Details

analyze102.0ms (3.2%)

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 (31.9%)

Results

944.0ms	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify46.0ms (1.4%)

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`

Counts

1 → 2

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

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)

localize7.0ms (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) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

series68.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(+.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)

rewrite62.0ms (1.9%)

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`

Counts

3 → 99

Calls

3 calls:

60.0ms	(hypot.f64 a b)
60.0ms	(pow.f64 (hypot.f64 a b) 4)
60.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Iterations

Useful iterations: 0 (0.0ms)

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

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`

Counts

171 → 148

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

prune192.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

Counts

150 → 3

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)
	12.4b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2995 to 1939 computations (35.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
✓	0.0b	(.f64 4 (.f64 b b))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series41.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

21.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
7.0ms	(+.f64 (.f64 a a) (.f64 b b))
2.0ms	(.f64 4 (.f64 b b))

rewrite74.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
459×	`fma-def_binary64`
214×	`fma-neg_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Counts

4 → 167

Calls

4 calls:

69.0ms	(+.f64 (.f64 a a) (.f64 b b))
69.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
69.0ms	(.f64 4 (.f64 b b))
69.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	242	40
2	2781	40
3	5325	40

simplify103.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

648×	`distribute-rgt-in_binary64`
590×	`distribute-lft-in_binary64`
416×	`fma-def_binary64`
383×	`*-commutative_binary64`
348×	`unswap-sqr_binary64`

Counts

251 → 190

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	1223
1	54	1143
2	152	1055
3	417	1031
4	1185	1031
5	1613	1031
6	1751	1031
7	1926	1031
8	2390	1031
9	3239	1031
10	4927	1031

prune158.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	190	3	193

Error

Counts

193 → 3

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)
▶	12.4b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 4262 to 2573 computations (39.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
✓	17.9b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))
✓	25.8b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))

series296.0ms (9.3%)

Counts

3 → 72

Calls

3 calls:

194.0ms	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
63.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))
38.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite111.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
214×	`prod-diff_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
198×	`log-pow_binary64`

Counts

3 → 90

Calls

3 calls:

109.0ms	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
109.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))
109.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	277	35
2	2680	35
3	4951	35
4	4916	35
5	4863	35

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-neg_binary64`
545×	`associate-r_binary64`
520×	`associate-l_binary64`
491×	`fma-def_binary64`
429×	`distribute-rgt-neg-in_binary64`

Counts

162 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	2207
1	336	2135
2	990	2011
3	3627	2011
4	5100	2011

prune135.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Error

Counts

161 → 3

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)
✓	12.4b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 3955 to 2578 computations (34.8% saved)

regimes523.0ms (16.4%)

Accuracy

Total 0.0b remaining (60.3%)

Threshold costs 0.0b (60.3%)

Counts

57 → 1

Compiler

Compiled 5751 to 4347 computations (24.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end75.0ms (2.4%)

Compiler: Compiled 82 to 56 computations (31.7% saved)

Details

analyze102.0ms (3.2%)

sample1.0s (31.9%)

simplify46.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series68.0ms (2.1%)

rewrite62.0ms (1.9%)

simplify72.0ms (2.3%)

prune192.0ms (6%)

localize11.0ms (0.3%)

series41.0ms (1.3%)

rewrite74.0ms (2.3%)

simplify103.0ms (3.2%)

prune158.0ms (5%)

localize12.0ms (0.4%)

series296.0ms (9.3%)

rewrite111.0ms (3.5%)

simplify78.0ms (2.4%)

prune135.0ms (4.2%)

regimes523.0ms (16.4%)

simplify2.0ms (0.1%)

end75.0ms (2.4%)

Profiling