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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample1.2s (18.9%)

Memory

36.9MiB live, 1 554.5MiB allocated

Samples

426.0ms	5 235×	0	valid
357.0ms	2 522×	1	valid
85.0ms	499×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 590.0ms

ival-pow2: 243.0ms (41.2% of total)

ival-<=: 92.0ms (15.6% of total)

ival-add: 89.0ms (15.1% of total)

adjust: 71.0ms (12% of total)

ival-sub: 54.0ms (9.1% of total)

ival-and: 21.0ms (3.6% of total)

exact: 17.0ms (2.9% of total)

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

Bogosity

explain128.0ms (2%)

Memory

-19.7MiB live, 101.3MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	79	0

Confusion

	Predicted +	Predicted -
+	79	0
-	0	177

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	79	0	0
-	0	0	177

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	177
1	79

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	326×	0	valid
17.0ms	146×	1	valid
6.0ms	40×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-pow2: 14.0ms (55.3% of total)

ival-add: 4.0ms (15.8% of total)

adjust: 3.0ms (11.9% of total)

ival-sub: 3.0ms (11.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess387.0ms (6%)

Memory

16.3MiB live, 245.4MiB 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 (fma.f64 #s(literal 2 binary64) x eps) eps)

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.3%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify535.0ms (8.3%)

Memory

-196.5MiB live, 251.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))
cost-diff	6464	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (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 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)

localize56.0ms (0.9%)

Memory

-15.4MiB live, 23.1MiB 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	16.364685283034355	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

39.0ms	163×	0	valid
8.0ms	73×	1	valid
3.0ms	20×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-pow2: 7.0ms (56.9% 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

5.6MiB live, 5.6MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#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.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 x eps) (patch (+.f64 x eps) #<representation:binary64>) () ())

Outputs
#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 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 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 (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 (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 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 (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 (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 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>) () ())) ())
#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 (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 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 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 (* 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 (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 (+.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 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 (* 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 (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 (+.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 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>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))

simplify136.0ms (2.1%)

Memory

18.1MiB live, 135.7MiB 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	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	378

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite176.0ms (2.7%)

Memory

17.8MiB live, 169.5MiB 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	5109	20
0	8219	20

Stop Event

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

Counts

4 → 371

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (hypot.f64 (+.f64 eps x) x) #s(literal 2 binary64))))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (.f64 (hypot.f64 (+.f64 eps x) x) (.f64 x x))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (hypot.f64 (+.f64 eps x) x) #s(literal 3 binary64)) (pow.f64 (+.f64 eps x) #s(literal 12 binary64)))) (fma.f64 (.f64 (hypot.f64 (+.f64 eps x) x) (.f64 x x)) (-.f64 (.f64 (hypot.f64 (+.f64 eps x) x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
(*.f64 (+.f64 (+.f64 eps x) x) (-.f64 (+.f64 eps x) x))
(*.f64 (pow.f64 (hypot.f64 (+.f64 eps x) x) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))
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(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 eps x)) (.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) x) (*.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps) (*.f64 (+.f64 eps x) x))
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)) x) (*.f64 (+.f64 eps x) eps))
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)) eps) (*.f64 (+.f64 eps x) x))
(fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x))
(fma.f64 (+.f64 eps x) x (*.f64 (+.f64 eps x) eps))
(fma.f64 eps (+.f64 eps x) (*.f64 (+.f64 eps x) x))
(fma.f64 x (+.f64 eps x) (*.f64 (+.f64 eps x) eps))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (+.f64 eps x))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(+.f64 (.f64 (+.f64 eps x) eps) (.f64 (+.f64 eps x) x))
(+.f64 (.f64 (+.f64 eps x) x) (.f64 (+.f64 eps x) eps))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (hypot.f64 eps x) (*.f64 eps x)))
(.f64 (/.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (pow.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 (+.f64 eps x)))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)) (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 (hypot.f64 eps x) (*.f64 eps x))))
(.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) (.f64 (+.f64 eps x) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (hypot.f64 eps x))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (hypot.f64 eps x) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (hypot.f64 (pow.f64 eps #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64))) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)))))
(/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (-.f64 (hypot.f64 eps x) (.f64 eps x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (hypot.f64 eps x) (*.f64 eps x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 eps eps) (hypot.f64 eps x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (hypot.f64 (pow.f64 eps #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (-.f64 (hypot.f64 eps x) (.f64 eps x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 eps x) (-.f64 x eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (exp.f64 (log.f64 (-.f64 x eps))))
(/.f64 (exp.f64 (log.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (exp.f64 (log.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (-.f64 x eps) (hypot.f64 eps x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (hypot.f64 eps x) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 (hypot.f64 (pow.f64 eps #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (hypot.f64 eps x) (*.f64 eps x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (hypot.f64 eps x) (*.f64 eps x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (hypot.f64 eps x) (.f64 eps x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(sqrt.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (+.f64 eps x)))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)

