Details

analyze177.0ms (5.2%)

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%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.2s (35%)

Results

1.1s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify40.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`fma-neg_binary64`
232×	`associate-+l+_binary64`
211×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	193	36
3	742	36
4	2867	32
5	4882	32

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 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Status

Error

Program

▶

0.0b

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

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

Compiler

Compiled 172 to 109 computations (36.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(*.f64 b (fma.f64 a -3 1))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
✓	0.1b	(.f64 b (.f64 b (fma.f64 a -3 1)))

series57.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

26.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
10.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
8.0ms	(*.f64 b (fma.f64 a -3 1))

rewrite54.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

556×	`log-prod_binary64`
379×	`prod-diff_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	262	45
2	2928	45

Stop Event

1×	node limit

Counts

4 → 92

Calls

4 calls:

52.0ms	(pow.f64 (hypot.f64 a b) 4)
52.0ms	(*.f64 b (fma.f64 a -3 1))
52.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
52.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

635×	`associate-l_binary64`
587×	`fma-def_binary64`
557×	`fma-neg_binary64`
550×	`unswap-sqr_binary64`
467×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	1413
1	105	1332
2	301	1162
3	910	1158
4	3738	1158

Stop Event

1×	node limit

Counts

188 → 122

prune118.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Error

0.0b

Counts

124 → 4

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 2)) 4) (pow.f64 (cbrt.f64 (hypot.f64 b a)) 4)) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (*.f64 b (fma.f64 a -3 1)))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
	10.6b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (*.f64 b (fma.f64 a -3 1)))) -1))
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 3587 to 1971 computations (45.1% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a a) (.f64 b b))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series27.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

10.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(+.f64 (.f64 a a) (.f64 b b))
2.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite68.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	42
1	336	38
2	4291	38

Stop Event

1×	node limit

Counts

4 → 117

Calls

4 calls:

59.0ms	(+.f64 (.f64 a a) (.f64 b b))
59.0ms	(.f64 (.f64 a a) (+.f64 1 a))
59.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
59.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
551×	`unswap-sqr_binary64`
550×	`associate-l_binary64`
409×	`associate-r_binary64`
183×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	1011
1	72	951
2	197	885
3	614	885
4	2644	885

Stop Event

1×	node limit

Counts

201 → 138

prune186.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 (hypot.f64 b a) 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))) (cbrt.f64 (pow.f64 (hypot.f64 b a) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
	10.6b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (*.f64 b (fma.f64 a -3 1)))) -1))

Compiler

Compiled 5120 to 3052 computations (40.4% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)
	0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	9.2b	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
✓	18.2b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))

series90.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

35.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))
28.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
27.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)

rewrite41.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
323×	`log-prod_binary64`
132×	`log-pow_binary64`
131×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	179	25
2	1907	25

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

40.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 2)
40.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 2))
40.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
565×	`associate-r_binary64`
534×	`associate-l_binary64`
410×	`fma-def_binary64`
203×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	2082
1	314	2040
2	977	1962
3	4166	1962

Stop Event

1×	node limit

Counts

154 → 122

prune264.0ms (7.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	150	4	154

Error

Counts

154 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 (hypot.f64 b a) 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))) (cbrt.f64 (pow.f64 (hypot.f64 b a) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
▶	10.6b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (*.f64 b (fma.f64 a -3 1)))) -1))

Compiler

Compiled 7582 to 4724 computations (37.7% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 b (.f64 b (fma.f64 a -3 1)))
✓	0.3b	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8)))
✓	18.2b	(cbrt.f64 (pow.f64 (hypot.f64 b a) 4))
✓	25.1b	(cbrt.f64 (pow.f64 (hypot.f64 b a) 8))

series103.0ms (3%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 8))
36.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 4))
26.0ms	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8)))

rewrite71.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`log1p-expm1-u_binary64`
707×	`expm1-log1p-u_binary64`
146×	`log1p-udef_binary64`
93×	`add-cbrt-cube_binary64`
92×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	225	25
2	2306	25

Stop Event

1×	node limit

Counts

3 → 67

Calls

3 calls:

70.0ms	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8)))
70.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 4))
70.0ms	(cbrt.f64 (pow.f64 (hypot.f64 b a) 8))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-r_binary64`
515×	`associate-l_binary64`
459×	`fma-neg_binary64`
428×	`distribute-rgt-neg-in_binary64`
377×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2022
1	301	1986
2	936	1908
3	4008	1908

Stop Event

1×	node limit

Counts

139 → 107

prune184.0ms (5.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 (hypot.f64 b a) 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 2))) (cbrt.f64 (pow.f64 (hypot.f64 b a) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
✓	10.6b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 b a) 4)) (cbrt.f64 (pow.f64 (hypot.f64 b a) 8))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (*.f64 b (fma.f64 a -3 1)))) -1))

Compiler

Compiled 5098 to 3032 computations (40.5% saved)

regimes339.0ms (9.9%)

Accuracy

Total 0.0b remaining (83.6%)

Threshold costs 0.0b (83.6%)

Counts

56 → 1

Compiler

Compiled 8989 to 5969 computations (33.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25

Stop Event

1×

saturated

end109.0ms (3.2%)

Compiler: Compiled 176 to 113 computations (35.8% saved)

Details

analyze177.0ms (5.2%)

sample1.2s (35%)

simplify40.0ms (1.2%)

prune4.0ms (0.1%)

localize13.0ms (0.4%)

series57.0ms (1.7%)

rewrite54.0ms (1.6%)

simplify49.0ms (1.4%)

prune118.0ms (3.5%)

localize15.0ms (0.4%)

series27.0ms (0.8%)

rewrite68.0ms (2%)

simplify48.0ms (1.4%)

prune186.0ms (5.5%)

localize21.0ms (0.6%)

series90.0ms (2.7%)

rewrite41.0ms (1.2%)

simplify56.0ms (1.7%)

prune264.0ms (7.7%)

localize20.0ms (0.6%)

series103.0ms (3%)

rewrite71.0ms (2.1%)

simplify60.0ms (1.8%)

prune184.0ms (5.4%)

regimes339.0ms (9.9%)

simplify2.0ms (0.1%)

end109.0ms (3.2%)

Profiling