Details

analyze1.7s (29.8%)

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)

sample1.8s (32.1%)

Results

1.2s	8256×	body	128	valid
542.0ms	3951×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify10.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

Compiler

Compiled 105 to 60 computations (42.9% 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))
✓	3.1b	(fma.f64 a (fma.f64 z b t) x)

series47.0ms (0.8%)

Counts

2 → 132

Calls

2 calls:

25.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
22.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite49.0ms (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`

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

Calls

2 calls:

48.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
48.0ms	(fma.f64 a (fma.f64 z b t) x)

simplify32.0ms (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

prune59.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	75	4	79

Error

0.0b

Counts

79 → 4

Alt Table

Status	Error	Program
▶	3.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	4.3b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	16.3b	(fma.f64 z (fma.f64 a b y) x)

Compiler

Compiled 1139 to 299 computations (73.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 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))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	6.1b	(.f64 (.f64 a z) b)

series50.0ms (0.9%)

Counts

4 → 204

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
12.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
9.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

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	49
1	311	37
2	4617	37

Stop Event

1×	node limit

Counts

4 → 135

Calls

4 calls:

70.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
70.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
70.0ms	(+.f64 x (*.f64 y z))
70.0ms	(.f64 (.f64 a z) b)

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	1867
1	80	1695
2	144	1693
3	183	1693

Stop Event

1×

saturated

Counts

339 → 160

prune93.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	160	4	164

Error

0.0b

Counts

164 → 4

Alt Table

Status	Error	Program
✓	3.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	4.3b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.1b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 3379 to 798 computations (76.4% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

16.0ms

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

rewrite38.0ms (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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	157	9
2	1879	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

37.0ms

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

29×	`fma-def_binary64`
7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	576
1	47	486
2	70	486
3	75	486

Stop Event

1×

saturated

Counts

83 → 38

prune25.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	38	4	42

Error

0.0b

Counts

42 → 4

Alt Table

Status	Error	Program
✓	3.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	4.3b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 594 to 184 computations (69% saved)

localize11.0ms (0.2%)

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))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)
	3.1b	(fma.f64 a (fma.f64 z b t) x)

series439.0ms (7.9%)

Counts

3 → 82

Calls

3 calls:

218.0ms	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
180.0ms	(pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)
41.0ms	(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))

rewrite55.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

536×	`log-prod_binary64`
268×	`prod-diff_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
200×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	259	33
2	2877	33

Stop Event

1×	node limit

Counts

3 → 103

Calls

3 calls:

53.0ms	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
53.0ms	(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))
53.0ms	(pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-r_binary64`
428×	`fma-def_binary64`
418×	`associate-l_binary64`
266×	`*-commutative_binary64`
227×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	5086
1	1287	4751
2	4562	4551

Stop Event

1×	node limit

Counts

185 → 213

prune178.0ms (3.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	250	5	255

Error

Counts

255 → 5

Alt Table

Status	Error	Program
✓	3.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	4.3b	(fma.f64 y z (pow.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) 3))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.1b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	32.4b	(fma.f64 y z (fma.f64 (sqrt.f64 a) (*.f64 (sqrt.f64 a) (fma.f64 z b t)) x))

Compiler

Compiled 8206 to 3648 computations (55.5% saved)

regimes625.0ms (11.2%)

Accuracy

Total 0.8b remaining (99.2%)

Threshold costs 0.8b (99.2%)

Counts

68 → 3

Compiler

Compiled 7462 to 4767 computations (36.1% saved)

bsearch52.0ms (0.9%)

Steps

Iters	Range		Point
6	4.730530102033039e-189	4.539981210940575e-188	4.3935108643919645e-188
9	-1.1086849906065875e+49	-6.02210968915655e+43	-6.404233806295518e+43

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	55
1	26	55

Stop Event

1×

saturated

end79.0ms (1.4%)

Compiler: Compiled 184 to 94 computations (48.9% saved)

Details

analyze1.7s (29.8%)

sample1.8s (32.1%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series47.0ms (0.8%)

rewrite49.0ms (0.9%)

simplify32.0ms (0.6%)

prune59.0ms (1.1%)

localize10.0ms (0.2%)

series50.0ms (0.9%)

rewrite73.0ms (1.3%)

simplify43.0ms (0.8%)

prune93.0ms (1.7%)

localize10.0ms (0.2%)

series16.0ms (0.3%)

rewrite38.0ms (0.7%)

simplify18.0ms (0.3%)

prune25.0ms (0.5%)

localize11.0ms (0.2%)

series439.0ms (7.9%)

rewrite55.0ms (1%)

simplify93.0ms (1.7%)

prune178.0ms (3.2%)

regimes625.0ms (11.2%)

bsearch52.0ms (0.9%)

simplify5.0ms (0.1%)

end79.0ms (1.4%)

Profiling