eval51.0ms (0.8%)

Memory: 5.5MiB live, 79.5MiB allocated
Compiler: Compiled 9 522 to 1 153 computations (87.9% saved)

prune29.0ms (0.5%)

Memory

-23.7MiB live, 20.5MiB 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
▶	74.4%	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	66.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
▶	71.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify253.0ms (3.9%)

Memory

-3.1MiB live, 228.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (+.f64 eps x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	0	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
cost-diff	384	(-.f64 (+.f64 eps x) x)
cost-diff	0	(fma.f64 x #s(literal 2 binary64) eps)
cost-diff	0	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
cost-diff	0	(*.f64 x eps)
cost-diff	0	(.f64 (.f64 x eps) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Rules

33 196×	`lower-fma.f32`
33 194×	`lower-fma.f64`
3 080×	`lower-+.f32`
3 076×	`lower-+.f64`
2 274×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	98
0	29	88
1	56	85
2	140	79
3	396	79
4	1321	79
5	4000	79
6	7300	79
0	8188	79

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

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

localize81.0ms (1.3%)

Memory

25.6MiB live, 63.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps x)
accuracy	0.015625	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
accuracy	0.0546875	(+.f64 (+.f64 eps x) x)
accuracy	29.43837589147418	(-.f64 (+.f64 eps x) x)
accuracy	0	(fma.f64 x #s(literal 2 binary64) eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
accuracy	0.015625	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
accuracy	0	(*.f64 x eps)
accuracy	0.02734375	(.f64 (.f64 x eps) #s(literal 2 binary64))
accuracy	21.651026888431975	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	17.968541383911084	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

37.0ms	131×	0	valid
23.0ms	101×	1	valid
8.0ms	24×	2	valid

Compiler

Compiled 85 to 19 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 9.0ms (27.6% of total)

ival-add: 7.0ms (21.5% of total)

ival-pow2: 7.0ms (21.5% of total)

adjust: 5.0ms (15.3% of total)

ival-sub: 3.0ms (9.2% of total)

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

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

exact: 0.0ms (0% of total)

series21.0ms (0.3%)

Memory

-22.1MiB live, 21.6MiB allocated

Counts

12 → 276

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* x eps) 2) (* x eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* x 2) eps) eps) (+ (* x 2) eps) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x))
2.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* x eps) 2) (* x eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* x 2) eps) eps) (+ (* x 2) eps) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x))
2.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* x eps) 2) (* x eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* x 2) eps) eps) (+ (* x 2) eps) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x))
2.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* x eps) 2) (* x eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* x 2) eps) eps) (+ (* x 2) eps) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* x eps) 2) (* x eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* x 2) eps) eps) (+ (* x 2) eps) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x))

simplify115.0ms (1.8%)

Memory

19.5MiB live, 129.5MiB 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	1266
1	159	1266
2	378	1266
3	1065	1266
4	2628	1266
5	4328	1266
6	6778	1266
0	8081	1140

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 240

Calls

Call 1

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

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

rewrite336.0ms (5.2%)

Memory

3.2MiB live, 415.6MiB allocated

Rules

5 340×	`lower-fma.f32`
5 338×	`lower-fma.f64`
4 852×	`lower-/.f64`
4 852×	`lower-/.f32`
4 416×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	89
0	29	88
1	128	80
2	1096	80
0	8138	80

