Details

analyze1.9s (4.1%)

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)

sample2.0s (4.3%)

Results

1.3s	8256×	body	128	valid
646.0ms	3979×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify10.0ms (0%)

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

prune8.0ms (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
	3.1b	(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)

localize18.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.6b	(.f64 (.f64 a z) b)

series45.0ms (0.1%)

Counts

3 → 144

Calls

3 calls:

29.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
10.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite77.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

93× egg-rr

Counts

3 → 93

Calls

2 calls:

74.0ms	((.f64 (.f64 a z) b) (+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b)) (+.f64 x (*.f64 y z)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	311	28
2	4341	28
3	5237	28
0	0	0
1	0	0

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

237 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	1400
1	70	1228
2	127	1226
3	168	1226
4	167	1226

prune83.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

0.0b

Counts

119 → 5

Alt Table

Status	Error	Program
	17.9b	(fma.f64 z (fma.f64 a b y) x)
	31.5b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))) 2)
	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	36.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))
▶	2.1b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 2473 to 613 computations (75.2% saved)

localize10.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.9b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

series27.0ms (0.1%)

Counts

1 → 72

Calls

1 calls:

27.0ms

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

rewrite84.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

30× egg-rr

Counts

1 → 30

Calls

2 calls:

83.0ms	((fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	217	16
2	2540	16
3	4850	16
4	5003	16
0	0	0
1	0	0

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

102 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	988
1	75	815
2	138	815
3	169	815
4	167	815

prune39.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	54	5	59

Error

0.0b

Counts

59 → 5

Alt Table

Status	Error	Program
	17.9b	(fma.f64 z (fma.f64 a b y) x)
	31.5b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))) 2)
▶	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	36.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))
✓	2.1b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 968 to 245 computations (74.7% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series42.0ms (0.1%)

Counts

2 → 132

Calls

2 calls:

25.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
17.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite55.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

47× egg-rr

Counts

2 → 47

Calls

2 calls:

54.0ms	((fma.f64 a (fma.f64 z b t) x) (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify37.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

87×	`fma-def_binary64`
16×	`+-commutative_binary64`
15×	`associate-+l+_binary64`
12×	`associate-+r+_binary64`
10×	`*-commutative_binary64`

Counts

179 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	1561
1	75	1301
2	138	1301
3	169	1301
4	167	1301

prune50.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	76	6	82

Error

Counts

82 → 6

Alt Table

Status	Error	Program
	17.9b	(fma.f64 z (fma.f64 a b y) x)
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	36.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))
	31.9b	(fma.f64 y z (pow.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) 2))
▶	4.0b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	2.1b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 1231 to 343 computations (72.1% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	0.6b	(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)
	2.9b	(fma.f64 a (fma.f64 z b t) x)

series40.6s (86.7%)

Counts

3 → 192

Calls

3 calls:

25.9s	(pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)
14.6s	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
202.0ms	(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))

rewrite60.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

3 → 103

Calls

2 calls:

58.0ms	((pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	245	33
2	2735	33
3	4987	33
0	0	0
1	0	0

simplify346.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

489×	`*-commutative_binary64`
366×	`+-commutative_binary64`
281×	`fma-def_binary64`
248×	`associate-+r+_binary64`
221×	`sub-neg_binary64`

Counts

295 → 362

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1252	20966
1	4071	18724
2	4982	18724
3	4923	18724

prune540.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	400	6	406

Error

Counts

406 → 6

Alt Table

Status	Error	Program
	17.9b	(fma.f64 z (fma.f64 a b y) x)
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	36.9b	(.f64 (-.f64 (pow.f64 (fma.f64 a t (fma.f64 z y x)) 2) (pow.f64 (.f64 (.f64 a z) b) 2)) (/.f64 1 (-.f64 (fma.f64 a t (fma.f64 z y x)) (.f64 (*.f64 a z) b))))
	31.9b	(fma.f64 y z (pow.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) 2))
✓	4.0b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	2.1b	(fma.f64 (*.f64 a z) b (fma.f64 a t (fma.f64 z y x)))

Compiler

Compiled 27741 to 14706 computations (47% saved)

regimes534.0ms (1.1%)

Accuracy

Total 0.5b remaining (98%)

Threshold costs 0.5b (98%)

Counts

50 → 3

Compiler

Compiled 5747 to 3549 computations (38.2% saved)

bsearch50.0ms (0.1%)

Steps

Iters	Range		Point
9	1.7769489874315093e+116	6.877637058708764e+123	2.4356118753451166e+116
3	-2.6607245361940163e+57	-1.040784229510417e+34	-9.112644010531083e+36

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify2.0ms (0%)

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

end100.0ms (0.2%)

Compiler: Compiled 220 to 108 computations (50.9% saved)

Details

analyze1.9s (4.1%)

sample2.0s (4.3%)

simplify10.0ms (0%)

prune8.0ms (0%)

localize18.0ms (0%)

series45.0ms (0.1%)

rewrite77.0ms (0.2%)

simplify40.0ms (0.1%)

prune83.0ms (0.2%)

localize10.0ms (0%)

series27.0ms (0.1%)

rewrite84.0ms (0.2%)

simplify26.0ms (0.1%)

prune39.0ms (0.1%)

localize9.0ms (0%)

series42.0ms (0.1%)

rewrite55.0ms (0.1%)

simplify37.0ms (0.1%)

prune50.0ms (0.1%)

localize13.0ms (0%)

series40.6s (86.7%)

rewrite60.0ms (0.1%)

simplify346.0ms (0.7%)

prune540.0ms (1.2%)

regimes534.0ms (1.1%)

bsearch50.0ms (0.1%)

simplify2.0ms (0%)

end100.0ms (0.2%)

Profiling