Details

analyze118.0ms (3.8%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample795.0ms (25.6%)

Results

708.0ms	8256×	body	128	valid
11.0ms	145×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify81.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-def_binary64`
506×	`rules-20_binary64`
347×	`fma-neg_binary64`
318×	`rules-33_binary64`
227×	`rules-4_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	18	8
2	46	8
3	132	8
4	329	8
5	1651	8
6	3989	8
7	4730	8
8	4936	8

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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.6b	(*.f64 x (fma.f64 y y 1))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 x (fma.f64 y y 1))

rewrite61.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`log1p-expm1-u_binary64`
495×	`expm1-log1p-u_binary64`
421×	`fma-neg_binary64`
258×	`log-prod_binary64`
243×	`fma-def_binary64`

Counts

1 → 137

Calls

1 calls:

58.0ms

(*.f64 x (fma.f64 y y 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	8
2	1487	8
3	4997	8
0	0	0
1	0	0

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

586×	`rules-5_binary64`
543×	`rules-15-rev_binary64`
297×	`rules-20_binary64`
279×	`fma-def_binary64`
211×	`rules-22-rev_binary64`

Counts

161 → 143

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	225
1	18	183
2	39	183
3	68	183
4	238	183
5	891	183
6	3190	183
7	5536	183

prune119.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)
✓	7.1b	(*.f64 x (fma.f64 y y 1))
	7.1b	(/.f64 x (/.f64 1 (fma.f64 y y 1)))
	8.2b	(fma.f64 (cbrt.f64 (.f64 x (fma.f64 y y 1))) (pow.f64 (cbrt.f64 (.f64 x (fma.f64 y y 1))) 2) 0)
	7.3b	(fma.f64 (cbrt.f64 (fma.f64 y y 1)) (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 y y 1)) 2)) 0)

Compiler

Compiled 2464 to 1542 computations (37.4% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 y)
✓	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.1b	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)

series50.0ms (1.6%)

Counts

3 → 60

Calls

3 calls:

29.0ms	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)
18.0ms	(*.f64 x (hypot.f64 1 y))
2.0ms	(hypot.f64 1 y)

rewrite79.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

591×	`log1p-expm1-u_binary64`
591×	`expm1-log1p-u_binary64`
502×	`fma-neg_binary64`
183×	`egg-rr`
160×	`prod-diff_binary64`

Counts

3 → 183

Calls

3 calls:

76.0ms	(hypot.f64 1 y)
76.0ms	(*.f64 x (hypot.f64 1 y))
76.0ms	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	169	21
2	1778	21
3	5062	21
0	0	0
1	0	0

simplify99.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

414×	`rules-21_binary64`
315×	`rules-4_binary64`
246×	`fma-neg_binary64`
242×	`rules-11_binary64`
196×	`fma-def_binary64`

Counts

243 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	701
1	231	632
2	871	624
3	4571	624
4	4908	624
5	5019	624

prune241.0ms (7.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	284	4	288
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	286	7	293

Error

Counts

293 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)
	0.4b	(fma.f64 (hypot.f64 1 y) (*.f64 x (pow.f64 (cbrt.f64 (hypot.f64 1 y)) 3)) 0)
	0.2b	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
▶	0.2b	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))
	30.6b	(.f64 (sqrt.f64 (.f64 (hypot.f64 1 y) x)) (.f64 (hypot.f64 1 y) (sqrt.f64 (.f64 (hypot.f64 1 y) x))))
	7.1b	(/.f64 x (/.f64 1 (fma.f64 y y 1)))
	7.3b	(fma.f64 (cbrt.f64 (fma.f64 y y 1)) (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 y y 1)) 2)) 0)

Compiler

Compiled 5325 to 3797 computations (28.7% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 y)
✓	0.0b	(*.f64 (hypot.f64 1 y) x)
✓	0.0b	(/.f64 1 (hypot.f64 1 y))
✓	0.1b	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))

series35.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

19.0ms	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))
13.0ms	(*.f64 (hypot.f64 1 y) x)
3.0ms	(/.f64 1 (hypot.f64 1 y))

rewrite83.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
248×	`prod-diff_binary64`
158×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Counts

3 → 158

Calls

3 calls:

80.0ms	(*.f64 (hypot.f64 1 y) x)
80.0ms	(/.f64 1 (hypot.f64 1 y))
80.0ms	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	179	24
2	2121	24
3	5145	24
0	0	0
1	0	0