Stop Event

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

Counts

12 → 945

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(.f64 (.f64 eps x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(*.f64 eps x)
(*.f64 x eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) eps) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (pow.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal -1 binary64)))
(.f64 (.f64 eps (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (pow.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)))
(.f64 (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)) #s(literal -1 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (fma.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) eps)) (neg.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps)) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)))) (neg.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) eps) (-.f64 (.f64 #s(literal 2 binary64) x) eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (.f64 eps (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (-.f64 (.f64 #s(literal 2 binary64) x) eps))
(/.f64 (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 eps (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 eps (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 eps eps))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 eps eps))
(fma.f64 eps (.f64 #s(literal 2 binary64) x) (.f64 eps eps))
(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 x (.f64 #s(literal 2 binary64) eps) (.f64 eps eps))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(.f64 (/.f64 (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (-.f64 eps #s(literal 0 binary64))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))) (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (/.f64 (pow.f64 (hypot.f64 (+.f64 eps x) x) #s(literal -1 binary64)) (-.f64 (hypot.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) x))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (hypot.f64 (+.f64 eps x) x) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x eps) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))) (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (/.f64 (pow.f64 (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (hypot.f64 (+.f64 eps x) x) (.f64 (+.f64 eps x) x))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (fma.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (/.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 #s(literal 4 binary64) (.f64 x x)))) (neg.f64 (-.f64 eps (.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (+.f64 eps x))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (hypot.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))))) (neg.f64 (neg.f64 (-.f64 eps #s(literal 0 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 eps #s(literal 0 binary64))) (.f64 (-.f64 eps #s(literal 0 binary64)) (.f64 x x))) (.f64 (-.f64 eps #s(literal 0 binary64)) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 eps eps))) (.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 (/.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) x eps)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64)))) (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 #s(literal 4 binary64) (.f64 x x))) (-.f64 eps (.f64 #s(literal 2 binary64) x)))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (-.f64 x (+.f64 eps x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (-.f64 eps #s(literal 0 binary64)) (hypot.f64 (+.f64 eps x) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 (+.f64 eps x) x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (hypot.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64)))) (neg.f64 (-.f64 eps #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 #s(literal 2 binary64) x)) (-.f64 (.f64 eps eps) (.f64 #s(literal 4 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 eps x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 eps #s(literal 0 binary64)) (hypot.f64 (+.f64 eps x) x)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 (+.f64 eps x) x))) (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps eps (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 2 binary64) x) eps))) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (-.f64 eps #s(literal 0 binary64)) (hypot.f64 (+.f64 eps x) x)))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 x x (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 (+.f64 eps x) x))))
(/.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 (hypot.f64 (+.f64 eps x) x) (*.f64 (+.f64 eps x) x)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 #s(literal 2 binary64) x) eps))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))) (-.f64 eps #s(literal 0 binary64)))
(fma.f64 (/.f64 (+.f64 eps x) (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))) (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (/.f64 (+.f64 eps x) (-.f64 (hypot.f64 (+.f64 eps x) x) (.f64 (+.f64 eps x) x))) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(fma.f64 (/.f64 (+.f64 eps x) (.f64 (/.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) x eps)) (/.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64))))) (/.f64 (+.f64 eps x) (-.f64 eps #s(literal 0 binary64))) (neg.f64 (/.f64 (.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(fma.f64 (/.f64 (+.f64 eps x) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (+.f64 eps x) (pow.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x eps) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(fma.f64 (/.f64 (+.f64 eps x) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 eps #s(literal 0 binary64)))) (.f64 (+.f64 eps x) (fma.f64 #s(literal 2 binary64) x eps)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (fma.f64 eps eps (*.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 x eps) (*.f64 eps x)) #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 eps x))
(fma.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 (+.f64 eps x)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 eps x))
(fma.f64 (fma.f64 x x (*.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) eps)
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 x x (*.f64 (neg.f64 x) x)))) eps)
(fma.f64 (neg.f64 (fma.f64 eps eps (*.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 eps x))) x)
(fma.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))) x)
(fma.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)))) x)
(fma.f64 (neg.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 x eps) (*.f64 eps x)))) x)
(fma.f64 #s(literal 1 binary64) (+.f64 eps x) x)
(fma.f64 (fma.f64 eps eps (*.f64 (neg.f64 x) x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) x)
(fma.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) x)
(fma.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (pow.f64 (-.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 eps x) (*.f64 eps x)) #s(literal -1 binary64)) x)
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 x eps) (*.f64 eps x)) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (pow.f64 (-.f64 eps #s(literal 0 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 #s(literal 2 binary64) x))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (+.f64 eps x))) (/.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 x (+.f64 eps x))))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (.f64 (-.f64 eps #s(literal 0 binary64)) (hypot.f64 (+.f64 eps x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 eps #s(literal 0 binary64)) (hypot.f64 (+.f64 eps x) x))))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (-.f64 eps #s(literal 0 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (hypot.f64 (+.f64 eps x) x)) (-.f64 eps #s(literal 0 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (hypot.f64 (+.f64 eps x) x)) (-.f64 eps #s(literal 0 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) (-.f64 eps #s(literal 0 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 x x) (hypot.f64 (+.f64 eps x) x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) (-.f64 eps #s(literal 0 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 eps #s(literal 0 binary64))) (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64))))
(-.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (/.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(hypot.f64 (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) (sqrt.f64 x))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 eps x)))
(hypot.f64 (sqrt.f64 (+.f64 eps x)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 eps x)))
(+.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 eps #s(literal 0 binary64))) (neg.f64 (/.f64 (*.f64 x x) (-.f64 eps #s(literal 0 binary64)))))
(+.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(+.f64 (*.f64 #s(literal 2 binary64) x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+.f64 x (+.f64 eps x))

