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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.5s (29.3%)

Memory

45.8MiB live, 1 928.4MiB allocated

Samples

559.0ms	5 197×	0	valid
436.0ms	2 485×	1	valid
121.0ms	574×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 814.0ms

ival-pow2: 372.0ms (45.7% of total)

ival-<=: 149.0ms (18.3% of total)

adjust: 99.0ms (12.2% of total)

ival-add: 98.0ms (12% of total)

ival-sub: 53.0ms (6.5% of total)

ival-and: 23.0ms (2.8% of total)

exact: 17.0ms (2.1% of total)

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

Bogosity

explain157.0ms (3%)

Memory

-11.8MiB live, 159.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
80	3	(-8.460730579486052e-39 8.375851622852277e-286)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`eps`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	83	0

Confusion

	Predicted +	Predicted -
+	80	1
-	3	172

Precision

0.963855421686747

Recall

0.9876543209876543

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	80	0	1
-	3	0	172

Precision?

0.963855421686747

Recall?

0.9876543209876543

Freqs

test

number	freq
0	173
1	83

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms	312×	0	valid
18.0ms	152×	1	valid
8.0ms	48×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-pow2: 14.0ms (52.6% of total)

adjust: 4.0ms (15% of total)

ival-add: 4.0ms (15% of total)

ival-sub: 3.0ms (11.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess362.0ms (6.9%)

Memory

1.8MiB live, 196.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.8%	(-.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)

simplify206.0ms (3.9%)

Memory

22.8MiB live, 212.6MiB 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)

localize64.0ms (1.2%)

Memory

-31.1MiB live, 58.9MiB 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	0.01953125	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	18.05911704338284	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

20.0ms	24×	2	valid
9.0ms	76×	1	valid
9.0ms	156×	0	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-pow2: 22.0ms (76.9% of total)

adjust: 2.0ms (7% of total)

ival-add: 2.0ms (7% of total)

ival-sub: 2.0ms (7% 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

6.8MiB live, 6.8MiB 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))

simplify127.0ms (2.4%)

Memory

-2.2MiB live, 150.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	390

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

rewrite150.0ms (2.9%)

Memory

4.7MiB live, 236.6MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	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)) (pow.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.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 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 eps x) #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (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 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #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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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x eps) (*.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 x eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 x eps) (fma.f64 (-.f64 eps x) eps (.f64 x x))) (.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)) #s(literal 2 binary64)) (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (+.f64 eps x) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(fma.f64 (.f64 eps (sqrt.f64 (+.f64 eps x))) (sqrt.f64 (+.f64 eps x)) (.f64 (+.f64 eps x) x))
(fma.f64 (.f64 eps (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (*.f64 (+.f64 eps x) x))
(fma.f64 (.f64 x (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (*.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 eps (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (+.f64 eps x) x))
(fma.f64 (.f64 x (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (*.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (.f64 (+.f64 eps x) eps))
(fma.f64 (.f64 (sqrt.f64 x) (+.f64 eps x)) (sqrt.f64 x) (.f64 (+.f64 eps x) eps))
(fma.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 1/2 binary64)) (*.f64 (+.f64 eps x) eps))
(fma.f64 (sqrt.f64 (+.f64 eps x)) (.f64 (sqrt.f64 (+.f64 eps x)) eps) (.f64 (+.f64 eps x) x))
(fma.f64 (sqrt.f64 (+.f64 eps x)) (.f64 (sqrt.f64 (+.f64 eps x)) x) (.f64 (+.f64 eps x) eps))
(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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) x) (*.f64 (+.f64 eps x) eps))
(fma.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x 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)))) (fma.f64 (+.f64 eps x) eps (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x 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 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x 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 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x 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))) (fma.f64 eps eps (.f64 x 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) (fma.f64 eps eps (*.f64 x 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 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x 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))) (fma.f64 (-.f64 eps x) eps (*.f64 x 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) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (log.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x 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) (fma.f64 eps eps (*.f64 x 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 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x 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 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 eps x) eps (.f64 x 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)

eval110.0ms (2.1%)

