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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample1.5s (25.6%)

Memory

-108.5MiB live, 1 838.8MiB allocated

Samples

409.0ms	5 191×	0	valid
352.0ms	2 547×	1	valid
114.0ms	518×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 632.0ms

ival-pow2: 277.0ms (43.8% of total)

ival-<=: 100.0ms (15.8% of total)

ival-add: 88.0ms (13.9% of total)

adjust: 71.0ms (11.2% of total)

ival-sub: 56.0ms (8.9% of total)

ival-and: 21.0ms (3.3% of total)

exact: 16.0ms (2.5% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain104.0ms (1.8%)

Memory

0.7MiB live, 121.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
63	1	(-1.7311814095257538e-72 -9.144509724213662e-253)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`eps`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	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	64	0

Confusion

	Predicted +	Predicted -
+	63	0
-	1	192

Precision

0.984375

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	1	0	192

Precision?

0.984375

Recall?

1.0

Freqs

test

number	freq
0	192
1	64

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms	146×	1	valid
19.0ms	338×	0	valid
5.0ms	28×	2	valid

Compiler

Compiled 61 to 25 computations (59% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-pow2: 14.0ms (49.7% of total)

adjust: 7.0ms (24.9% of total)

ival-add: 4.0ms (14.2% of total)

ival-sub: 3.0ms (10.7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess452.0ms (7.9%)

Memory

35.5MiB live, 348.2MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.1%	(-.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)

simplify263.0ms (4.6%)

Memory

-2.4MiB live, 226.6MiB 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)

localize33.0ms (0.6%)

Memory

-4.4MiB live, 44.3MiB 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	0.02734375	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	13.332801731278689	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

15.0ms	169×	0	valid
8.0ms	73×	1	valid
2.0ms	14×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 6.0ms (49% of total)

adjust: 2.0ms (16.3% of total)

ival-add: 2.0ms (16.3% of total)

ival-sub: 2.0ms (16.3% 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	@	inf	(- (pow (+ x eps) 2) (pow x 2))
0.0ms	x	@	0	(pow x 2)
0.0ms	eps	@	0	(- (pow (+ x eps) 2) (pow x 2))

simplify221.0ms (3.9%)

Memory

-16.3MiB live, 229.3MiB 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)

rewrite235.0ms (4.1%)

Memory

14.4MiB live, 251.6MiB 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)))
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(sqrt.f64 (*.f64 (+.f64 x eps) (+.f64 x eps)))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (/.f64 (.f64 x x) (.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(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)))

eval52.0ms (0.9%)

Memory: 4.0MiB live, 78.2MiB allocated
Compiler: Compiled 14 368 to 1 131 computations (92.1% saved)

prune61.0ms (1.1%)

Memory

-17.2MiB live, 103.4MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	445	4	449
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	446	4	450

Accuracy

100.0%

Counts

450 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.1%	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
▶	64.4%	#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)))
▶	76.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 36 to 20 computations (44.4% saved)

simplify340.0ms (5.9%)

Memory

21.8MiB live, 329.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x (+.f64 x eps))
cost-diff	0	(-.f64 eps x)
cost-diff	0	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
cost-diff	384	(+.f64 x (-.f64 eps x))
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

29 718×	`lower-fma.f32`
29 716×	`lower-fma.f64`
3 538×	`lower-*.f32`
3 530×	`lower-*.f64`
2 478×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	101
0	31	97
1	60	97
2	134	92
3	406	82
4	1026	82
5	2271	82
6	5183	82
7	6417	82
8	7501	82
0	8209	82

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

localize87.0ms (1.5%)

Memory

-15.3MiB live, 103.2MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0.0078125	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
accuracy	0.03125	(+.f64 x (+.f64 x eps))
accuracy	28.89697411651997	(+.f64 x (-.f64 eps x))
accuracy	0	(.f64 x (.f64 #s(literal 2 binary64) eps))
accuracy	0	(*.f64 #s(literal 2 binary64) eps)
accuracy	22.791776059678615	#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	0.0078125	(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))
accuracy	0	(*.f64 eps eps)
accuracy	15.070564660634586	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

27.0ms	99×	1	valid
18.0ms	21×	2	valid
17.0ms	136×	0	valid

Compiler

Compiled 88 to 19 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

adjust: 16.0ms (33.5% of total)

ival-mult: 13.0ms (27.2% of total)

ival-add: 7.0ms (14.6% of total)

ival-pow2: 7.0ms (14.6% of total)

ival-sub: 4.0ms (8.4% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

26.8MiB live, 26.8MiB allocated

Counts

13 → 288

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

72 calls:

