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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

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 25 to 18 computations (28% saved)

sample1.3s (24.8%)

Memory

35.5MiB live, 1 531.2MiB allocated

Samples

501.0ms	5 239×	0	valid
354.0ms	2 509×	1	valid
83.0ms	508×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 720.0ms

ival-pow2: 297.0ms (41.3% of total)

ival-<=: 125.0ms (17.4% of total)

ival-add: 102.0ms (14.2% of total)

ival-sub: 82.0ms (11.4% of total)

adjust: 73.0ms (10.1% of total)

ival-and: 21.0ms (2.9% of total)

exact: 16.0ms (2.2% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain102.0ms (1.9%)

Memory

-1.6MiB live, 157.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
80	-	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	-	`eps`
0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	-	-	`(+.f64 x eps)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	80	0

Confusion

	Predicted +	Predicted -
+	80	0
-	0	176

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	80	0	0
-	0	0	176

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	176
1	80

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

21.0ms	324×	0	valid
17.0ms	156×	1	valid
5.0ms	32×	2	valid

Compiler

Compiled 61 to 25 computations (59% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-pow2: 16.0ms (58.5% of total)

ival-add: 4.0ms (14.6% of total)

adjust: 3.0ms (11% of total)

ival-sub: 3.0ms (11% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess472.0ms (8.7%)

Memory

-18.2MiB live, 414.5MiB allocated

Algorithm

1×	egg-herbie

Rules

18 770×	`lower-fma.f64`
18 770×	`lower-fma.f32`
2 836×	`lower-*.f64`
2 836×	`lower-*.f32`
2 498×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	45	47
2	149	45
3	542	35
4	1660	35
5	3800	35
6	5269	35
7	5989	35
8	6216	35
9	6322	35
10	6343	35
11	6343	35
12	6343	35
13	6343	35
14	6434	35
15	6762	35
16	7560	35
17	7996	35
0	7	9
0	11	9
1	16	9
2	36	9
3	96	9
4	276	7
5	861	7
6	2374	7
7	4277	7
8	5921	7
9	6913	7
10	7338	7
11	7606	7
12	7612	7
13	7612	7
0	8047	6

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 eps (+.f64 eps (+.f64 x x)))

Compiler

Compiled 11 to 7 computations (36.4% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.6%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify306.0ms (5.7%)

Memory

15.0MiB live, 331.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	512	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
cost-diff	5952	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Rules

18 770×	`lower-fma.f64`
18 770×	`lower-fma.f32`
2 836×	`lower-*.f64`
2 836×	`lower-*.f32`
2 498×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	16	23
2	36	23
3	96	23
4	276	21
5	861	21
6	2374	21
7	4277	21
8	5921	21
9	6913	21
10	7338	21
11	7606	21
12	7612	21
13	7612	21
0	8047	20

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 eps (+.f64 eps (+.f64 x x)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(*.f64 (+.f64 x eps) (+.f64 x eps))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)

localize59.0ms (1.1%)

Memory

-2.9MiB live, 47.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 x eps)
accuracy	0.0234375	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	16.208030567065837	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

30.0ms	78×	1	valid
12.0ms	16×	2	valid
9.0ms	162×	0	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-sub: 23.0ms (53.2% of total)

ival-pow2: 16.0ms (37% of total)

adjust: 2.0ms (4.6% of total)

ival-add: 2.0ms (4.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	inf	(pow (+ x eps) 2)
0.0ms	x	@	inf	(pow x 2)
0.0ms	x	@	0	(pow (+ x eps) 2)
0.0ms	x	@	0	(pow x 2)
0.0ms	eps	@	0	(- (pow (+ x eps) 2) (pow x 2))

simplify189.0ms (3.5%)

Memory

19.8MiB live, 207.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
3 242×	`lower-*.f64`
3 242×	`lower-*.f32`
1 646×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	492
1	214	450
2	574	450
3	1825	438
4	4173	438
5	7244	438
0	8097	390

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Outputs
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow x 2)
(*.f64 x x)
(+ (* 2 (* eps x)) (pow x 2))
(*.f64 x (fma.f64 #s(literal 2 binary64) eps x))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 x x (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* 2 (* eps x))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)

rewrite239.0ms (4.4%)

Memory

4.6MiB live, 355.6MiB allocated

Rules

5 048×	`lower-fma.f64`
5 048×	`lower-fma.f32`
4 066×	`lower-*.f64`
4 066×	`lower-*.f32`
2 090×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5107	20
0	8219	20