Memory: -11.6MiB live, 109.5MiB allocated
Compiler: Compiled 9 940 to 1 152 computations (88.4% saved)

prune9.0ms (0.2%)

Memory

-5.7MiB live, 31.9MiB 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
▶	71.8%	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	66.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
▶	70.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 36 to 25 computations (30.6% saved)

simplify161.0ms (3.1%)

Memory

19.7MiB live, 214.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 eps x)
cost-diff	0	(-.f64 x eps)
cost-diff	0	(*.f64 (-.f64 x eps) (+.f64 eps x))
cost-diff	1920	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 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

22 820×	`lower-fma.f32`
22 816×	`lower-fma.f64`
2 738×	`lower-+.f32`
2 736×	`lower-+.f64`
2 332×	`lower-*.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	119
0	36	106
1	70	106
2	147	106
3	410	103
4	1304	97
5	4641	97
0	8219	97

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

localize136.0ms (2.6%)

Memory

-1.9MiB live, 160.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (neg.f64 x) x)
accuracy	0	(neg.f64 x)
accuracy	0.03125	(/.f64 (+.f64 eps x) (-.f64 x eps))
accuracy	18.06201213574011	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 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	0.00390625	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
accuracy	0	(*.f64 x eps)
accuracy	0.03125	(.f64 (.f64 x eps) #s(literal 2 binary64))
accuracy	21.444903089448214	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	19.229285615923953	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

68.0ms	76×	1	valid
40.0ms	156×	0	valid
10.0ms	24×	2	valid

Compiler

Compiled 107 to 23 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

adjust: 49.0ms (48.9% of total)

ival-pow2: 23.0ms (23% of total)

ival-mult: 14.0ms (14% of total)

ival-add: 7.0ms (7% of total)

ival-sub: 4.0ms (4% of total)

ival-div: 3.0ms (3% of total)

ival-neg: 1.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.5%)

Memory

-10.6MiB live, 35.8MiB allocated

Counts

15 → 324

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 (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())
#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 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 (+ (* -1 (pow x 2)) (pow x 2)) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ x (* -1 x))) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2)) (taylor 0 eps) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 eps)) (taylor 0 eps) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 eps)) (taylor 0 eps) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 eps)) (taylor 0 eps) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<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 1 (taylor 0 eps) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 2 (/ eps x))) (taylor 0 eps) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* eps (+ (* 2 (/ eps (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 eps) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* eps (+ (* eps (+ (* 2 (/ eps (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 eps) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.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 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>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) (taylor inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x))))) (taylor inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ eps x)))) (taylor inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ eps x)))) (taylor inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ eps x)))) (taylor inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 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 1 (taylor inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ eps x)) (* -1 (/ eps x))) (taylor inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (/ eps x) (/ (* eps (- eps (* -1 eps))) (pow x 2)))) (* -1 (/ eps x))) (taylor inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (/ eps x) (/ (* (pow eps 2) (- eps (* -1 eps))) (pow x 3)))) (+ (* -1 (/ eps x)) (* -1 (/ (* eps (- eps (* -1 eps))) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -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 (* -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 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 (* -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 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 (* -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 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 (* -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 (* -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 (* -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>) () ())) ())
#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 (* -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 (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) (patch (fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x)))) (taylor -inf x) (#s(alt (.f64 (-.f64 x eps) (+.f64 eps x)) (patch (.f64 (-.f64 x eps) (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ eps x) 1))) (taylor -inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ eps x) 1))) (taylor -inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ eps x) 1))) (taylor -inf x) (#s(alt (-.f64 x eps) (patch (-.f64 x eps) #<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 1 (taylor -inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (/ eps x)) (* -1 (/ eps x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- eps (* -1 eps))) (* -1 (/ (* eps (- eps (* -1 eps))) x))) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (+ (* -1 (- eps (* -1 eps))) (* -1 (/ (+ (* eps (- eps (* -1 eps))) (/ (* (pow eps 2) (- eps (* -1 eps))) x)) x))) x))) (taylor -inf x) (#s(alt (/.f64 (+.f64 eps x) (-.f64 x eps)) (patch (/.f64 (+.f64 eps x) (-.f64 x eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	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) (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) (* (- x eps) (+ eps x)) (- x eps) (+ eps x) (/ (+ eps x) (- x eps)) (neg x) (* (neg 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) (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) (* (- x eps) (+ eps x)) (- x eps) (+ eps x) (/ (+ eps x) (- x eps)) (neg x) (* (neg 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) (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) (* (- x eps) (+ eps x)) (- x eps) (+ eps x) (/ (+ eps x) (- x eps)) (neg x) (* (neg 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) (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) (* (- x eps) (+ eps x)) (- x eps) (+ eps x) (/ (+ eps x) (- x eps)) (neg x) (* (neg 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) (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) (* (- x eps) (+ eps x)) (- x eps) (+ eps x) (/ (+ eps x) (- x eps)) (neg x) (* (neg x) x))

