Details

analyze225.0ms (6.5%)

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)

sample1.4s (40.2%)

Results

1.3s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune5.0ms (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 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -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 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -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 108 computations (37.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series58.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

33.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
13.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
1.0ms	(fma.f64 a -3 1)

rewrite115.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

440×	`prod-diff_binary64`
320×	`fma-udef_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
209×	`log-pow_binary64`

Counts

4 → 98

Calls

4 calls:

113.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
113.0ms	(fma.f64 a -3 1)
113.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
113.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	64
1	283	64
2	2972	64
3	4897	64
4	4993	64
5	4944	64
0	0	0
1	0	0

simplify86.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
541×	`+-commutative_binary64`
524×	`sub-neg_binary64`
420×	`associate--l+_binary64`
415×	`fma-neg_binary64`

Counts

182 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	1651
1	195	1531
2	588	1259
3	2320	1236
4	4266	1236
5	5079	1236

prune150.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4)) -1)
	15.3b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)

Compiler

Compiled 3933 to 2211 computations (43.8% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4))
✓	0.0b	(+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))
✓	0.0b	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))))
✓	0.7b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))

series88.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

27.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))
25.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4))
24.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))))
13.0ms	(+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))

rewrite93.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

581×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
196×	`add-log-exp_binary64`

Counts

4 → 117

Calls

4 calls:

89.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4))
89.0ms	(+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))
89.0ms	(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12)))))
89.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	106
1	432	98
2	4769	98
3	5858	98
0	0	0
1	0	0

simplify148.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
676×	`associate-l_binary64`
473×	`associate-r_binary64`
465×	`associate-+l+_binary64`
359×	`fma-neg_binary64`

Counts

213 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	2671
1	215	2256
2	627	1880
3	2441	1800
4	4855	1800
5	4998	1800
6	4998	1800
7	4976	1800

prune215.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	171	3	174

Error

Counts

174 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4)) -1)
▶	15.3b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)

Compiler

Compiled 6312 to 4092 computations (35.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 b b))
✓	0.0b	(*.f64 a (+.f64 a 4))
✓	1.3b	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b)))))

series23.0ms (0.7%)

Counts

3 → 48

Calls

3 calls:

16.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b)))))
4.0ms	(.f64 2 (.f64 b b))
2.0ms	(*.f64 a (+.f64 a 4))

rewrite70.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

368×	`fma-neg_binary64`
259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`

Counts

3 → 69

Calls

3 calls:

68.0ms	(.f64 2 (.f64 b b))
68.0ms	(*.f64 a (+.f64 a 4))
68.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	302	35
2	3906	35
3	4979	35
0	0	0
1	0	0

simplify119.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
466×	`distribute-rgt-out_binary64`
452×	`unswap-sqr_binary64`
449×	`associate-l_binary64`
369×	`associate-+l+_binary64`

Counts

117 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	799
1	79	672
2	205	651
3	590	589
4	1947	589
5	3498	589
6	3881	589
7	4300	589
8	4512	589
9	4747	589
10	4864	589

prune84.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (+.f64 (.f64 a 2) -12))))) (pow.f64 a 4)) -1)
✓	15.3b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 a 4)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)

Compiler

Compiled 2070 to 1292 computations (37.6% saved)

regimes403.0ms (11.6%)

Accuracy

Total 0.1b remaining (84.4%)

Threshold costs 0.1b (84.4%)

Counts

76 → 1

Compiler

Compiled 8887 to 6316 computations (28.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	18	25
2	17	25

end82.0ms (2.4%)

Compiler: Compiled 118 to 77 computations (34.7% saved)

Details

analyze225.0ms (6.5%)

sample1.4s (40.2%)

simplify61.0ms (1.8%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series58.0ms (1.7%)

rewrite115.0ms (3.3%)

simplify86.0ms (2.5%)

prune150.0ms (4.3%)

localize17.0ms (0.5%)

series88.0ms (2.5%)

rewrite93.0ms (2.7%)

simplify148.0ms (4.3%)

prune215.0ms (6.2%)

localize12.0ms (0.3%)

series23.0ms (0.7%)

rewrite70.0ms (2%)

simplify119.0ms (3.4%)

prune84.0ms (2.4%)

regimes403.0ms (11.6%)

simplify4.0ms (0.1%)

end82.0ms (2.4%)

Profiling