Stop Event

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

Counts

4 → 371

Calls

Call 1

Inputs
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(+.f64 x eps)

Outputs
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 x)))
(.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 x))) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(+.f64 (.f64 x (+.f64 x eps)) (.f64 eps (+.f64 x eps)))
(+.f64 (.f64 eps (+.f64 x eps)) (.f64 x (+.f64 x eps)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x eps))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (+.f64 x eps))))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x eps)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 (+.f64 x eps))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(fma.f64 x (+.f64 x eps) (*.f64 eps (+.f64 x eps)))
(fma.f64 eps (+.f64 x eps) (*.f64 x (+.f64 x eps)))
(fma.f64 (+.f64 x eps) x (*.f64 eps (+.f64 x eps)))
(fma.f64 (+.f64 x eps) eps (*.f64 x (+.f64 x eps)))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) eps) (.f64 x (+.f64 x eps)))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) x) (.f64 eps (+.f64 x eps)))
(fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) eps) (*.f64 x (+.f64 x eps)))
(fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x) (*.f64 eps (+.f64 x eps)))
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(fma.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(neg.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (neg.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(neg.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (fma.f64 x x (.f64 eps (-.f64 eps x)))))
(neg.f64 (/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (-.f64 x eps)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x x (.f64 eps (-.f64 eps x))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 x x (.f64 eps (-.f64 eps x)))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps))))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (.f64 (-.f64 x eps) (fma.f64 x x (*.f64 eps eps))))
(/.f64 (exp.f64 (log.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (exp.f64 (log.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (exp.f64 (log.f64 (-.f64 x eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (.f64 eps eps)) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 eps eps) (fma.f64 x x (*.f64 eps eps)))) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x x (*.f64 eps (-.f64 eps x))))
(/.f64 (.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps)))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (fma.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps)) (fma.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))) (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 x x) (-.f64 x eps))) (.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)))))
(/.f64 (.f64 (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (+.f64 x eps) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 x eps)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (+.f64 x eps)) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x))))))
(.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(.f64 (neg.f64 (.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (sqrt.f64 (+.f64 x eps)) (sqrt.f64 (+.f64 x eps)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(.f64 (pow.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x)))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (-.f64 eps x))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 eps (+.f64 x eps) (.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))

eval105.0ms (1.9%)

Memory: -50.2MiB live, 64.7MiB allocated
Compiler: Compiled 14 368 to 1 131 computations (92.1% saved)

prune60.0ms (1.1%)

Memory

-1.2MiB live, 111.8MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	446	3	449
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	447	3	450

Accuracy

100.0%

Counts

450 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
▶	71.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Status

Accuracy

Program

▶

64.7%

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))

▶

100.0%

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))

▶

71.3%

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 23 to 13 computations (43.5% saved)

simplify284.0ms (5.3%)

Memory

-2.9MiB live, 272.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 x (.f64 #s(literal 2 binary64) eps))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
cost-diff	128	(*.f64 #s(literal 2 binary64) eps)
cost-diff	0	(fma.f64 x #s(literal 2 binary64) eps)
cost-diff	0	(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Rules

18 770×	`lower-fma.f32`
18 768×	`lower-fma.f64`
2 836×	`lower-*.f32`
2 828×	`lower-*.f64`
2 498×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	72
0	21	75
1	36	75
2	64	75
3	116	71
4	260	63
5	843	63
6	2379	63
7	4307	63
8	5965	63
9	6968	63
10	7390	63
11	7658	63
12	7664	63
13	7664	63
0	8099	63

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
eps
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
(.f64 x (.f64 #s(literal 2 binary64) eps))
x
(*.f64 #s(literal 2 binary64) eps)
#s(literal 2 binary64)
eps

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x (+.f64 x eps))))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(*.f64 eps (+.f64 x (+.f64 x eps)))
eps
(fma.f64 x #s(literal 2 binary64) eps)
(+.f64 x (+.f64 x eps))
x
#s(literal 2 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x x)))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(*.f64 eps (+.f64 x x))
x
(*.f64 #s(literal 2 binary64) eps)
(+.f64 eps eps)
#s(literal 2 binary64)
eps

localize68.0ms (1.3%)

