Metrics for ENA, Section 1.4, Exercise 4b, n=2

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.5s (59.1%)

Results

869.0ms	6097×	body	256	valid
312.0ms	1118×	body	512	valid
285.0ms	1020×	body	1024	valid
10.0ms	21×	body	2048	valid

Bogosity

preprocess104.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1358×	`fma-def`
852×	`unswap-sqr`
758×	`distribute-lft-out`
646×	`distribute-lft-neg-in`
640×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	116
1	64	100
2	168	100
3	714	76
4	4082	76

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 (neg.f64 x) eps) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (+.f64 x (neg.f64 eps)) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(-.f64 (pow.f64 (+.f64 (neg.f64 x) eps) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (+.f64 eps (neg.f64 x)) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (-.f64 eps x) 2) (*.f64 x x))
(.f64 eps (+.f64 eps (.f64 x -2)))
(-.f64 (pow.f64 (+.f64 x (neg.f64 eps)) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps (neg.f64 x)) 2) (pow.f64 (neg.f64 x) 2))
(-.f64 (pow.f64 (-.f64 eps x) 2) (*.f64 x x))
(.f64 eps (+.f64 eps (.f64 x -2)))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 eps eps))
(*.f64 x (+.f64 x (+.f64 eps eps)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1174×	`distribute-lft-in`
1074×	`distribute-rgt-in`
1026×	`cancel-sign-sub-inv`
942×	`fma-def`
940×	`fma-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	21	25
2	52	25
3	164	25
4	652	15
5	2899	15

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (fma.f64 2 x eps))

eval1.0ms (0%)

Compiler: Compiled 26 to 15 computations (42.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Accurracy

100.0%

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 eps (fma.f64 2 x eps))
▶	100.0%	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize27.0ms (1.1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 16 to 9 computations (43.8% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	-inf	(*.f64 eps (fma.f64 2 x eps))
0.0ms	x	@	0	(*.f64 eps (fma.f64 2 x eps))
0.0ms	eps	@	inf	(*.f64 eps (fma.f64 2 x eps))
0.0ms	eps	@	0	(*.f64 eps (fma.f64 2 x eps))
0.0ms	x	@	inf	(*.f64 eps (fma.f64 2 x eps))

rewrite182.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1472×	`pow1`
1344×	`add-exp-log`
1344×	`log1p-expm1-u`
1344×	`expm1-log1p-u`
1314×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	159	15
2	1818	15

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 eps (fma.f64 2 x eps))

Outputs
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps (.f64 2 x)) (*.f64 eps eps))
(-.f64 (+.f64 1 (*.f64 eps (fma.f64 2 x eps))) 1)
(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 1)
(pow.f64 (cbrt.f64 (*.f64 eps (fma.f64 2 x eps))) 3)
(pow.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))) 2)
(sqrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 2))
(log.f64 (pow.f64 (exp.f64 eps) (fma.f64 2 x eps)))
(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
(expm1.f64 (log1p.f64 (*.f64 eps (fma.f64 2 x eps))))
(exp.f64 (log.f64 (*.f64 eps (fma.f64 2 x eps))))
(log1p.f64 (expm1.f64 (*.f64 eps (fma.f64 2 x eps))))

simplify126.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1576×	`fma-def`
1172×	`log-prod`
650×	`*-commutative`
638×	`associate-r`
626×	`distribute-lft-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	525
1	104	525
2	334	525
3	2351	525
4	5603	525

Stop Event

1×	node limit

Counts

37 → 19

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps (.f64 2 x)) (*.f64 eps eps))
(-.f64 (+.f64 1 (*.f64 eps (fma.f64 2 x eps))) 1)
(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 1)
(pow.f64 (cbrt.f64 (*.f64 eps (fma.f64 2 x eps))) 3)
(pow.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))) 2)
(sqrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 2))
(log.f64 (pow.f64 (exp.f64 eps) (fma.f64 2 x eps)))
(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
(expm1.f64 (log1p.f64 (*.f64 eps (fma.f64 2 x eps))))
(exp.f64 (log.f64 (*.f64 eps (fma.f64 2 x eps))))
(log1p.f64 (expm1.f64 (*.f64 eps (fma.f64 2 x eps))))