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

345×	`rules-4_binary64`
278×	`fma-neg_binary64`
272×	`rules-11_binary64`
211×	`rules-20_binary64`
186×	`rules-15-rev_binary64`

Counts

218 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	738
1	246	673
2	976	664
3	4945	664
4	4976	664

prune284.0ms (9.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	315	7	322

Error

Counts

322 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (hypot.f64 1 y) (*.f64 x (hypot.f64 1 y)) 0)
	0.4b	(fma.f64 (hypot.f64 1 y) (*.f64 x (pow.f64 (cbrt.f64 (hypot.f64 1 y)) 3)) 0)
▶	0.2b	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
✓	0.2b	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))
	30.6b	(.f64 (sqrt.f64 (.f64 (hypot.f64 1 y) x)) (.f64 (hypot.f64 1 y) (sqrt.f64 (.f64 (hypot.f64 1 y) x))))
	7.1b	(/.f64 x (/.f64 1 (fma.f64 y y 1)))
	7.3b	(fma.f64 (cbrt.f64 (fma.f64 y y 1)) (*.f64 x (pow.f64 (cbrt.f64 (fma.f64 y y 1)) 2)) 0)

Compiler

Compiled 5971 to 4391 computations (26.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 y)
✓	0.1b	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
✓	0.2b	(/.f64 (hypot.f64 1 y) (/.f64 1 x))

series39.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
14.0ms	(/.f64 (hypot.f64 1 y) (/.f64 1 x))

rewrite59.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
183×	`prod-diff_binary64`
104×	`egg-rr`
77×	`add-sqr-sqrt_binary64`

Counts

2 → 104

Calls

2 calls:

57.0ms	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
57.0ms	(/.f64 (hypot.f64 1 y) (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	193	17
2	2093	17
3	4940	17
0	0	0
1	0	0

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-neg_binary64`
875×	`fma-def_binary64`
248×	`rules-4_binary64`
206×	`rules-21_binary64`
165×	`rules-11_binary64`

Counts

152 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	542
1	148	481
2	551	472
3	2991	472
4	4919	472
5	4982	472

prune200.0ms (6.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	240	6	246

Error

Counts

246 → 6

Alt Table

Status	Error	Program
	30.6b	(.f64 (sqrt.f64 (.f64 (hypot.f64 1 y) x)) (.f64 (hypot.f64 1 y) (sqrt.f64 (.f64 (hypot.f64 1 y) x))))
	7.1b	(/.f64 (.f64 x (+.f64 1 (.f64 y y))) 1)
	0.4b	(fma.f64 (hypot.f64 1 y) (*.f64 x (pow.f64 (cbrt.f64 (hypot.f64 1 y)) 3)) 0)
✓	0.2b	(fma.f64 (hypot.f64 1 y) (/.f64 (hypot.f64 1 y) (/.f64 1 x)) 0)
✓	0.2b	(/.f64 (*.f64 (hypot.f64 1 y) x) (/.f64 1 (hypot.f64 1 y)))
	0.2b	(/.f64 (hypot.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 y)))

Compiler

Compiled 4248 to 3089 computations (27.3% saved)

regimes451.0ms (14.5%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts

85 → 1

Compiler

Compiled 6543 to 4595 computations (29.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	9	13
2	8	13

end91.0ms (2.9%)

Compiler: Compiled 107 to 81 computations (24.3% saved)

Details

analyze118.0ms (3.8%)

sample795.0ms (25.6%)

simplify81.0ms (2.6%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.3%)

rewrite61.0ms (1.9%)

simplify62.0ms (2%)

prune119.0ms (3.8%)

localize5.0ms (0.2%)

series50.0ms (1.6%)

rewrite79.0ms (2.5%)

simplify99.0ms (3.2%)

prune241.0ms (7.8%)

localize6.0ms (0.2%)

series35.0ms (1.1%)

rewrite83.0ms (2.7%)

simplify67.0ms (2.2%)

prune284.0ms (9.1%)

localize6.0ms (0.2%)

series39.0ms (1.3%)

rewrite59.0ms (1.9%)

simplify62.0ms (2%)

prune200.0ms (6.4%)

regimes451.0ms (14.5%)

simplify2.0ms (0.1%)

end91.0ms (2.9%)

Profiling