Memory

9.7MiB live, 47.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 x (.f64 #s(literal 2 binary64) eps))
accuracy	0	(*.f64 #s(literal 2 binary64) eps)
accuracy	22.578919396219987	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
accuracy	0	(fma.f64 x #s(literal 2 binary64) eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
accuracy	0.015625	(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
accuracy	0	(*.f64 eps eps)
accuracy	18.391036273901925	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

39.0ms	162×	0	valid
13.0ms	78×	1	valid
4.0ms	16×	2	valid

Compiler

Compiled 59 to 15 computations (74.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 7.0ms (33.2% of total)

ival-pow2: 6.0ms (28.4% of total)

adjust: 3.0ms (14.2% of total)

ival-add: 3.0ms (14.2% of total)

ival-sub: 2.0ms (9.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

8 → 168

Calls

Call 1

Inputs
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (patch (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())

Outputs
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (/ eps x))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -2 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor -inf eps) (#s(alt (.f64 #s(literal 2 binary64) eps) (patch (.f64 #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf eps) (#s(alt (.f64 x (.f64 #s(literal 2 binary64) eps)) (patch (.f64 x (.f64 #s(literal 2 binary64) eps)) #<representation binary64>) () ())) ())

Calls

42 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(* x (* 2 eps))
1.0ms	eps	@	0	(* eps (+ (* x 2) eps))
0.0ms	x	@	inf	(* x (* 2 eps))
0.0ms	x	@	0	(* x (* 2 eps))
0.0ms	eps	@	inf	(* x (* 2 eps))

simplify143.0ms (2.6%)

Memory

14.2MiB live, 132.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`lower-*.f64`
4 690×	`lower-*.f32`
2 808×	`lower-fma.f64`
2 808×	`lower-fma.f32`
1 166×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	1038
1	121	894
2	287	894
3	744	894
4	1879	894
5	3585	894
6	5322	894
7	6384	894
8	6969	894
0	8124	804

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 165

Calls

Call 1

Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))

Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))

rewrite275.0ms (5.1%)

Memory

-13.7MiB live, 262.2MiB allocated

Rules

7 608×	`lower-fma.f32`
7 606×	`lower-fma.f64`
4 552×	`lower-*.f32`
4 544×	`lower-*.f64`
2 864×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	81	65
2	547	65
3	6813	65
0	8378	65

Stop Event

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

Counts

8 → 139

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
(*.f64 #s(literal 2 binary64) eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
(.f64 x (.f64 #s(literal 2 binary64) eps))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps)))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(+.f64 (.f64 eps eps) (.f64 x (*.f64 eps #s(literal 2 binary64))))
(+.f64 (.f64 x (.f64 eps #s(literal 2 binary64))) (*.f64 eps eps))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(fma.f64 x (.f64 eps #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 eps eps (.f64 x (.f64 eps #s(literal 2 binary64))))
(fma.f64 eps (.f64 x #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 x eps) (.f64 eps eps))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(fma.f64 (.f64 x eps) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 eps #s(literal 2 binary64))) (*.f64 eps eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 x (.f64 eps #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
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(/.f64 (.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal 64 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 64 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 64 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (fma.f64 (.f64 eps eps) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (fma.f64 x (.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal -1 binary64))
(.f64 (fma.f64 x #s(literal 2 binary64) eps) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(.f64 (fma.f64 x #s(literal 2 binary64) eps) (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (.f64 (fma.f64 x #s(literal 2 binary64) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))))
(.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (/.f64 (fma.f64 x #s(literal 2 binary64) eps) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) eps))
(.f64 (neg.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))))
(.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -2 binary64) (neg.f64 (neg.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))) (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps)))
(.f64 (fma.f64 eps eps (.f64 #s(literal -4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (*.f64 eps eps))) (fma.f64 x #s(literal 2 binary64) eps))
(.f64 (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 eps (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 64 binary64)))) (fma.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (-.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)) (.f64 eps (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (fma.f64 x #s(literal 2 binary64) eps) (.f64 (*.f64 x x) #s(literal 4 binary64))))
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 eps #s(literal 2 binary64))))
(.f64 x (.f64 eps #s(literal 2 binary64)))
(.f64 eps (.f64 x #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x eps))
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(.f64 (.f64 x #s(literal 2 binary64)) eps)
(.f64 (.f64 x eps) #s(literal 2 binary64))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))

eval28.0ms (0.5%)

Memory: 14.1MiB live, 51.0MiB allocated
Compiler: Compiled 4 653 to 396 computations (91.5% saved)

prune27.0ms (0.5%)