simplify152.0ms (2.9%)

Memory

4.1MiB live, 190.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 066×	`lower-fma.f64`
12 066×	`lower-fma.f32`
3 784×	`lower-+.f64`
3 784×	`lower-+.f32`
3 256×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	234	2274
1	747	2170
2	2192	2030
3	7689	2029
0	8308	1911

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 312

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))
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(pow x 2)
(+ (* eps (+ x (* -1 x))) (pow x 2))
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2))
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2))
x
(+ x (* -1 eps))
(+ x (* -1 eps))
(+ x (* -1 eps))
x
(+ eps x)
(+ eps x)
(+ eps x)
1
(+ 1 (* 2 (/ eps x)))
(+ 1 (* eps (+ (* 2 (/ eps (pow x 2))) (* 2 (/ 1 x)))))
(+ 1 (* eps (+ (* eps (+ (* 2 (/ eps (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 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))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* -1 (pow eps 2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ x eps)) 1))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1))
(* -1 eps)
(* eps (- (/ x eps) 1))
(* eps (- (/ x eps) 1))
(* eps (- (/ x eps) 1))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
-1
(- (* -1 (/ x eps)) (+ 1 (/ x eps)))
(- (+ (* -1 (/ x eps)) (/ (* x (- (* -1 x) x)) (pow eps 2))) (+ 1 (/ x eps)))
(- (+ (* -1 (/ x eps)) (/ (* (pow x 2) (- (* -1 x) x)) (pow eps 3))) (+ 1 (+ (* -1 (/ (* x (- (* -1 x) x)) (pow eps 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)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* -1 (pow eps 2))
(* (pow eps 2) (- (* -1 (/ (+ x (* -1 x)) eps)) 1))
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1))
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
(* -1 (* eps (+ 1 (* -1 (/ x eps)))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
-1
(- (* -1 (/ (- x (* -1 x)) eps)) 1)
(- (* -1 (/ (- (+ x (/ (* x (- x (* -1 x))) eps)) (* -1 x)) eps)) 1)
(- (* -1 (/ (- (+ x (* -1 (/ (- (* -1 (/ (* (pow x 2) (- x (* -1 x))) eps)) (* x (- x (* -1 x)))) 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 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))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* x (+ eps (* -1 eps))))
(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps)))))
(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps)))))
(* -1 eps)
(- x eps)
(- x eps)
(- x eps)
eps
(+ eps x)
(+ eps x)
(+ eps x)
-1
(- (* -2 (/ x eps)) 1)
(- (* x (- (* -2 (/ x (pow eps 2))) (* 2 (/ 1 eps)))) 1)
(- (* x (- (* x (- (* -2 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) 1)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* 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)))
(* 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) (+ 1 (+ (* -1 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x)))))
x
(* x (+ 1 (* -1 (/ eps x))))
(* x (+ 1 (* -1 (/ eps x))))
(* x (+ 1 (* -1 (/ eps x))))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
1
(- (+ 1 (/ eps x)) (* -1 (/ eps x)))
(- (+ 1 (+ (/ eps x) (/ (* eps (- eps (* -1 eps))) (pow x 2)))) (* -1 (/ eps x)))
(- (+ 1 (+ (/ eps x) (/ (* (pow eps 2) (- eps (* -1 eps))) (pow x 3)))) (+ (* -1 (/ eps x)) (* -1 (/ (* eps (- eps (* -1 eps))) (pow x 2)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* 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)))
(* 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) (+ 1 (+ (* -1 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x))))
x
(* -1 (* x (- (/ eps x) 1)))
(* -1 (* x (- (/ eps x) 1)))
(* -1 (* x (- (/ eps x) 1)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
1
(- (+ 1 (/ eps x)) (* -1 (/ eps x)))
(+ 1 (* -1 (/ (+ (* -1 (- eps (* -1 eps))) (* -1 (/ (* eps (- eps (* -1 eps))) x))) x)))
(+ 1 (* -1 (/ (+ (* -1 (- eps (* -1 eps))) (* -1 (/ (+ (* eps (- eps (* -1 eps))) (/ (* (pow eps 2) (- eps (* -1 eps))) x)) x))) x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))

