Details

analyze184.0ms (1.3%)

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)

sample1.3s (9%)

Results

1.2s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify65.0ms (0.5%)

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%)

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
	0.3b	(-.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 (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)

Status

Error

Program

0.3b

(-.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 (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)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.1b	(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	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series47.0ms (0.3%)

Counts

4 → 84

Calls

4 calls:

28.0ms	(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))
10.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
8.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
1.0ms	(fma.f64 a -3 1)

rewrite122.0ms (0.9%)

Algorithm

1×	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 → 94

Calls

4 calls:

120.0ms	(fma.f64 a -3 1)
120.0ms	(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))
120.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
120.0ms	(.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

simplify79.0ms (0.6%)

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

178 → 139

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

prune211.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
	1.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)
	21.1b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4)) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (pow.f64 (hypot.f64 b a) 4))) -1)
	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)

Compiler

Compiled 3997 to 2252 computations (43.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3))))
✓	0.4b	(.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))

series85.0ms (0.6%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
29.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4))
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3))))
13.0ms	(.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))

rewrite83.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

959×	`prod-diff_binary64`
171×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
162×	`add-cbrt-cube_binary64`

Counts

4 → 108

Calls

4 calls:

78.0ms	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
78.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4))
78.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3))))
78.0ms	(.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	99
1	362	91
2	4093	91
3	5939	91

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary64`
710×	`fma-neg_binary64`
379×	`associate--l+_binary64`
341×	`associate-+r+_binary64`
302×	`associate--r+_binary64`

Counts

204 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	2414
1	236	2229
2	773	1843
3	2827	1786
4	4983	1786

prune179.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	1.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)
	21.1b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4)) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (pow.f64 (hypot.f64 b a) 4))) -1)
	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)

Compiler

Compiled 5191 to 2920 computations (43.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1))
	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.9b	(exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1))))
✓	2.0b	(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1)

series10.0s (71.7%)

Counts

3 → 72

Calls

3 calls:

5.3s

(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) 1)

4.6s

(exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1))))

101.0ms

(fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) 1))

rewrite120.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`prod-diff_binary64`
480×	`fma-udef_binary64`
226×	`fma-neg_binary64`
221×	`fma-def_binary64`
205×	`log1p-udef_binary64`

Counts

3 → 134

Calls

3 calls:

117.0ms

(fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) 1))

117.0ms

(exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1))))

117.0ms

(-.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 b b) (fma.f64 a -3 1)))) 1)

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	245	44
2	2724	42
3	4688	42
4	4681	42
5	5000	42

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

832×	`prod-exp_binary64`
815×	`fma-neg_binary64`
720×	`cancel-sign-sub-inv_binary64`
716×	`div-sub_binary64`
414×	`div-exp_binary64`

Counts

206 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1292
1	289	1138
2	832	927
3	2392	891
4	3792	891
5	4512	891
6	4437	891
7	5413	891

prune236.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	204	4	208

Error

Counts

208 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	1.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)
	21.1b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4)) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (pow.f64 (hypot.f64 b a) 4))) -1)
▶	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)

Compiler

Compiled 6826 to 4121 computations (39.6% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 a 4))

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (pow.f64 a 3) (+.f64 a 4))

rewrite39.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

712×	`log1p-expm1-u_binary64`
712×	`expm1-log1p-u_binary64`
217×	`prod-diff_binary64`
129×	`log1p-udef_binary64`
73×	`add-sqr-sqrt_binary64`

Counts

1 → 26

Calls

1 calls:

39.0ms

(*.f64 (pow.f64 a 3) (+.f64 a 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	160	10
2	1805	10
3	4852	10

simplify153.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

769×	`sqr-pow_binary64`
591×	`pow-sqr_binary64`
582×	`fabs-mul_binary64`
542×	`cube-prod_binary64`
528×	`fma-def_binary64`

Counts

38 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	114
1	22	114
2	46	114
3	84	105
4	197	105
5	587	105
6	1188	105
7	1442	105
8	1591	105
9	1759	105
10	1989	105
11	2248	105
12	2517	105
13	2858	105
14	3379	105
15	4049	105
16	4283	105
17	4497	105
18	4633	105
19	4690	105
20	4727	105
21	4806	105

prune38.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	30	4	34

Error

Counts

34 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (+.f64 1 (*.f64 a -3)))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	1.3b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 b b) (fma.f64 a -3 1)))) 1)) (pow.f64 (hypot.f64 a b) 4)) -1)
	21.1b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4)) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (.f64 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) 4) (pow.f64 (hypot.f64 b a) 4))) -1)
✓	13.0b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) -1)

Compiler

Compiled 552 to 422 computations (23.6% saved)

regimes662.0ms (4.7%)

Accuracy

Total 0.0b remaining (44%)

Threshold costs 0.0b (44%)

Counts

125 → 1

Compiler

Compiled 16660 to 11278 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	21	32
2	20	32

end102.0ms (0.7%)

Compiler: Compiled 182 to 114 computations (37.4% saved)

Details

analyze184.0ms (1.3%)

sample1.3s (9%)

simplify65.0ms (0.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series47.0ms (0.3%)

rewrite122.0ms (0.9%)

simplify79.0ms (0.6%)

prune211.0ms (1.5%)

localize14.0ms (0.1%)

series85.0ms (0.6%)

rewrite83.0ms (0.6%)

simplify114.0ms (0.8%)

prune179.0ms (1.3%)

localize16.0ms (0.1%)

series10.0s (71.7%)

rewrite120.0ms (0.9%)

simplify112.0ms (0.8%)

prune236.0ms (1.7%)

localize5.0ms (0%)

series3.0ms (0%)

rewrite39.0ms (0.3%)

simplify153.0ms (1.1%)

prune38.0ms (0.3%)

regimes662.0ms (4.7%)

simplify2.0ms (0%)

end102.0ms (0.7%)

Profiling