Memory

10.0MiB live, 48.1MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	303	4	307

Accuracy

100.0%

Counts

307 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
✓	64.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	71.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 34 to 19 computations (44.1% saved)

simplify315.0ms (5.8%)

Memory

-3.0MiB live, 360.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
cost-diff	128	(*.f64 x #s(literal 2 binary64))
cost-diff	192	(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))

Rules

18 770×	`lower-fma.f32`
18 768×	`lower-fma.f64`
2 836×	`lower-*.f32`
2 832×	`lower-*.f64`
2 498×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
0	15	35
1	27	35
2	57	35
3	111	35
4	256	31
5	823	31
6	2349	31
7	4272	31
8	5905	31
9	6904	31
10	7325	31
11	7593	31
12	7599	31
13	7599	31
0	8034	28

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
eps
(*.f64 eps eps)

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x (+.f64 x eps))))
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
x
#s(literal 2 binary64)
eps
(*.f64 eps eps)

localize48.0ms (0.9%)

Memory

-21.1MiB live, 87.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0	(*.f64 eps eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
accuracy	0.00390625	(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))

Samples

13.0ms	162×	0	valid
12.0ms	78×	1	valid
6.0ms	16×	2	valid

Compiler

Compiled 29 to 13 computations (55.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-pow2: 7.0ms (32.1% of total)

ival-add: 6.0ms (27.5% of total)

ival-mult: 5.0ms (22.9% of total)

adjust: 2.0ms (9.2% of total)

ival-sub: 2.0ms (9.2% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())
#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())

Outputs
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) (patch (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* x 2)
0.0ms	x	@	0	(+ (* (* x 2) eps) (* eps eps))
0.0ms	x	@	-inf	(* x 2)
0.0ms	x	@	0	(* x 2)
0.0ms	x	@	inf	(+ (* (* x 2) eps) (* eps eps))

simplify133.0ms (2.5%)

Memory

11.0MiB live, 175.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 314×	`lower-fma.f64`
4 314×	`lower-fma.f32`
3 424×	`lower-*.f64`
3 424×	`lower-*.f32`
1 470×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	444
1	76	372
2	187	372
3	450	372
4	1291	372
5	2373	372
6	4434	372
7	6985	372
0	8156	336

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)

Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)

rewrite417.0ms (7.7%)

Memory

12.7MiB live, 285.6MiB allocated

Rules

8 950×	`lower-fma.f32`
8 948×	`lower-fma.f64`
5 092×	`lower-*.f32`
5 088×	`lower-*.f64`
2 880×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
0	15	30
1	75	30
2	548	30
3	7058	30
0	8723	28

Stop Event

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

Counts

4 → 107

Calls

Call 1

Inputs
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(*.f64 x #s(literal 2 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
(*.f64 eps eps)

