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, 0.6MiB 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)

sample1.9s (20.9%)

Memory

43.1MiB live, 1 761.2MiB allocated

Samples

865.0ms	2 521×	1	valid
450.0ms	5 225×	0	valid
92.0ms	510×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-<=: 436.0ms (38.1% of total)

ival-pow2: 302.0ms (26.4% of total)

ival-sub: 159.0ms (13.9% of total)

adjust: 129.0ms (11.3% of total)

ival-add: 72.0ms (6.3% of total)

ival-and: 23.0ms (2% of total)

exact: 18.0ms (1.6% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain181.0ms (2%)

Memory

3.2MiB live, 128.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
83	18	(-7.826263279041486e-42 -2.7448768540186384e-285)	-	`(-.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	101	0

Confusion

	Predicted +	Predicted -
+	83	0
-	18	155

Precision

0.8217821782178217

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	83	0	0
-	18	0	155

Precision?

0.8217821782178217

Recall?

1.0

Freqs

test

number	freq
0	155
1	101

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

52.0ms	318×	0	valid
19.0ms	162×	1	valid
5.0ms	32×	2	valid

Compiler

Compiled 105 to 45 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-pow2: 14.0ms (53.8% of total)

adjust: 4.0ms (15.4% of total)

ival-add: 4.0ms (15.4% of total)

ival-sub: 3.0ms (11.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess957.0ms (10.8%)

Memory

-8.4MiB live, 121.3MiB allocated

Algorithm

1×	egg-herbie

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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify999.0ms (11.3%)

Memory

17.2MiB live, 130.2MiB 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)))

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)

localize653.0ms (7.4%)

Memory

-28.1MiB live, 58.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 x eps)
accuracy	0.02734375	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	18.28524108781746	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

419.0ms	16×	2	valid
165.0ms	81×	1	valid
9.0ms	159×	0	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 585.0ms

ival-add: 575.0ms (98.3% of total)

ival-pow2: 7.0ms (1.2% of total)

adjust: 2.0ms (0.3% of total)

ival-sub: 2.0ms (0.3% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

4 → 23

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

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	x	@	0	((- (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))

simplify133.0ms (1.5%)

Memory

2.6MiB live, 121.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	214	151
2	570	151
3	1802	143
4	4139	143
5	7201	143
0	8049	124

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

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

rewrite225.0ms (2.5%)

Memory

-12.4MiB live, 182.9MiB allocated

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))))
(.f64 (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 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 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 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 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 6 binary64))))
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(.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)

eval80.0ms (0.9%)

Memory: 27.6MiB live, 103.2MiB allocated
Compiler: Compiled 9 307 to 1 150 computations (87.6% saved)

prune61.0ms (0.7%)

Memory

-25.5MiB live, 59.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	372	6	378
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	373	6	379

Accuracy

100.0%

Counts

379 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.8%	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
	63.8%	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
▶	71.4%	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	60.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	69.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 160 to 100 computations (37.5% saved)

simplify178.0ms (2%)

Memory

40.6MiB live, 273.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	512	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
cost-diff	0	(+.f64 (+.f64 eps x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	0	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
cost-diff	384	(-.f64 (+.f64 eps x) x)
cost-diff	0	(*.f64 eps x)
cost-diff	0	(.f64 (.f64 eps x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #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))
cost-diff	0	(fma.f64 #s(literal 2 binary64) x eps)
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	120
0	36	105
1	74	102
2	168	96
3	393	96
4	1590	96
5	5579	96
6	7886	96
0	8089	96

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

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

localize99.0ms (1.1%)

Memory

-15.6MiB live, 190.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps x)
accuracy	0	(*.f64 (neg.f64 x) x)
accuracy	0	(neg.f64 x)
accuracy	23.148828073227993	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
accuracy	0	(+.f64 eps x)
accuracy	0.02734375	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
accuracy	0.03515625	(+.f64 (+.f64 eps x) x)
accuracy	27.58356281384896	(-.f64 (+.f64 eps x) x)
accuracy	0	(*.f64 eps x)
accuracy	0.03125	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	25.11137490485042	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	19.66465128137681	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy	0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.02734375	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

45.0ms	96×	1	valid
29.0ms	140×	0	valid
8.0ms	20×	2	valid

Compiler

Compiled 228 to 46 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-sub: 20.0ms (32.9% of total)

ival-mult: 17.0ms (28% of total)

ival-add: 8.0ms (13.2% of total)

ival-pow2: 7.0ms (11.5% of total)

adjust: 6.0ms (9.9% 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)

series23.0ms (0.3%)

Memory

-15.4MiB live, 23.0MiB allocated

Counts

15 → 28

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (* (neg x) x) (neg x))
2.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (* (neg x) x) (neg x))
2.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (* (neg x) x) (neg x))
2.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (* (neg x) x) (neg x))
2.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (+ eps x) x) (* (- (+ eps x) x) (+ (+ eps x) x)) (+ eps x) (+ (+ eps x) x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (* (neg x) x) (neg x))

simplify194.0ms (2.2%)

