f64 (fma.f64 x.re y.re (.f64 y.im x.im))) (hypot.f64 y.im y.re))))
	50.0b	(.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 -1/2 (fma.f64 (/.f64 (pow.f64 y.im 3) (pow.f64 y.re 3)) x.im (/.f64 (.f64 x.re (pow.f64 y.im 2)) (pow.f64 y.re 2))) (fma.f64 (/.f64 y.im y.re) x.im x.re)))
✓	25.9b	(/.f64 (fma.f64 x.re y.re (.f64 x.im y.im)) (fma.f64 y.re y.re (.f64 y.im y.im)))
	24.1b	(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (pow.f64 y.re 2))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (pow.f64 y.re 2))))
	45.3b	(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
✓	15.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (.f64 y.re x.re))) (hypot.f64 y.im y.re))
	45.0b	(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
	46.8b	(/.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re) (hypot.f64 y.im y.re))
✓	15.9b	(.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)))
	42.8b	(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))

Compiler

Compiled 21750 to 9030 computations (58.5% saved)

regimes1.2s (21.1%)

Accuracy

Total 10.7b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7573 to 4469 computations (41% saved)

bsearch113.0ms (2%)

Steps

Iters	Range		Point
9	1.430864073055698e+132	1.716731880528953e+140	5.106771931752182e+135
10	-8.183394120266732e+178	-7.121536022167132e+168	-7.183038243223042e+168

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	84
1	30	84
2	34	84
3	37	84
4	38	84
5	38	84

end1.0ms (0%)

Compiler: Compiled 47 to 20 computations (57.4% saved)

sample1.1s (19.1%)

Algorithm

1×

intervals

Results

583.0ms	8000×	body	128	valid
25.0ms	486×	body	128	invalid

Compiler

Compiled 283 to 153 computations (45.9% saved)

Details

analyze715.0ms (12.8%)

sample26.0ms (0.5%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

rewrite5.0ms (0.1%)

series146.0ms (2.6%)

simplify134.0ms (2.4%)

prune78.0ms (1.4%)

localize9.0ms (0.2%)

rewrite22.0ms (0.4%)

series295.0ms (5.3%)

simplify241.0ms (4.3%)

prune204.0ms (3.6%)

localize11.0ms (0.2%)

rewrite15.0ms (0.3%)

series211.0ms (3.8%)

simplify197.0ms (3.5%)

prune164.0ms (2.9%)

localize13.0ms (0.2%)

rewrite16.0ms (0.3%)

series227.0ms (4.1%)

simplify146.0ms (2.6%)

prune326.0ms (5.8%)

regimes1.2s (21.1%)

bsearch113.0ms (2%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.1s (19.1%)

Profiling