Outputs
(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 x eps)))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x eps)) (*.f64 eps eps))
(+.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(-.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(fma.f64 x (.f64 #s(literal 2 binary64) eps) (.f64 eps eps))
(fma.f64 x (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 #s(literal 2 binary64) (.f64 x eps) (.f64 eps eps))
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(fma.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps (.f64 #s(literal 2 binary64) (.f64 x eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 eps (.f64 x #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 eps eps (.f64 #s(literal 2 binary64) (.f64 x eps)))
(fma.f64 eps (/.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x eps)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x eps)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 x eps) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 eps eps))
(fma.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (/.f64 (.f64 eps eps) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 #s(literal 2 binary64) eps)) (*.f64 eps eps))
(fma.f64 (.f64 x (.f64 #s(literal 2 binary64) (.f64 x eps))) (/.f64 (.f64 #s(literal 2 binary64) eps) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 eps (.f64 #s(literal 2 binary64) (.f64 x eps))) (/.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 eps (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 #s(literal 2 binary64) (.f64 x eps)))
(fma.f64 (/.f64 eps eps) (/.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 eps eps) eps) (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 x eps) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 x #s(literal 2 binary64)) eps) (/.f64 (.f64 eps (.f64 #s(literal 2 binary64) (.f64 x eps))) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 x x) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x eps)) eps) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x eps)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) eps) (/.f64 (.f64 eps eps) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 x (.f64 #s(literal 2 binary64) (.f64 x eps))) eps) (/.f64 (.f64 #s(literal 2 binary64) eps) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 eps (.f64 (.f64 x x) #s(literal 4 binary64))) eps) (/.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 eps (.f64 #s(literal 2 binary64) (.f64 x eps))) eps) (/.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
(fma.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(fma.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (fma.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x #s(literal 2 binary64) eps))) (neg.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(neg.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))))
(neg.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (neg.f64 (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(neg.f64 (/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(neg.f64 (/.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 eps eps) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (neg.f64 (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))))
(/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))))
(/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (fma.f64 x (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x))) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 eps eps)))))))
(/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 eps eps)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) #s(literal 1 binary64)) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x))) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 eps eps))))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))))) (neg.f64 (neg.f64 (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))))) (neg.f64 (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))) (fma.f64 x (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (.f64 eps (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 eps (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) #s(literal 1 binary64)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))) (fma.f64 x (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x))) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 eps eps))))))
(/.f64 (.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))) (.f64 (.f64 eps eps) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 eps eps))))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) eps) (-.f64 (.f64 x #s(literal 2 binary64)) eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -1 binary64))
(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
(.f64 (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))))
(.f64 (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64))))))
(.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(.f64 #s(literal 1 binary64) (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(.f64 (neg.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))))
(.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(.f64 (/.f64 (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)) eps) (/.f64 (.f64 eps (-.f64 (.f64 x #s(literal 2 binary64)) eps)) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)))) (.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 eps (.f64 x #s(literal 2 binary64)))))))) (fma.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (-.f64 (.f64 (.f64 eps (.f64 eps eps)) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x))) (.f64 x (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 x (.f64 (.f64 (*.f64 eps eps) #s(literal 4 binary64)) x))))))
(.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))))
(.f64 (/.f64 (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps))))) (fma.f64 x (.f64 (.f64 (.f64 eps eps) #s(literal 4 binary64)) x) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x #s(literal 2 binary64) eps))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps)))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(*.f64 eps eps)
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))

eval42.0ms (0.8%)

Memory: -6.7MiB live, 31.0MiB allocated
Compiler: Compiled 4 469 to 298 computations (93.3% saved)

prune42.0ms (0.8%)

Memory

-16.4MiB live, 79.0MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	179	4	183

Accuracy

100.0%

Counts

183 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
✓	64.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	71.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 71 to 33 computations (53.5% saved)

regimes7.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))

Calls

3 calls:

2.0ms	eps
2.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes8.0ms (0.2%)

Memory

-20.7MiB live, 16.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x (*.f64 #s(literal 2 binary64) eps)))

#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))

Calls

3 calls:

4.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes5.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
91.8%	3	`x`
85.4%	3	`eps`
96.8%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Calls

3 calls:

1.0ms	x
1.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
71.3%	1	`eps`
71.3%	1	`x`
71.3%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	6.03e-321

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify8.0ms (0.1%)

Memory

-24.1MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	87
1	32	87
2	36	87
3	38	87
4	39	87

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 eps #s(literal 2 binary64)))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

soundness600.0ms (11.1%)

Memory

3.1MiB live, 277.1MiB allocated

Rules

9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
7 608×	`lower-fma.f32`
7 606×	`lower-fma.f64`
4 552×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	492
1	214	450
2	574	450
3	1825	438
4	4173	438
5	7244	438
0	8097	390
0	15	65
0	21	65
1	81	65
2	547	65
3	6813	65
0	8378	65

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 74 to 37 computations (50% saved)

preprocess55.0ms (1%)

Memory: 14.3MiB live, 131.3MiB allocated
Compiler: Compiled 110 to 48 computations (56.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (24.8%)

explain102.0ms (1.9%)

preprocess472.0ms (8.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify306.0ms (5.7%)

localize59.0ms (1.1%)

series6.0ms (0.1%)

simplify189.0ms (3.5%)

rewrite239.0ms (4.4%)

eval105.0ms (1.9%)

prune60.0ms (1.1%)

simplify284.0ms (5.3%)

localize68.0ms (1.3%)

series11.0ms (0.2%)

simplify143.0ms (2.6%)

rewrite275.0ms (5.1%)

eval28.0ms (0.5%)

prune27.0ms (0.5%)

simplify315.0ms (5.8%)

localize48.0ms (0.9%)

series3.0ms (0.1%)

simplify133.0ms (2.5%)

rewrite417.0ms (7.7%)

eval42.0ms (0.8%)

prune42.0ms (0.8%)

regimes7.0ms (0.1%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness600.0ms (11.1%)

preprocess55.0ms (1%)

end0.0ms (0%)

Profiling