Details

analyze97.0ms (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)

sample931.0ms (25.9%)

Results

888.0ms	8256×	body	128	valid
2.0ms	5×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify21.0ms (0.6%)

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

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (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)

series63.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

28.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
25.0ms	(pow.f64 (hypot.f64 a b) 4)
9.0ms	(hypot.f64 a b)

rewrite48.0ms (1.3%)

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

Calls

3 calls:

46.0ms	(hypot.f64 a b)
46.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
46.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify44.0ms (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

prune159.0ms (4.4%)

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
▶	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

Compiler

Compiled 2914 to 1914 computations (34.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series48.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1))
15.0ms	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)
12.0ms	(.f64 b (fma.f64 2 (.f64 a a) 4))

rewrite57.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`prod-diff_binary64`
275×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	248	47
2	2951	47

Stop Event

1×	node limit

Counts

3 → 98

Calls

3 calls:

55.0ms	(+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1))
55.0ms	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)
55.0ms	(.f64 b (fma.f64 2 (.f64 a a) 4))

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
366×	`fma-neg_binary64`
352×	`unswap-sqr_binary64`
351×	`associate-l_binary64`
317×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1279
1	67	1071
2	157	1003
3	485	1003
4	1920	1003

Stop Event

1×	node limit

Counts

170 → 120

prune117.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	120	3	123

Error

Counts

123 → 3

Alt Table

Status	Error	Program
✓	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)))
▶	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

Compiler

Compiled 3121 to 2040 computations (34.6% saved)

localize8.0ms (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))

series79.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
35.0ms	(pow.f64 (hypot.f64 a b) 2)

rewrite44.0ms (1.2%)

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

Calls

2 calls:

43.0ms	(pow.f64 (hypot.f64 a b) 2)
43.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))

simplify33.0ms (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

prune178.0ms (5%)

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
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
✓	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
▶	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

Compiler

Compiled 4460 to 2611 computations (41.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)
✓	0.2b	(cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
✓	0.3b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

series357.0ms (9.9%)

Counts

2 → 48

Calls

2 calls:

286.0ms	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)
70.0ms	(cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

rewrite48.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
141×	`fma-neg_binary64`
119×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	271	36
2	3046	36

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

46.0ms	(cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
46.0ms	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

489×	`fma-def_binary64`
432×	`associate-+r+_binary64`
301×	`associate-r_binary64`
281×	`associate-+l+_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	373	4076
1	1240	3843

Stop Event

1×	node limit

Counts

114 → 122

prune258.0ms (7.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
✓	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)))
✓	0.2b	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

Compiler

Compiled 8340 to 6178 computations (25.9% saved)

regimes801.0ms (22.3%)

Accuracy

Total 0.0b remaining (53.3%)

Threshold costs 0.0b (53.3%)

Counts

141 → 1

Compiler

Compiled 14091 to 10320 computations (26.8% saved)

simplify2.0ms (0%)

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

end78.0ms (2.2%)

Compiler: Compiled 99 to 70 computations (29.3% saved)

Details

analyze97.0ms (2.7%)

sample931.0ms (25.9%)

simplify21.0ms (0.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series63.0ms (1.8%)

rewrite48.0ms (1.3%)

simplify44.0ms (1.2%)

prune159.0ms (4.4%)

localize10.0ms (0.3%)

series48.0ms (1.3%)

rewrite57.0ms (1.6%)

simplify39.0ms (1.1%)

prune117.0ms (3.3%)

localize8.0ms (0.2%)

series79.0ms (2.2%)

rewrite44.0ms (1.2%)

simplify33.0ms (0.9%)

prune178.0ms (5%)

localize9.0ms (0.3%)

series357.0ms (9.9%)

rewrite48.0ms (1.3%)

simplify53.0ms (1.5%)

prune258.0ms (7.2%)

regimes801.0ms (22.3%)

simplify2.0ms (0%)

end78.0ms (2.2%)

Profiling