Details

analyze2.1s (31.3%)

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 22 to 14 computations (36.4% saved)

sample2.3s (34.1%)

Results

1.5s	8256×	body	128	valid
629.0ms	4066×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune3.0ms (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
	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.0b	(.f64 (.f64 a z) b)

series58.0ms (0.9%)

Counts

4 → 204

Calls

4 calls:

27.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
19.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
8.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite89.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`expm1-udef_binary64`
296×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Counts

4 → 136

Calls

4 calls:

86.0ms	(+.f64 x (*.f64 y z))
86.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
86.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
86.0ms	(.f64 (.f64 a z) b)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	311	37
2	4341	37
3	5237	37

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
16×	`associate-+l+_binary64`
14×	`associate-+r+_binary64`
13×	`+-commutative_binary64`
9×	`*-commutative_binary64`

Counts

340 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1867
1	72	1695
2	129	1693
3	168	1693
4	167	1693

prune211.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	159	5	164

Error

0.0b

Counts

164 → 5

Alt Table

Status	Error	Program
	24.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
	44.9b	(+.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 z y x) 3) (pow.f64 (.f64 a t) 3)) (+.f64 (pow.f64 (fma.f64 z y x) 2) (.f64 (.f64 a t) (-.f64 (.f64 a t) (fma.f64 z y x))))) (.f64 (.f64 a z) b))
	4.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 3471 to 845 computations (75.7% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.8b	(fma.f64 a (fma.f64 z b t) x)

series14.0ms (0.2%)

Counts

1 → 60

Calls

1 calls:

14.0ms

(fma.f64 a (fma.f64 z b t) x)

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
128×	`prod-diff_binary64`

Counts

1 → 24

Calls

1 calls:

46.0ms

(fma.f64 a (fma.f64 z b t) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	157	9
2	1811	9
3	4988	9

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

29×	`fma-def_binary64`
10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-r_binary64`

Counts

84 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	627
1	37	486
2	59	486
3	65	486
4	64	486

prune41.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
	24.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
	44.9b	(+.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 z y x) 3) (pow.f64 (.f64 a t) 3)) (+.f64 (pow.f64 (fma.f64 z y x) 2) (.f64 (.f64 a t) (-.f64 (.f64 a t) (fma.f64 z y x))))) (.f64 (.f64 a z) b))
▶	4.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 722 to 249 computations (65.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	3.8b	(fma.f64 z (fma.f64 a b y) x)

series47.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

29.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
18.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite57.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
192×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
94×	`add-log-exp_binary64`

Counts

2 → 49

Calls

2 calls:

56.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
56.0ms	(fma.f64 z (fma.f64 a b y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	197	22
2	2289	22
3	5801	22

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

87×	`fma-def_binary64`
17×	`+-commutative_binary64`
14×	`associate-+l+_binary64`
12×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Counts

181 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	1564
1	80	1301
2	142	1301
3	169	1301
4	167	1301

prune67.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
▶	3.1b	(fma.f64 a t (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x)))
	24.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
✓	4.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 1142 to 293 computations (74.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x)))
✓	0.0b	(+.f64 (*.f64 y z) x)
✓	0.0b	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x))
✓	5.2b	(.f64 a (.f64 b z))

series82.0ms (1.2%)

Counts

4 → 133

Calls

4 calls:

48.0ms	(fma.f64 a t (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x)))
17.0ms	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x))
13.0ms	(.f64 a (.f64 b z))
5.0ms	(+.f64 (*.f64 y z) x)

rewrite80.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`fma-def_binary64`
369×	`fma-neg_binary64`
266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
175×	`egg-rr`

Counts

4 → 175

Calls

4 calls:

77.0ms	(fma.f64 a t (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x)))
77.0ms	(+.f64 (*.f64 y z) x)
77.0ms	(+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x))
77.0ms	(.f64 a (.f64 b z))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	282	40
2	3728	34
3	5618	34

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

86×	`fma-def_binary64`
18×	`+-commutative_binary64`
17×	`associate-+l+_binary64`
14×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Counts

308 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	1382
1	72	1221
2	130	1221
3	169	1221
4	167	1221

prune155.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	200	5	205

Error

0.0b

Counts

205 → 5

Alt Table

Status	Error	Program
✓	3.1b	(fma.f64 a t (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 y z) x)))
	24.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 (.f64 a z) b)) 2))
✓	4.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	11.5b	(fma.f64 a t (fma.f64 (.f64 (.f64 a b) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z) (fma.f64 z y x)))
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 3582 to 890 computations (75.2% saved)

regimes974.0ms (14.8%)

Accuracy

Total 0.6b remaining (98.4%)

Threshold costs 0.6b (98.4%)

Counts

87 → 3

Compiler

Compiled 11109 to 6664 computations (40% saved)

bsearch56.0ms (0.8%)

Steps

Iters	Range		Point
1	6456529734930061.0	17154844714267362.0	10530352464693246.0
10	-2.4277917034178723e+192	-1.407585728849712e+182	-1.4296327524937482e+182

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	57
1	22	57
2	22	57

end99.0ms (1.5%)

Compiler: Compiled 201 to 102 computations (49.3% saved)

Details

analyze2.1s (31.3%)

sample2.3s (34.1%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize14.0ms (0.2%)

series58.0ms (0.9%)

rewrite89.0ms (1.3%)

simplify49.0ms (0.7%)

prune211.0ms (3.2%)

localize9.0ms (0.1%)

series14.0ms (0.2%)

rewrite47.0ms (0.7%)

simplify16.0ms (0.2%)

prune41.0ms (0.6%)

localize8.0ms (0.1%)

series47.0ms (0.7%)

rewrite57.0ms (0.9%)

simplify43.0ms (0.6%)

prune67.0ms (1%)

localize10.0ms (0.1%)

series82.0ms (1.2%)

rewrite80.0ms (1.2%)

simplify45.0ms (0.7%)

prune155.0ms (2.3%)

regimes974.0ms (14.8%)

bsearch56.0ms (0.8%)

simplify3.0ms (0.1%)

end99.0ms (1.5%)

Profiling