eval216.0ms (3.4%)

Memory: -11.6MiB live, 209.9MiB allocated
Compiler: Compiled 37 458 to 2 782 computations (92.6% saved)

prune36.0ms (0.6%)

Memory

27.2MiB live, 74.8MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 253	3	1 256
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 255	5	1 260

Accuracy

100.0%

Counts

1 260 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	66.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x #s(literal 2 binary64)) eps))
✓	71.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 34 to 29 computations (14.7% saved)

simplify232.0ms (3.6%)

Memory

-12.6MiB live, 214.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 eps eps)
cost-diff	0	(*.f64 eps x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
cost-diff	320	(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(+.f64 (+.f64 eps x) x)
cost-diff	0	(*.f64 (+.f64 (+.f64 eps x) x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x #s(literal 2 binary64)) eps))

Rules

18 196×	`lower-fma.f32`
18 194×	`lower-fma.f64`
2 596×	`lower-*.f32`
2 586×	`lower-*.f64`
2 534×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	95
0	27	93
1	45	93
2	80	93
3	126	93
4	267	87
5	825	87
6	2340	87
7	4339	87
8	6015	87
9	7028	87
10	7456	87
11	7725	87
12	7731	87
13	7731	87
0	8047	79

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

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

localize112.0ms (1.7%)

Memory

4.2MiB live, 135.6MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 eps x)
accuracy	0	(*.f64 eps eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
accuracy	0.02734375	(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
accuracy	0	(+.f64 eps x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.015625	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.0546875	(+.f64 (+.f64 eps x) x)
accuracy	0	(.f64 (.f64 x #s(literal 2 binary64)) eps)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	21.651026888431975	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x #s(literal 2 binary64)) eps))

Samples

49.0ms	73×	1	valid
25.0ms	20×	2	valid
19.0ms	163×	0	valid

Compiler

Compiled 75 to 18 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-sub: 18.0ms (38.3% of total)

ival-mult: 12.0ms (25.5% of total)

ival-pow2: 7.0ms (14.9% of total)

ival-add: 6.0ms (12.8% of total)

adjust: 4.0ms (8.5% 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

-11.5MiB live, 26.2MiB allocated

Counts

11 → 240

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* x 2) eps) (* x 2) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ (+ eps x) x) (+ eps x) (+ (* (* eps x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* x 2) eps) (* x 2) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ (+ eps x) x) (+ eps x) (+ (* (* eps x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* x 2) eps) (* x 2) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ (+ eps x) x) (+ eps x) (+ (* (* eps x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* x 2) eps) (* x 2) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ (+ eps x) x) (+ eps x) (+ (* (* eps x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* x 2) eps) (* x 2) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ (+ eps x) x) (+ eps x) (+ (* (* eps x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps))

simplify138.0ms (2.2%)

Memory

17.4MiB live, 175.6MiB 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	1176
1	159	1176
2	376	1176
3	1067	1176
4	2677	1176
5	4376	1176
6	6824	1176
0	8127	1068

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 231

Calls

Call 1

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

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

rewrite260.0ms (4.1%)

