Details

analyze389.0ms (5.9%)

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%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample2.4s (36.2%)

Results

2.3s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune9.0ms (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 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

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 3 a))))) 1)

▶

0.0b

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

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.5b	(.f64 (.f64 b b) (+.f64 a 3))

series160.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

65.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
58.0ms	(pow.f64 (hypot.f64 a b) 4)
21.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
15.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite116.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
306×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`

Counts

4 → 101

Calls

4 calls:

111.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
111.0ms	(pow.f64 (hypot.f64 a b) 4)
110.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
110.0ms	(.f64 (.f64 b b) (+.f64 a 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	371	70
2	4305	70
3	5096	70
0	0	0
1	0	0

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-l_binary64`
719×	`fma-def_binary64`
624×	`fma-neg_binary64`
505×	`associate-+l+_binary64`
341×	`distribute-lft-out_binary64`

Counts

197 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1855
1	207	1761
2	710	1597
3	2967	1573
4	5116	1573

prune359.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Error

Counts

151 → 2

Alt Table

Status	Error	Program
	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 3 a))))) 1)
▶	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

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 3 a))))) 1)

▶

0.0b

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

Compiler

Compiled 4637 to 2698 computations (41.8% saved)

localize38.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
	0.5b	(.f64 (.f64 b b) (+.f64 a 3))
✓	1.6b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series55.0ms (0.8%)

Counts

2 → 0

Calls

2 calls:

29.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
25.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite91.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

634×	`log1p-expm1-u_binary64`
634×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
132×	`expm1-udef_binary64`
132×	`log1p-udef_binary64`

Counts

2 → 36

Calls

2 calls:

89.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
89.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	1691	17
3	5013	17
0	0	0
1	0	0

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune270.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	103	2	105

Error

Counts

105 → 2

Alt Table

Status	Error	Program
▶	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 3 a))))) 1)
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

▶

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 3 a))))) 1)

✓

0.0b

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

Compiler

Compiled 4108 to 2699 computations (34.3% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.5b	(.f64 (.f64 b b) (+.f64 3 a))

series106.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

53.0ms	(+.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 3 a)))))
24.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite135.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

777×	`prod-diff_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
198×	`add-sqr-sqrt_binary64`
192×	`add-log-exp_binary64`

Counts

4 → 85

Calls

4 calls:

131.0ms	(+.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 3 a)))))
131.0ms	(.f64 (.f64 a a) (-.f64 1 a))
131.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
131.0ms	(.f64 (.f64 b b) (+.f64 3 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	419	63
2	4655	63
3	6113	63
0	0	0
1	0	0

simplify144.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-l_binary64`
576×	`fma-def_binary64`
550×	`unswap-sqr_binary64`
455×	`associate-r_binary64`
392×	`cancel-sign-sub-inv_binary64`

Counts

169 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1546
1	169	1502
2	537	1319
3	2089	1305
4	4495	1305
5	5734	1305

prune299.0ms (4.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status	Error	Program
✓	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 3 a))))) 1)
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

✓

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 3 a))))) 1)

✓

0.0b

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

Compiler

Compiled 4504 to 2628 computations (41.7% saved)

regimes1.7s (26.1%)

Accuracy

Total 0.0b remaining (37.4%)

Threshold costs 0.0b (37.4%)

Counts

182 → 1

Compiler

Compiled 25792 to 18180 computations (29.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	50
1	35	50
2	38	50
3	40	50
4	41	50
5	40	50

end88.0ms (1.3%)

Compiler: Compiled 140 to 98 computations (30% saved)

Details

analyze389.0ms (5.9%)

sample2.4s (36.2%)

simplify64.0ms (1%)

prune9.0ms (0.1%)

localize29.0ms (0.4%)

series160.0ms (2.4%)

rewrite116.0ms (1.7%)

simplify116.0ms (1.8%)

prune359.0ms (5.4%)

localize38.0ms (0.6%)

series55.0ms (0.8%)

rewrite91.0ms (1.4%)

simplify10.0ms (0.1%)

prune270.0ms (4.1%)

localize27.0ms (0.4%)

series106.0ms (1.6%)

rewrite135.0ms (2%)

simplify144.0ms (2.2%)

prune299.0ms (4.5%)

regimes1.7s (26.1%)

simplify3.0ms (0%)

end88.0ms (1.3%)

Profiling