Time	Variable		Point	Expression
1.0ms	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))

simplify170.0ms (3%)

Memory

-13.2MiB live, 219.8MiB allocated

Algorithm

1×	egg-herbie

Rules

5 680×	`lower-fma.f64`
5 680×	`lower-fma.f32`
3 782×	`lower-*.f64`
3 782×	`lower-*.f32`
1 318×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	1473
1	197	1293
2	491	1293
3	1249	1293
4	2966	1293
5	4223	1293
6	6380	1293
0	8118	1167

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 249

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

rewrite418.0ms (7.3%)

Memory

-9.3MiB live, 434.9MiB allocated

Rules

8 502×	`lower-fma.f32`
8 500×	`lower-fma.f64`
4 408×	`lower-/.f64`
4 408×	`lower-/.f32`
4 234×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	92
0	31	89
1	132	89
2	1106	83
0	9049	83

Stop Event

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

Counts

13 → 936

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

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

eval182.0ms (3.2%)

Memory: 46.4MiB live, 265.9MiB allocated
Compiler: Compiled 37 349 to 2 452 computations (93.4% saved)

prune173.0ms (3%)

Memory

-38.4MiB live, 332.9MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 183	2	1 185
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 185	4	1 189

Accuracy

100.0%

Counts

1 189 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
▶	64.4%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	76.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 33 to 17 computations (48.5% saved)

simplify349.0ms (6.1%)

Memory

27.5MiB live, 287.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

18 196×	`lower-fma.f64`
18 196×	`lower-fma.f32`
2 596×	`lower-*.f32`
2 592×	`lower-*.f64`
2 534×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
0	19	61
1	29	61
2	63	61
3	123	61
4	260	55
5	814	55
6	2320	55
7	4317	55
8	6000	55
9	7006	55
10	7434	55
11	7703	55
12	7709	55
13	7709	55
0	8025	50

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

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

localize91.0ms (1.6%)

Memory

-14.5MiB live, 99.3MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
accuracy	0.0078125	(*.f64 (+.f64 x (+.f64 x eps)) eps)
accuracy	0.03125	(+.f64 x (+.f64 x eps))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) eps)
accuracy	22.791776059678615	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))

Samples

33.0ms	169×	0	valid
31.0ms	73×	1	valid
3.0ms	14×	2	valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

adjust: 22.0ms (56.9% of total)

ival-pow2: 7.0ms (18.1% of total)

ival-add: 5.0ms (12.9% of total)

ival-mult: 4.0ms (10.3% of total)

ival-sub: 2.0ms (5.2% of total)

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

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

series4.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

7 → 156

Calls

Call 1

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

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

39 calls:

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

simplify161.0ms (2.8%)

Memory

-16.3MiB live, 214.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4 622×	`lower-fma.f64`
4 622×	`lower-fma.f32`
3 318×	`lower-*.f64`
3 318×	`lower-*.f32`
1 398×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	876
1	159	768
2	378	768
3	1058	768
4	2682	768
5	4380	768
6	6837	768
0	8135	696

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 147

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

rewrite56.0ms (1%)

Memory

4.4MiB live, 58.7MiB allocated

Rules

414×	`lower-fma.f64`
414×	`lower-fma.f32`
282×	`lower-*.f32`
278×	`lower-*.f64`
218×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	19	55
1	80	55
0	599	52