Memory

-18.5MiB live, 260.0MiB allocated

Rules

16 484×	`lower-fma.f32`
16 482×	`lower-fma.f64`
5 906×	`lower-*.f32`
5 896×	`lower-*.f64`
3 182×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	87
0	27	85
1	113	85
2	852	85
0	8535	77

Stop Event

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

Counts

11 → 470

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)))
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(.f64 (.f64 eps x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(.f64 #s(literal 2 binary64) (.f64 eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (.f64 eps x))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps) (.f64 eps x))
(fma.f64 eps x (*.f64 eps x))
(fma.f64 x eps (*.f64 eps x))
(+.f64 (.f64 eps x) (.f64 eps x))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3/2 binary64)))
(.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.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)))
(*.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))
(.f64 (.f64 #s(literal 2 binary64) x) (.f64 #s(literal 4 binary64) (.f64 x x)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 3 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))
(+.f64 x x)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(.f64 (.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) eps) (pow.f64 (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (*.f64 (+.f64 eps #s(literal 0 binary64)) eps)) (pow.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 eps (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (+.f64 eps #s(literal 0 binary64))) (pow.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 (-.f64 eps x) x))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (.f64 x x)))))))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) #s(literal -1 binary64)))
(.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (pow.f64 (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) eps))
(.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (.f64 x x)))) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (pow.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x)))) #s(literal -1 binary64))))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (pow.f64 (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) #s(literal -1 binary64))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (+.f64 eps #s(literal 0 binary64))) (*.f64 (pow.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal -1 binary64)) eps))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))) (.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))) (fma.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(/.f64 (-.f64 (.f64 (.f64 eps (+.f64 eps x)) (.f64 eps (+.f64 eps x))) (pow.f64 (.f64 eps x) #s(literal 2 binary64))) (-.f64 (.f64 eps (+.f64 eps x)) (.f64 eps x)))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) eps) (.f64 (+.f64 eps x) eps)) (pow.f64 (.f64 eps x) #s(literal 2 binary64))) (-.f64 (.f64 (+.f64 eps x) eps) (.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (.f64 (.f64 eps (+.f64 eps x)) (.f64 eps (+.f64 eps x)))) (-.f64 (.f64 eps x) (.f64 eps (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (.f64 (.f64 (+.f64 eps x) eps) (.f64 (+.f64 eps x) eps))) (-.f64 (.f64 eps x) (.f64 (+.f64 eps x) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (fma.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))))
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(/.f64 (neg.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))) (.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(/.f64 (*.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) eps) (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (.f64 (+.f64 eps #s(literal 0 binary64)) eps)) (+.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (+.f64 eps #s(literal 0 binary64))) (+.f64 eps #s(literal 0 binary64)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 eps (-.f64 (-.f64 eps x) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps #s(literal 0 binary64)) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (.f64 (+.f64 eps #s(literal 0 binary64)) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 eps) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 eps (hypot.f64 (pow.f64 (+.f64 eps x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps #s(literal 0 binary64)) (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps) (+.f64 eps #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 (-.f64 eps x) x)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (*.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (*.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x)))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x eps)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(neg.f64 (/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x))))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(neg.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (.f64 eps eps) (fma.f64 eps (-.f64 (-.f64 eps x) x) (.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
(fma.f64 (.f64 eps (sqrt.f64 (+.f64 eps x))) (sqrt.f64 (+.f64 eps x)) (.f64 eps x))
(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (.f64 eps (+.f64 eps x)))
(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 eps (.f64 (+.f64 eps x) (-.f64 x eps))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 eps x))
(fma.f64 (.f64 eps (.f64 (+.f64 eps x) (-.f64 eps x))) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) (*.f64 eps x))
(fma.f64 (.f64 eps (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)) (*.f64 eps x))
(fma.f64 (.f64 eps (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (hypot.f64 x eps) (.f64 eps x)) #s(literal -1 binary64)) (*.f64 eps x))
(fma.f64 (/.f64 (.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) eps) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) eps) eps) (/.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 eps x)) eps) (/.f64 (.f64 eps x) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) eps) eps) (/.f64 (.f64 #s(literal 2 binary64) x) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) x) eps) (/.f64 (.f64 #s(literal 2 binary64) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) eps) (/.f64 (.f64 eps eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 #s(literal 4 binary64) eps) (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 eps eps) eps) (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 eps x) eps) (/.f64 (.f64 #s(literal 4 binary64) (.f64 eps x)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) x) eps) (/.f64 (.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 (.f64 x x) eps) (/.f64 (.f64 #s(literal 4 binary64) (.f64 eps eps)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 (.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 eps eps) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) eps) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (/.f64 x eps) (/.f64 (.f64 (.f64 #s(literal 4 binary64) (.f64 eps eps)) x) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 (+.f64 eps x)) (.f64 (sqrt.f64 (+.f64 eps x)) eps) (.f64 eps x))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 #s(literal 2 binary64) eps)) (*.f64 eps eps))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps) (.f64 eps (+.f64 eps x)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps) (.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 eps eps))
(fma.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (.f64 (pow.f64 (-.f64 eps x) #s(literal -1 binary64)) eps) (*.f64 eps x))
(fma.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps) (*.f64 eps x))
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (pow.f64 (-.f64 (hypot.f64 eps x) (.f64 eps x)) #s(literal -1 binary64)) eps) (*.f64 eps x))
(fma.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (pow.f64 (-.f64 (hypot.f64 x eps) (.f64 eps x)) #s(literal -1 binary64)) eps) (*.f64 eps x))
(fma.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 (+.f64 eps x) eps (*.f64 eps x))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 eps eps))
(fma.f64 eps (+.f64 eps x) (*.f64 eps x))
(fma.f64 eps (.f64 #s(literal 2 binary64) x) (.f64 eps eps))
(fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64)))
(fma.f64 eps x (*.f64 eps (+.f64 eps x)))
(fma.f64 eps x (*.f64 (+.f64 eps x) eps))
(fma.f64 x (.f64 #s(literal 2 binary64) eps) (.f64 eps eps))
(fma.f64 x eps (*.f64 eps (+.f64 eps x)))
(fma.f64 x eps (*.f64 (+.f64 eps x) eps))
(-.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (-.f64 (-.f64 eps x) x))) (/.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 eps (-.f64 (-.f64 eps x) x))))
(-.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(+.f64 (.f64 eps (+.f64 eps x)) (.f64 eps x))
(+.f64 (.f64 (+.f64 eps x) eps) (.f64 eps x))
(+.f64 (.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(+.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) (*.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (*.f64 eps x) #s(literal 2 binary64)))
(+.f64 (.f64 eps x) (.f64 eps (+.f64 eps x)))
(+.f64 (.f64 eps x) (.f64 (+.f64 eps x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps))
(*.f64 eps x)
(*.f64 x eps)
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))

