Details

analyze1.8s (31.1%)

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)

sample1.7s (30.2%)

Results

1.2s	8256×	body	128	valid
532.0ms	3840×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess48.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1158×	`fma-def_binary64`
334×	`associate-+l+_binary64`
305×	`associate-+r+_binary64`
240×	`+-commutative_binary64`
65×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	352
1	249	254
2	785	236
3	1753	236
4	1909	236
5	1931	236
6	1931	208
7	2475	208
8	2475	208
0	6	6

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
21×	`associate-+r+_binary64`
18×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	69	15
3	147	13
4	192	13
5	204	13
6	207	13

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))
✓	7.0b	(.f64 (.f64 a z) b)

series48.0ms (0.8%)

Counts

3 → 168

Calls

42 calls:

6.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	z	0
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	z	inf
1.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))	t	0
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	x	-inf
1.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))	x	0

rewrite73.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
154×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	311	32
2	4617	32

Stop Event

1×	node limit

Counts

3 → 98

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1708
1	78	1536
2	142	1534
3	181	1534

Stop Event

1×

saturated

Counts

266 → 124

prune96.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	120	6	126

Error

0.0b

Counts

126 → 6

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
	18.0b	(fma.f64 z (fma.f64 a b y) x)
	25.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 a (.f64 z b))) 2))
	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	4.0b	(.f64 (cbrt.f64 (fma.f64 a (.f64 z b) (fma.f64 a t (fma.f64 z y x)))) (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))) 2))

Compiler

Compiled 2679 to 643 computations (76% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z y x))
✓	2.7b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))

series38.0ms (0.7%)

Counts

2 → 132

Calls

33 calls:

3.0ms	(fma.f64 a t (fma.f64 z y x))	z	inf
2.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	z	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	a	inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	a	-inf
1.0ms	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))	x	inf

rewrite52.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

535×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
202×	`prod-diff_binary64`
193×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	217	25
2	2636	25

Stop Event

1×	node limit

Counts

2 → 60

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	1395
1	81	1284
2	144	1282
3	183	1282

Stop Event

1×

saturated

Counts

192 → 87

prune60.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	87	6	93

Error

0.0b

Counts

93 → 6

Alt Table

Status	Error	Program
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.8b	(fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))
	18.0b	(fma.f64 z (fma.f64 a b y) x)
	25.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 a (.f64 z b))) 2))
▶	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	4.0b	(.f64 (cbrt.f64 (fma.f64 a (.f64 z b) (fma.f64 a t (fma.f64 z y x)))) (pow.f64 (cbrt.f64 (fma.f64 a (*.f64 z b) (fma.f64 a t (fma.f64 z y x)))) 2))

Compiler

Compiled 1559 to 381 computations (75.6% saved)

localize8.0ms (0.1%)

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))
✓	2.7b	(fma.f64 a (fma.f64 z b t) x)

series38.0ms (0.7%)

Counts

2 → 132

Calls

33 calls:

2.0ms	(fma.f64 a (fma.f64 z b t) x)	z	-inf
2.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))	a	0
1.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))	x	inf
1.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))	x	-inf
1.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))	a	-inf

rewrite64.0ms (1.1%)

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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	197	22
2	2375	22

Stop Event

1×	node limit

Counts

2 → 47

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	1561
1	89	1301
2	156	1301
3	187	1301

Stop Event

1×

saturated

Counts

179 → 77

prune53.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	78	5	83

Error

0.0b

Counts

83 → 5

Alt Table

Status	Error	Program
	26.6b	(fma.f64 a t (*.f64 z (fma.f64 a b y)))
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	25.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 a (.f64 z b))) 2))
▶	4.0b	(*.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) (pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2))
✓	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 1194 to 322 computations (73% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) (pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2)
✓	0.5b	(cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))
	2.7b	(fma.f64 a (fma.f64 z b t) x)

series240.0ms (4.2%)

Counts

3 → 120

Calls

54 calls:

33.0ms	(pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2)	z
24.0ms	(cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))	x
22.0ms	(pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2)	a
15.0ms	(cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))	a
14.0ms	(cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))	z

rewrite60.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
208×	`log-pow_binary64`
192×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	279	46
2	3004	46

Stop Event

1×	node limit

Counts

3 → 88

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-r_binary64`
584×	`associate-l_binary64`
490×	`fma-def_binary64`
165×	`*-commutative_binary64`
138×	`sqr-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	6417
1	1500	5563

Stop Event

1×	node limit

Counts

208 → 210

prune284.0ms (5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	359	1	360
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	359	6	365

Error

0.0b

Counts

365 → 6

Alt Table

Status	Error	Program
	26.6b	(fma.f64 a t (*.f64 z (fma.f64 a b y)))
✓	2.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	25.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (pow.f64 (sqrt.f64 (.f64 a (.f64 z b))) 2))
	4.3b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x)))) 2)) (pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2))
✓	4.0b	(*.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) (pow.f64 (cbrt.f64 (fma.f64 y z (fma.f64 a (fma.f64 z b t) x))) 2))
✓	2.8b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 17290 to 6025 computations (65.2% saved)

regimes686.0ms (12.1%)

Accuracy

Total 1.5b remaining (99.5%)

Threshold costs 0b (0%)

Counts

79 → 2

Compiler

Compiled 10402 to 6167 computations (40.7% saved)

bsearch8.0ms (0.1%)

Algorithm

1×	binary-search

Calls

1 calls:

5.0ms

Steps

Iters	Point		Range
2.2714426383117235e-113	∈ [	3.8945855108537736e-115	,	8.790981101733973e-113	]

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	18	35
1	19	35

Stop Event

1×

saturated

end93.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 218 to 109 computations (50% saved)

Details

analyze1.8s (31.1%)

sample1.7s (30.2%)

preprocess48.0ms (0.8%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

series48.0ms (0.8%)

rewrite73.0ms (1.3%)

simplify37.0ms (0.7%)

prune96.0ms (1.7%)

localize9.0ms (0.2%)

series38.0ms (0.7%)

rewrite52.0ms (0.9%)

simplify35.0ms (0.6%)

prune60.0ms (1.1%)

localize8.0ms (0.1%)

series38.0ms (0.7%)

rewrite64.0ms (1.1%)

simplify34.0ms (0.6%)

prune53.0ms (0.9%)

localize12.0ms (0.2%)

series240.0ms (4.2%)

rewrite60.0ms (1.1%)

simplify100.0ms (1.8%)

prune284.0ms (5%)

regimes686.0ms (12.1%)

bsearch8.0ms (0.1%)

simplify3.0ms (0.1%)

end93.0ms (1.6%)

Profiling