Details

analyze166.0ms (4.7%)

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)

sample1.3s (37.2%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify62.0ms (1.8%)

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

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 (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))
	0.2b	(-.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)

Status

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))

0.2b

(-.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)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	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	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(.f64 (.f64 b b) (+.f64 a 3))

series115.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

69.0ms	(pow.f64 (hypot.f64 a b) 4)
28.0ms	(+.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))
10.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
7.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite83.0ms (2.4%)

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 → 105

Calls

4 calls:

80.0ms	(pow.f64 (hypot.f64 a b) 4)
80.0ms	(+.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))
80.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
80.0ms	(.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

simplify72.0ms (2.1%)

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

201 → 153

Iterations

Useful iterations: 3 (0.0ms)

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

prune151.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -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 3 a))))) 1)
	15.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Compiler

Compiled 4699 to 2726 computations (42% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	0.0b	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
✓	0.2b	(.f64 (+.f64 3 a) (.f64 b b))

series49.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

29.0ms

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

13.0ms

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

7.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite86.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

300×	`expm1-udef_binary64`
300×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`

Counts

3 → 101

Calls

3 calls:

77.0ms

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

77.0ms

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

77.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	63
1	356	63
2	4240	63
3	5017	63
0	0	0
1	0	0

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-l_binary64`
692×	`fma-def_binary64`
615×	`fma-neg_binary64`
513×	`associate-+l+_binary64`
353×	`distribute-lft-out_binary64`

Counts

173 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1447
1	201	1359
2	695	1219
3	2939	1195
4	5102	1195

prune165.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	166	3	169

Error

Counts

169 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -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 3 a))))) 1)
	15.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Compiler

Compiled 5176 to 3174 computations (38.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.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))
✓	0.2b	(.f64 (.f64 b b) (+.f64 3 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series37.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

15.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
7.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite89.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

322×	`log1p-udef_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
182×	`add-sqr-sqrt_binary64`
177×	`add-log-exp_binary64`

Counts

4 → 111

Calls

4 calls:

87.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
87.0ms	(.f64 (.f64 a a) (-.f64 1 a))
87.0ms	(.f64 (.f64 b b) (+.f64 3 a))
87.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	54
1	389	53
2	4889	53
3	5323	53
0	0	0
1	0	0

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-neg_binary64`
710×	`cancel-sign-sub-inv_binary64`
669×	`associate-l_binary64`
552×	`unswap-sqr_binary64`
488×	`associate-r_binary64`

Counts

195 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	1326
1	107	1232
2	307	1152
3	929	1152
4	2408	1152
5	5051	1152

prune147.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

150 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -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 3 a))))) 1)
▶	15.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Compiler

Compiled 5233 to 2826 computations (46% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)
2.0ms	(+.f64 (fma.f64 a a 4) (*.f64 a -4))

rewrite101.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

759×	`prod-diff_binary64`
563×	`fma-udef_binary64`
299×	`fma-def_binary64`
197×	`fma-neg_binary64`
171×	`expm1-udef_binary64`

Counts

2 → 84

Calls

2 calls:

99.0ms	(+.f64 (fma.f64 a a 4) (*.f64 a -4))
99.0ms	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	207	25
2	2337	25
3	4764	25
4	4638	25
5	4895	25
0	0	0
1	0	0

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
646×	`cancel-sign-sub-inv_binary64`
389×	`fma-def_binary64`
318×	`difference-of-squares_binary64`
270×	`sub-neg_binary64`

Counts

108 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	277
1	76	250
2	164	217
3	464	198
4	1450	198
5	2774	198
6	4907	198

prune87.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -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 3 a))))) 1)
✓	15.5b	(fma.f64 (.f64 a a) (+.f64 (fma.f64 a a 4) (.f64 a -4)) -1)

Compiler

Compiled 1898 to 1142 computations (39.8% saved)

regimes481.0ms (13.7%)

Accuracy

Total 0.0b remaining (77.4%)

Threshold costs 0.0b (77.4%)

Counts

97 → 1

Compiler

Compiled 11146 to 7763 computations (30.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-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	15	30
1	19	30
2	23	30
3	25	30
4	26	30
5	26	30

end76.0ms (2.2%)

Compiler: Compiled 117 to 78 computations (33.3% saved)

Details

analyze166.0ms (4.7%)

sample1.3s (37.2%)

simplify62.0ms (1.8%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series115.0ms (3.3%)

rewrite83.0ms (2.4%)

simplify72.0ms (2.1%)

prune151.0ms (4.3%)

localize15.0ms (0.4%)

series49.0ms (1.4%)

rewrite86.0ms (2.5%)

simplify63.0ms (1.8%)

prune165.0ms (4.7%)

localize14.0ms (0.4%)

series37.0ms (1.1%)

rewrite89.0ms (2.5%)

simplify61.0ms (1.7%)

prune147.0ms (4.2%)

localize7.0ms (0.2%)

series5.0ms (0.1%)

rewrite101.0ms (2.9%)

simplify48.0ms (1.4%)

prune87.0ms (2.5%)

regimes481.0ms (13.7%)

simplify2.0ms (0.1%)

end76.0ms (2.2%)

Profiling