Stop Event

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

Counts

7 → 88

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x x)))
(+.f64 (.f64 x eps) (.f64 x eps))
(fma.f64 x eps (*.f64 x eps))
(fma.f64 eps x (*.f64 x eps))
(/.f64 (.f64 eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 eps #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) eps) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 0 binary64) eps) #s(literal 0 binary64))
(*.f64 eps (+.f64 x x))
(.f64 #s(literal 2 binary64) (.f64 x eps))
(*.f64 (+.f64 x x) eps)
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(+.f64 x x)
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x (+.f64 x eps))))
(+.f64 (.f64 eps (+.f64 x x)) (.f64 eps eps))
(+.f64 (.f64 x eps) (.f64 (+.f64 x eps) eps))
(+.f64 (.f64 x eps) (.f64 eps (+.f64 x eps)))
(+.f64 (.f64 (+.f64 x eps) eps) (.f64 x eps))
(+.f64 (.f64 eps (+.f64 x eps)) (.f64 x eps))
(fma.f64 x eps (*.f64 (+.f64 x eps) eps))
(fma.f64 x eps (*.f64 eps (+.f64 x eps)))
(fma.f64 eps x (*.f64 (+.f64 x eps) eps))
(fma.f64 eps x (*.f64 eps (+.f64 x eps)))
(fma.f64 eps (+.f64 x x) (*.f64 eps eps))
(fma.f64 eps (+.f64 x eps) (*.f64 x eps))
(fma.f64 #s(literal 2 binary64) (.f64 x eps) (.f64 eps eps))
(fma.f64 (+.f64 x x) eps (*.f64 eps eps))
(fma.f64 (+.f64 x eps) eps (*.f64 x eps))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(/.f64 (.f64 eps (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps)))) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x)))
(/.f64 (.f64 eps (.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps))) eps) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x)))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps)) eps) (-.f64 #s(literal 0 binary64) eps))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(*.f64 (+.f64 x (+.f64 x eps)) eps)
(+.f64 x (+.f64 x eps))
(+.f64 eps (+.f64 x x))
(+.f64 (+.f64 x x) eps)
(+.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) x)
(fma.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) eps)
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) eps)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (+.f64 x eps))
(fma.f64 (pow.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x eps) #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x eps) x)) (-.f64 (+.f64 x eps) x))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps))) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (*.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps)))) (neg.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x))))
(/.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (+.f64 (pow.f64 (+.f64 x x) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 eps (+.f64 x x)))))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x))))
(.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(+.f64 x eps)
(+.f64 eps x)
(exp.f64 (*.f64 (log.f64 (+.f64 x eps)) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) eps)
(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 eps eps (-.f64 (.f64 x x) (*.f64 x eps))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 x eps))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(pow.f64 (+.f64 x eps) #s(literal 1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (pow.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x eps) #s(literal 1/2 binary64)))

eval24.0ms (0.4%)

Memory: -8.3MiB live, 29.9MiB allocated
Compiler: Compiled 2 342 to 236 computations (89.9% saved)

prune35.0ms (0.6%)

Memory

-15.3MiB live, 23.9MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	235	4	239

Accuracy

100.0%

Counts

239 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
✓	64.4%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	76.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 86 to 36 computations (58.1% saved)

regimes8.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

7 → 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 (+.f64 x x) 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)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x 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)) (*.f64 (+.f64 x (+.f64 x eps)) eps))

Calls

3 calls:

3.0ms	eps
3.0ms	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)

regimes6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

4 → 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 (+.f64 x x) 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:

2.0ms	x
2.0ms	eps
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)

regimes7.0ms (0.1%)

Memory

-27.4MiB live, 10.7MiB allocated

Counts

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

Calls

3 calls:

3.0ms	x
2.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
92.1%	3	`x`
89.3%	3	`eps`
96.6%	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

8.4MiB live, 8.4MiB 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	eps
1.0ms	x
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
76.5%	1	`eps`
76.5%	1	`x`
76.5%	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	4.37278536e-316

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
8×	`+-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	86
1	32	86
2	36	86
3	38	86
4	39	86

Stop Event

1×

saturated

Calls

Call 1

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

soundness637.0ms (11.1%)

Memory

12.7MiB live, 290.6MiB allocated

Rules

9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
8 502×	`lower-fma.f32`
8 500×	`lower-fma.f64`
4 408×	`lower-/.f64`

Iterations

Useful iterations: 2 (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	20	92
0	31	89
1	132	89
2	1106	83
0	9049	83

Stop Event

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

Compiler

Compiled 81 to 42 computations (48.1% saved)

preprocess62.0ms (1.1%)

Memory: -2.8MiB live, 115.3MiB allocated
Compiler: Compiled 108 to 48 computations (55.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (25.6%)

explain104.0ms (1.8%)

preprocess452.0ms (7.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify263.0ms (4.6%)

localize33.0ms (0.6%)

series6.0ms (0.1%)

simplify221.0ms (3.9%)

rewrite235.0ms (4.1%)

eval52.0ms (0.9%)

prune61.0ms (1.1%)

simplify340.0ms (5.9%)

localize87.0ms (1.5%)

series14.0ms (0.2%)

simplify170.0ms (3%)

rewrite418.0ms (7.3%)

eval182.0ms (3.2%)

prune173.0ms (3%)

simplify349.0ms (6.1%)

localize91.0ms (1.6%)

series4.0ms (0.1%)

simplify161.0ms (2.8%)

rewrite56.0ms (1%)

eval24.0ms (0.4%)

prune35.0ms (0.6%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness637.0ms (11.1%)

preprocess62.0ms (1.1%)

end0.0ms (0%)

Profiling