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

rewrite194.0ms (3.7%)

Memory

9.9MiB live, 202.2MiB allocated

Rules

6 898×	`lower-fma.f32`
6 894×	`lower-fma.f64`
4 416×	`lower-/.f32`
4 414×	`lower-/.f64`
3 952×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	110
0	36	110
1	149	100
2	1331	100
0	8471	100

Stop Event

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

Counts

15 → 810

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

eval240.0ms (4.6%)

Memory: -13.6MiB live, 304.1MiB allocated
Compiler: Compiled 37 806 to 3 105 computations (91.8% saved)

prune33.0ms (0.6%)

Memory

-6.6MiB live, 78.9MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 326	3	1 329
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 328	5	1 333

Accuracy

100.0%

Counts

1 333 → 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 #s(literal 2 binary64) x) eps (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	66.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
✓	70.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	37.7%	#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 28 to 27 computations (3.6% saved)

simplify162.0ms (3.1%)

Memory

24.8MiB live, 132.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

22 820×	`lower-fma.f32`
22 818×	`lower-fma.f64`
2 738×	`lower-+.f64`
2 738×	`lower-+.f32`
2 332×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	84
0	27	82
1	60	79
2	138	79
3	401	79
4	1297	65
5	4637	65
0	8160	60

Stop Event

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

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps)))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps
(*.f64 eps eps)

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

localize93.0ms (1.8%)

Memory

-3.2MiB live, 115.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 eps eps)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps)))
accuracy	0.0078125	(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
accuracy	0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	21.444903089448214	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
accuracy	39.88169564357666	#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

Samples

47.0ms	76×	1	valid
24.0ms	156×	0	valid
9.0ms	24×	2	valid

Compiler

Compiled 70 to 22 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

adjust: 31.0ms (48.4% of total)

ival-mult: 12.0ms (18.7% of total)

ival-pow2: 7.0ms (10.9% of total)

ival-add: 6.0ms (9.4% of total)

ival-sub: 4.0ms (6.2% of total)

ival-div: 3.0ms (4.7% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory

16.4MiB live, 16.4MiB allocated

Counts

7 → 144

Calls

Call 1

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

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

Calls

6 calls:

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

simplify135.0ms (2.6%)

Memory

-1.3MiB live, 126.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 984×	`lower-fma.f64`
13 984×	`lower-fma.f32`
2 374×	`lower--.f64`
2 374×	`lower--.f32`
2 130×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	1753
1	142	1000
2	421	786
3	1296	786
4	3445	786
5	7611	786
0	8442	715

