Details

analyze3.6s (33.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample3.9s (36%)

Results

2.4s	8253×	body	128	valid
1.3s	4697×	body	128	invalid
1.0ms	1×	body	1024	valid
1.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 83 to 59 computations (28.9% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
474×	`distribute-neg-in_binary64`
463×	`associate--l-_binary64`
362×	`associate--r-_binary64`
354×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	49	27
2	141	25
3	466	25
4	1615	25
5	3794	25
6	4547	25
7	4966	25

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Compiler

Compiled 93 to 60 computations (35.5% saved)

localize25.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

series91.0ms (0.8%)

Counts

2 → 132

Calls

2 calls:

62.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
28.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))

rewrite90.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

958×	`prod-diff_binary64`
182×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
169×	`add-log-exp_binary64`

Counts

2 → 48

Calls

2 calls:

88.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
88.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	353	40
2	4493	40
3	6268	40
0	0	0
1	0	0

simplify225.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

497×	`unsub-neg_binary64`
482×	`associate--l+_binary64`
480×	`associate--r+_binary64`
470×	`distribute-neg-in_binary64`
433×	`sub-neg_binary64`

Counts

180 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	2654
1	249	2652
2	764	2595
3	2529	2593
4	3681	2593
5	4627	2593
6	4914	2593
7	4908	2593
8	4915	2593

prune282.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
▶	12.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
	13.5b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1886 to 961 computations (49% saved)

localize20.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))

series36.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

36.0ms

(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))

rewrite85.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

626×	`fma-def_binary64`
302×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`

Counts

1 → 71

Calls

1 calls:

82.0ms

(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	251	17
2	3430	15
3	5059	15
0	0	0
1	0	0

simplify273.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2146×	`fma-neg_binary64`
693×	`fma-def_binary64`
364×	`sub-neg_binary64`
247×	`distribute-rgt-in_binary64`
220×	`associate--r+_binary64`

Counts

119 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	740
1	107	737
2	248	697
3	502	620
4	1147	620
5	2249	620
6	2202	620
7	2287	620
8	2309	620
9	2309	620
10	2309	620
11	2309	620
12	3873	620
13	3873	620
14	3873	620
15	3873	620
16	3804	620

prune142.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Error

Counts

95 → 3

Alt Table

Status	Error	Program
✓	12.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
▶	13.5b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1926 to 848 computations (56% saved)

localize52.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 b z) (*.f64 b -2))
✓	0.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
✓	0.0b	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))

series102.0ms (0.9%)

Counts

3 → 144

Calls

3 calls:

51.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
34.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
16.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))

rewrite114.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

289×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Counts

3 → 100

Calls

3 calls:

108.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))
108.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
108.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	302	48
2	4256	48
3	5098	48
0	0	0
1	0	0

simplify213.0ms (2%)

Algorithm

1×	egg-herbie

Rules

839×	`sub-neg_binary64`
693×	`fma-def_binary64`
520×	`unsub-neg_binary64`
413×	`associate--l-_binary64`
334×	`neg-sub0_binary64`

Counts

244 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	2240
1	166	2211
2	388	2067
3	923	1893
4	2204	1893
5	3255	1893
6	3997	1893
7	4193	1893
8	4840	1893
9	4957	1893

prune196.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	137	3	140

Error

Counts

140 → 3

Alt Table

Status	Error	Program
✓	12.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	0.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	13.5b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 2988 to 1327 computations (55.6% saved)

regimes1.1s (10.4%)

Accuracy

Total 0.0b remaining (61.2%)

Threshold costs 0.0b (61.2%)

Counts

94 → 1

Compiler

Compiled 10841 to 7600 computations (29.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	26	25
2	34	25
3	38	25
4	40	25
5	38	25

end133.0ms (1.2%)

Compiler: Compiled 112 to 74 computations (33.9% saved)

Details

analyze3.6s (33.6%)

sample3.9s (36%)

simplify65.0ms (0.6%)

prune7.0ms (0.1%)

localize25.0ms (0.2%)

series91.0ms (0.8%)

rewrite90.0ms (0.8%)

simplify225.0ms (2.1%)

prune282.0ms (2.6%)

localize20.0ms (0.2%)

series36.0ms (0.3%)

rewrite85.0ms (0.8%)

simplify273.0ms (2.5%)

prune142.0ms (1.3%)

localize52.0ms (0.5%)

series102.0ms (0.9%)

rewrite114.0ms (1.1%)

simplify213.0ms (2%)

prune196.0ms (1.8%)

regimes1.1s (10.4%)

simplify5.0ms (0%)

end133.0ms (1.2%)

Profiling