Details

analyze106.0ms (2.7%)

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
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample979.0ms (25.3%)

Results

963.0ms	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess31.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

931×	`fma-def_binary64`
495×	`fma-neg_binary64`
420×	`associate-+l+_binary64`
334×	`associate-+r+_binary64`
241×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	48	42
2	99	42
3	288	42
4	1136	34
5	3734	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
603×	`associate-l_binary64`
311×	`fma-neg_binary64`
233×	`associate-+l+_binary64`
216×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	64	21
3	193	21
4	779	17
5	2634	17

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 97 to 64 computations (34% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series68.0ms (1.7%)

Counts

3 → 72

Calls

18 calls:

6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	-inf
6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	b	-inf
5.0ms	(pow.f64 (hypot.f64 a b) 4)	b	inf
5.0ms	(pow.f64 (hypot.f64 a b) 4)	a	0
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	inf

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
243×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	212	28
2	2603	28

Stop Event

1×	node limit

Counts

3 → 93

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
306×	`fma-def_binary64`
224×	`distribute-neg-frac_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1453
1	219	1409
2	691	1303
3	3004	1303

Stop Event

1×	node limit

Counts

165 → 143

prune168.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
	11.9b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
▶	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))

Compiler

Compiled 2942 to 1932 computations (34.3% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
✓	0.1b	(.f64 b (fma.f64 2 (.f64 a a) 4))

series52.0ms (1.3%)

Counts

3 → 72

Calls

18 calls:

5.0ms	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)	b	-inf
5.0ms	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))	a	0
5.0ms	(.f64 b (fma.f64 2 (.f64 a a) 4))	b	-inf
4.0ms	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))	b	-inf
3.0ms	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))	b	0

rewrite65.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`fma-def_binary64`
273×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	303	53
2	3875	53

Stop Event

1×	node limit

Counts

3 → 107

simplify44.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-neg_binary64`
404×	`associate-l_binary64`
400×	`unswap-sqr_binary64`
342×	`distribute-rgt-neg-in_binary64`
316×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	1307
1	89	1129
2	232	1059
3	837	1059
4	2367	1059

Stop Event

1×	node limit

Counts

179 → 138

prune165.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	138	3	141

Error

Counts

141 → 3

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
	11.9b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))

Compiler

Compiled 3667 to 2321 computations (36.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a b)
✓	0.0b	(pow.f64 (hypot.f64 a b) 2)
✓	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))

series87.0ms (2.3%)

Counts

2 → 48

Calls

12 calls:

9.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))	b	-inf
9.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))	a	inf
8.0ms	(pow.f64 (hypot.f64 a b) 2)	b	-inf
8.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))	b	0
8.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))	a	-inf

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`log1p-expm1-u_binary64`
832×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
100×	`prod-diff_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	217	24
2	2328	24

Stop Event

1×	node limit

Counts

2 → 47

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
720×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
325×	`associate-l_binary64`
306×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	779
1	68	705
2	202	639
3	788	613
4	2938	613

Stop Event

1×	node limit

Counts

95 → 68

prune199.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
▶	11.9b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))

Compiler

Compiled 4488 to 2629 computations (41.4% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
✓	0.1b	(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)
✓	0.2b	(-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2))
✓	11.0b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))

series203.0ms (5.2%)

Counts

4 → 84

Calls

21 calls:

42.0ms	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))	a	0
41.0ms	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))	b	0
13.0ms	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))	a	-inf
13.0ms	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))	a	inf
12.0ms	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))	b	inf

rewrite84.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
174×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
170×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	90
1	386	68
2	4692	68

Stop Event

1×	node limit

Counts

4 → 135

simplify92.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
357×	`times-frac_binary64`
323×	`associate-/l*_binary64`
251×	`associate-/r*_binary64`
191×	`associate--l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6237
1	1592	6137

Stop Event

1×	node limit

Counts

219 → 226

prune359.0ms (9.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	226	3	229

Error

Counts

229 → 3

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
✓	11.9b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))

Compiler

Compiled 13205 to 9668 computations (26.8% saved)

regimes843.0ms (21.7%)

Accuracy

Total 0.0b remaining (54.3%)

Threshold costs 0.0b (54.3%)

Counts

150 → 1

Compiler

Compiled 15712 to 11472 computations (27% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	17	27

Stop Event

1×

saturated

end83.0ms (2.2%)

Stop Event

1×

done

Compiler

Compiled 113 to 79 computations (30.1% saved)

Details

analyze106.0ms (2.7%)

sample979.0ms (25.3%)

preprocess31.0ms (0.8%)

simplify20.0ms (0.5%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series68.0ms (1.7%)

rewrite54.0ms (1.4%)

simplify47.0ms (1.2%)

prune168.0ms (4.3%)

localize11.0ms (0.3%)

series52.0ms (1.3%)

rewrite65.0ms (1.7%)

simplify44.0ms (1.1%)

prune165.0ms (4.2%)

localize9.0ms (0.2%)

series87.0ms (2.3%)

rewrite42.0ms (1.1%)

simplify35.0ms (0.9%)

prune199.0ms (5.1%)

localize16.0ms (0.4%)

series203.0ms (5.2%)

rewrite84.0ms (2.2%)

simplify92.0ms (2.4%)

prune359.0ms (9.3%)

regimes843.0ms (21.7%)

simplify2.0ms (0.1%)

end83.0ms (2.2%)

Profiling