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

rewrite191.0ms (3.6%)

Memory

-3.0MiB live, 156.0MiB allocated

Rules

6 042×	`lower-fma.f32`
6 040×	`lower-fma.f64`
4 472×	`lower-/.f64`
4 472×	`lower-/.f32`
3 790×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	74
0	27	72
1	141	61
2	1361	61
0	8468	59

Stop Event

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

Counts

7 → 73

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps)))
(*.f64 eps eps)

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

eval21.0ms (0.4%)

Memory: -1.1MiB live, 36.4MiB allocated
Compiler: Compiled 2 671 to 275 computations (89.7% saved)

prune12.0ms (0.2%)

Memory

-12.4MiB live, 25.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	231	5	236

Accuracy

100.0%

Counts

236 → 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 #s(literal 2 binary64) x) eps (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
✓	66.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
✓	70.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	37.7%	#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 90 to 56 computations (37.8% saved)

regimes9.0ms (0.2%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) 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 (fma.f64 x #s(literal 2 binary64) eps) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps)))
(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (/.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (neg.f64 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:

3.0ms	eps
3.0ms	x
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)

regimes6.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) 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 #s(literal 2 binary64) 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
92.8%	3	`x`
87.8%	3	`eps`
97.7%	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)

regimes7.0ms (0.1%)

Memory

-38.8MiB live, 8.0MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))
#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:

4.0ms	eps
2.0ms	x
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
70.0%	1	`eps`
70.0%	1	`x`
70.0%	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)

regimes4.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

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
37.7%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
37.7%	1	`x`
37.7%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5e-324

Compiler

Compiled 12 to 12 computations (0% saved)

simplify23.0ms (0.4%)

Memory

-3.7MiB live, 35.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`-commutative-binary64-.f64`
6×	`+-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	31	91
1	37	91
2	41	91
3	43	91
4	44	91

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))
(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 #s(literal 2 binary64) 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))
#s(approx (+ (* (* (- x eps) (+ eps x)) (/ (+ eps x) (- x eps))) (* (neg x) x)) #s(literal 0 binary64))

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

soundness868.0ms (16.5%)

Memory

29.2MiB live, 409.8MiB allocated

Rules

12 066×	`lower-fma.f64`
12 066×	`lower-fma.f32`
9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
6 898×	`lower-fma.f32`

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
0	22	110
0	36	110
1	149	100
2	1331	100
0	8471	100
0	234	2274
1	747	2170
2	2192	2030
3	7689	2029
0	8308	1911
0	69	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	390

Stop Event

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

Compiler

Compiled 81 to 55 computations (32.1% saved)

preprocess41.0ms (0.8%)

Memory: 17.0MiB live, 66.6MiB allocated
Compiler: Compiled 88 to 52 computations (40.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (29.3%)

explain157.0ms (3%)

preprocess362.0ms (6.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify206.0ms (3.9%)

localize64.0ms (1.2%)

series6.0ms (0.1%)

simplify127.0ms (2.4%)

rewrite150.0ms (2.9%)

eval110.0ms (2.1%)

prune9.0ms (0.2%)

simplify161.0ms (3.1%)

localize136.0ms (2.6%)

series24.0ms (0.5%)

simplify152.0ms (2.9%)

rewrite194.0ms (3.7%)

eval240.0ms (4.6%)

prune33.0ms (0.6%)

simplify162.0ms (3.1%)

localize93.0ms (1.8%)

series9.0ms (0.2%)

simplify135.0ms (2.6%)

rewrite191.0ms (3.6%)

eval21.0ms (0.4%)

prune12.0ms (0.2%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify23.0ms (0.4%)

soundness868.0ms (16.5%)

preprocess41.0ms (0.8%)

end0.0ms (0%)

Profiling