Outputs
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 eps 2)
(*.f64 eps eps)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(*.f64 eps (fma.f64 2 x eps))
(+.f64 (.f64 eps (.f64 2 x)) (*.f64 eps eps))
(*.f64 eps (fma.f64 2 x eps))
(-.f64 (+.f64 1 (*.f64 eps (fma.f64 2 x eps))) 1)
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 (*.f64 eps (fma.f64 2 x eps)) 1)
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 (cbrt.f64 (*.f64 eps (fma.f64 2 x eps))) 3)
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3) 1/3)
(*.f64 eps (fma.f64 2 x eps))
(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))) 2)
(*.f64 eps (fma.f64 2 x eps))
(sqrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 2))
(*.f64 eps (fma.f64 2 x eps))
(log.f64 (pow.f64 (exp.f64 eps) (fma.f64 2 x eps)))
(*.f64 eps (fma.f64 2 x eps))
(cbrt.f64 (pow.f64 (*.f64 eps (fma.f64 2 x eps)) 3))
(*.f64 eps (fma.f64 2 x eps))
(expm1.f64 (log1p.f64 (*.f64 eps (fma.f64 2 x eps))))
(*.f64 eps (fma.f64 2 x eps))
(exp.f64 (log.f64 (*.f64 eps (fma.f64 2 x eps))))
(*.f64 eps (fma.f64 2 x eps))
(log1p.f64 (expm1.f64 (*.f64 eps (fma.f64 2 x eps))))
(*.f64 eps (fma.f64 2 x eps))

eval3.0ms (0.1%)

Compiler: Compiled 147 to 90 computations (38.8% saved)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	3	20

Accurracy

100.0%

Counts

20 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	65.5%	(.f64 eps (.f64 2 x))
▶	70.2%	(*.f64 eps eps)
▶	100.0%	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	65.5%	(.f64 eps (.f64 2 x))
▶	70.2%	(*.f64 eps eps)

Compiler

Compiled 46 to 30 computations (34.8% saved)

localize120.0ms (4.8%)

Compiler: Compiled 41 to 20 computations (51.2% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	65.5%	(.f64 eps (.f64 2 x))
✓	70.2%	(*.f64 eps eps)

Compiler

Compiled 57 to 34 computations (40.4% saved)

regimes13.0ms (0.5%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(*.f64 eps (fma.f64 2 x eps))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

Calls

3 calls:

5.0ms	eps
4.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`

Compiler

Compiled 51 to 31 computations (39.2% saved)

regimes20.0ms (0.8%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))

Outputs
(.f64 eps (.f64 2 x))
(*.f64 eps eps)
(.f64 eps (.f64 2 x))

Calls

2 calls:

10.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
93.8%	3	`x`
88.3%	3	`eps`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes7.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)

Outputs
(*.f64 eps eps)

Calls

2 calls:

4.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
70.2%	1	`eps`
70.2%	1	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch41.0ms (1.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
24.0ms	9.51530025731175e-104	4.263092851582244e-100
17.0ms	-2.0138903734753365e-81	-8.925878385525517e-82

Results

20.0ms	115×	body	256	valid
11.0ms	71×	body	512	valid
8.0ms	22×	body	1024	valid

Compiler

Compiled 198 to 142 computations (28.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`
2×	`+-commutative`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	77
1	28	77

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(+.f64 (*.f64 (*.f64 2 x) eps) (*.f64 eps eps))

(if (<=.f64 x -8202190217936295/8543948143683640329580086824678208458410818089426611079788166431288878903122562200091848347746304) (*.f64 eps (*.f64 2 x)) (if (<=.f64 x 71416136230965/4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352) (*.f64 eps eps) (*.f64 eps (*.f64 2 x))))

(*.f64 eps eps)

Outputs
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 x) eps))
(if (<=.f64 x -8202190217936295/8543948143683640329580086824678208458410818089426611079788166431288878903122562200091848347746304) (.f64 eps (.f64 2 x)) (if (<=.f64 x 71416136230965/4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(if (or (<=.f64 x -8202190217936295/8543948143683640329580086824678208458410818089426611079788166431288878903122562200091848347746304) (not (<=.f64 x 71416136230965/4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352))) (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(*.f64 eps eps)

Compiler

Compiled 35 to 23 computations (34.3% saved)

soundness303.0ms (12%)

Rules

1576×	`fma-def`
1576×	`fma-def`
1472×	`pow1`
1344×	`add-exp-log`
1344×	`log1p-expm1-u`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	21	25
2	52	25
3	164	25
4	652	15
5	2899	15
0	8	15
1	159	15
2	1818	15
0	43	525
1	104	525
2	334	525
3	2351	525
4	5603	525
0	43	525
1	104	525
2	334	525
3	2351	525
4	5603	525

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 174 to 73 computations (58% saved)

end0.0ms (0%)

preprocess34.0ms (1.4%)

Compiler: Compiled 84 to 50 computations (40.5% saved)

analyze0.0ms (0%)

sample1.5s (59.1%)

preprocess104.0ms (4.1%)

simplify30.0ms (1.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize27.0ms (1.1%)

series3.0ms (0.1%)

rewrite182.0ms (7.2%)

simplify126.0ms (5%)

eval3.0ms (0.1%)

prune4.0ms (0.2%)

localize120.0ms (4.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes13.0ms (0.5%)

regimes20.0ms (0.8%)

regimes7.0ms (0.3%)

bsearch41.0ms (1.6%)

simplify6.0ms (0.2%)

soundness303.0ms (12%)

end0.0ms (0%)

preprocess34.0ms (1.4%)

Profiling