eval161.0ms (2.5%)

Memory: -10.6MiB live, 162.0MiB allocated
Compiler: Compiled 11 349 to 1 418 computations (87.5% saved)

prune21.0ms (0.3%)

Memory

26.8MiB live, 63.9MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	699	2	701
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	701	5	706

Accuracy

100.0%

Counts

706 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	66.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	71.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 34 to 27 computations (20.6% saved)

simplify361.0ms (5.6%)

Memory

-31.4MiB live, 288.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

22 440×	`lower-fma.f32`
22 438×	`lower-fma.f64`
3 088×	`lower-*.f32`
3 084×	`lower-*.f64`
3 016×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
0	20	59
1	31	57
2	60	57
3	124	57
4	303	53
5	857	53
6	2678	53
7	4224	53
8	5885	53
9	6697	53
10	7040	53
11	7218	53
12	7220	53
13	7220	53
14	7853	53
15	7917	53
16	7917	53
17	7917	53
0	8206	49

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

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

localize46.0ms (0.7%)

Memory

5.5MiB live, 90.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps x)
accuracy	0	(*.f64 eps x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
accuracy	0.0234375	(fma.f64 (+.f64 eps x) eps (*.f64 eps x))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) eps)
accuracy	21.651026888431975	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))

Samples

15.0ms	73×	1	valid
14.0ms	163×	0	valid
4.0ms	20×	2	valid

Compiler

Compiled 47 to 14 computations (70.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-pow2: 7.0ms (29.3% of total)

ival-add: 5.0ms (20.9% of total)

ival-mult: 5.0ms (20.9% of total)

ival-sub: 4.0ms (16.7% of total)

adjust: 3.0ms (12.5% of total)

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

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

series9.0ms (0.1%)

