Details

analyze135.0ms (4.4%)

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)

sample1.0s (33.3%)

Results

952.0ms	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	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)

series66.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

30.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
27.0ms	(pow.f64 (hypot.f64 a b) 4)
9.0ms	(hypot.f64 a b)

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
447×	`log-prod_binary64`
243×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	212	28
2	2417	28
3	5319	28

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

54.0ms	(hypot.f64 a b)
54.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
54.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify72.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
307×	`fma-def_binary64`
297×	`neg-mul-1_binary64`
289×	`neg-sub0_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1453
1	217	1409
2	654	1303
3	2646	1303
4	4298	1303
5	5065	1303

Stop Event

1×	node limit

Counts

171 → 148

prune130.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Error

Counts

150 → 3

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 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))

Compiler

Compiled 3015 to 1957 computations (35.1% saved)

localize8.0ms (0.3%)

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))

series84.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))
37.0ms	(pow.f64 (hypot.f64 a b) 2)

rewrite43.0ms (1.4%)

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	2166	24
3	5231	24

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

42.0ms	(pow.f64 (hypot.f64 a b) 2)
42.0ms	(fma.f64 (pow.f64 (hypot.f64 a b) 2) (pow.f64 (hypot.f64 a b) 2) (fma.f64 b (*.f64 b 4) -1))

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-def_binary64`
720×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
337×	`sub-neg_binary64`
324×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	779
1	68	705
2	197	639
3	609	613
4	1831	613
5	4647	613
6	4878	613
7	5175	613

Stop Event

1×	node limit

Counts

95 → 68

prune189.0ms (6.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	201	3	204

Error

Counts

204 → 3

Alt Table

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

Compiler

Compiled 4642 to 2680 computations (42.3% saved)

localize10.0ms (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)

series414.0ms (13.4%)

Counts

2 → 48

Calls

2 calls:

346.0ms	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)
67.0ms	(cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

rewrite93.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
482×	`fma-udef_binary64`
273×	`fma-def_binary64`
207×	`fma-neg_binary64`
207×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	258	36
2	2801	36
3	4815	36
4	4727	36
5	4891	36

Stop Event

1×	node limit

Counts

2 → 83

Calls

2 calls:

91.0ms	(cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
91.0ms	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)

simplify83.0ms (2.7%)

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	1238	3843
2	5252	3843

Stop Event

1×	node limit

Counts

131 → 138

prune273.0ms (8.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	234	3	237

Error

Counts

237 → 3

Alt Table

Status	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))) 3)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 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))

Compiler

Compiled 8692 to 6355 computations (26.9% saved)

regimes200.0ms (6.5%)

Accuracy

Total -0.0b remaining (-10%)

Threshold costs -0.0b (-10%)

Counts

34 → 1

Compiler

Compiled 3386 to 2433 computations (28.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	16	27
2	16	27

Stop Event

1×

saturated

end80.0ms (2.6%)

Compiler: Compiled 92 to 65 computations (29.3% saved)

Details

analyze135.0ms (4.4%)

sample1.0s (33.3%)

simplify39.0ms (1.3%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series66.0ms (2.1%)

rewrite56.0ms (1.8%)

simplify72.0ms (2.3%)

prune130.0ms (4.2%)

localize8.0ms (0.3%)

series84.0ms (2.7%)

rewrite43.0ms (1.4%)

simplify65.0ms (2.1%)

prune189.0ms (6.1%)

localize10.0ms (0.3%)

series414.0ms (13.4%)

rewrite93.0ms (3%)

simplify83.0ms (2.7%)

prune273.0ms (8.9%)

regimes200.0ms (6.5%)

simplify2.0ms (0.1%)

end80.0ms (2.6%)

Profiling