Memory

24.0MiB live, 24.0MiB 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 (fma.f64 (+.f64 eps x) eps (.f64 eps x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 eps x)) #<representation:binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (.f64 eps x))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (.f64 eps x))) #<representation:binary64>) () ())
#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation:binary64>) () ())
#s(alt (.f64 eps x) (patch (.f64 eps x) #<representation:binary64>) () ())

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

Calls

6 calls:

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

simplify157.0ms (2.5%)

Memory

-29.5MiB live, 171.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 028×	`lower-fma.f64`
5 028×	`lower-fma.f32`
3 486×	`lower-*.f64`
3 486×	`lower-*.f32`
1 364×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	738
1	125	738
2	298	738
3	876	738
4	2222	738
5	4085	738
6	6688	738
0	8044	684

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 150

Calls

Call 1

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

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

rewrite53.0ms (0.8%)

Memory

29.5MiB live, 67.3MiB allocated

Rules

536×	`lower-fma.f32`
534×	`lower-fma.f64`
424×	`lower-*.f32`
420×	`lower-*.f64`
286×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	20	55
1	92	53
0	760	53

Stop Event

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

Counts

7 → 71

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

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

eval29.0ms (0.4%)

Memory: -33.3MiB live, 48.7MiB allocated
Compiler: Compiled 2 256 to 279 computations (87.6% saved)

prune7.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	221	5	226

Accuracy

100.0%

Counts

226 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	66.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	71.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 109 to 59 computations (45.9% saved)

regimes12.0ms (0.2%)

Memory

-13.3MiB live, 25.5MiB allocated

Counts

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

Calls

3 calls:

5.0ms	x
3.0ms	eps
3.0ms	(-.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 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

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

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:

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

Results

Accuracy	Segments	Branch
92.4%	3	`x`
89.3%	3	`eps`
97.6%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB 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
71.9%	1	`eps`
71.9%	1	`x`
71.9%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	4.15183904026e-311

Compiler

Compiled 12 to 12 computations (0% saved)

simplify52.0ms (0.8%)

Memory

-2.6MiB live, 35.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`-commutative-binary64-.f64`
8×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`
2×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	86
1	33	86
2	37	86
3	39	86
4	40	86

Stop Event

1×

saturated

Calls

Call 1

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

soundness906.0ms (14.1%)

Memory

-0.2MiB live, 401.3MiB allocated

Rules

16 484×	`lower-fma.f32`
16 482×	`lower-fma.f64`
9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
5 906×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	87
0	27	85
1	113	85
2	852	85
0	8535	77
0	50	1266
1	159	1266
2	378	1266
3	1065	1266
4	2628	1266
5	4328	1266
6	6778	1266
0	8081	1140
0	19	89
0	29	88
1	128	80
2	1096	80
0	8138	80
0	69	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	378

Stop Event

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

Compiler

Compiled 68 to 51 computations (25% saved)

preprocess53.0ms (0.8%)

Memory: -2.4MiB live, 73.3MiB allocated
Compiler: Compiled 100 to 56 computations (44% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (18.9%)

explain128.0ms (2%)

preprocess387.0ms (6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify535.0ms (8.3%)

localize56.0ms (0.9%)

series6.0ms (0.1%)

simplify136.0ms (2.1%)

rewrite176.0ms (2.7%)

eval51.0ms (0.8%)

prune29.0ms (0.5%)

simplify253.0ms (3.9%)

localize81.0ms (1.3%)

series21.0ms (0.3%)

simplify115.0ms (1.8%)

rewrite336.0ms (5.2%)

eval216.0ms (3.4%)

prune36.0ms (0.6%)

simplify232.0ms (3.6%)

localize112.0ms (1.7%)

series14.0ms (0.2%)

simplify138.0ms (2.2%)

rewrite260.0ms (4.1%)

eval161.0ms (2.5%)

prune21.0ms (0.3%)

simplify361.0ms (5.6%)

localize46.0ms (0.7%)

series9.0ms (0.1%)

simplify157.0ms (2.5%)

rewrite53.0ms (0.8%)

eval29.0ms (0.4%)

prune7.0ms (0.1%)

regimes12.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify52.0ms (0.8%)

soundness906.0ms (14.1%)

preprocess53.0ms (0.8%)

end0.0ms (0%)

Profiling