Memory

0.4MiB live, 183.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	144
1	226	124
2	606	124
3	1944	124
4	5014	124
0	8224	111

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 26

Calls

Call 1

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

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

rewrite250.0ms (2.8%)

Memory

-26.0MiB live, 294.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	106
0	36	105
1	159	94
2	1357	94
0	9042	94

Stop Event

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

Counts

15 → 1 297

Calls

Call 1

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

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

eval144.0ms (1.6%)

Memory: 19.5MiB live, 167.7MiB allocated
Compiler: Compiled 36 479 to 2 776 computations (92.4% saved)

prune37.0ms (0.4%)

Memory

6.6MiB live, 45.8MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	937	4	941
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	941	6	947

Accuracy

100.0%

Counts

947 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	60.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	69.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	31.6%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 93 to 63 computations (32.3% saved)

simplify209.0ms (2.4%)

Memory

17.2MiB live, 218.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	110
0	31	105
1	58	105
2	109	105
3	207	105
4	461	97
5	1176	97
6	3873	97
7	5997	97
8	7128	97
0	8059	88

Stop Event

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

Calls

Call 1

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

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

localize101.0ms (1.1%)

Memory

-46.0MiB live, 82.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 eps eps)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
accuracy	0.01171875	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
accuracy	0	(+.f64 eps x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.02734375	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.03515625	(+.f64 (+.f64 eps x) x)
accuracy	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	25.11137490485042	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	43.761993488647704	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Samples

43.0ms	159×	0	valid
33.0ms	81×	1	valid
6.0ms	16×	2	valid

Compiler

Compiled 198 to 46 computations (76.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 45.0ms (66.6% of total)

ival-add: 8.0ms (11.8% of total)

ival-pow2: 6.0ms (8.9% of total)

adjust: 4.0ms (5.9% of total)

ival-sub: 2.0ms (3% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

11 → 26

Calls

Call 1

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

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

Calls

6 calls:

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

simplify135.0ms (1.5%)

Memory

11.7MiB live, 126.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	138
1	224	118
2	608	118
3	1932	118
4	4937	118
0	8117	105

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 24

Calls

Call 1

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

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

rewrite186.0ms (2.1%)

Memory

10.1MiB live, 163.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
0	31	93
1	141	93
2	1103	93
0	8478	84

Stop Event

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

Counts

11 → 339

Calls

Call 1

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

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

eval32.0ms (0.4%)

Memory: 13.7MiB live, 49.5MiB allocated
Compiler: Compiled 7 888 to 1 080 computations (86.3% saved)

prune9.0ms (0.1%)

Memory

-20.3MiB live, 17.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	0	0
Picked	1	3	4
Done	0	2	2
Total	261	6	267

Accuracy

100.0%

Counts

267 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	60.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	69.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	31.6%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 93 to 62 computations (33.3% saved)

simplify290.0ms (3.3%)

Memory

25.9MiB live, 183.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	15	34
1	25	34
2	50	34
3	112	34
4	299	32
5	855	32
6	2707	32
7	4252	32
8	5931	32
9	6737	32
10	7080	32
11	7258	32
12	7260	32
13	7260	32
14	7893	32
15	7957	32
16	7957	32
17	7957	32
0	8246	29

Stop Event

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

Calls

Call 1

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

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

localize68.0ms (0.8%)

Memory

-17.5MiB live, 71.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
accuracy	0.00390625	(*.f64 (+.f64 x eps) eps)
accuracy	0.01953125	(fma.f64 x eps (*.f64 (+.f64 x eps) eps))

Samples

44.0ms	159×	0	valid
14.0ms	81×	1	valid
3.0ms	16×	2	valid

Compiler

Compiled 66 to 22 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 36.0ms (71.3% of total)

ival-pow2: 7.0ms (13.9% of total)

ival-add: 4.0ms (7.9% of total)

adjust: 2.0ms (4% of total)

ival-sub: 2.0ms (4% of total)

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

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

series4.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

4 → 20

Calls

Call 1

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

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

Calls

6 calls:

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

simplify126.0ms (1.4%)

Memory

-12.8MiB live, 102.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	98
1	158	88
2	382	88
3	1023	88
4	2573	88
5	4037	88
6	6142	88
7	7613	88
0	8098	83

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 18

Calls

Call 1

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

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

rewrite174.0ms (2%)

Memory

-1.4MiB live, 194.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	15	32
1	72	32
2	549	32
3	7677	32
0	8312	30

Stop Event

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

Counts

4 → 216

Calls

Call 1

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

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

eval27.0ms (0.3%)

Memory: 11.8MiB live, 50.2MiB allocated
Compiler: Compiled 7 618 to 947 computations (87.6% saved)

prune6.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	222	6	228

Accuracy

100.0%

Counts

228 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	60.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	69.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	31.6%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 264 to 108 computations (59.1% saved)

regimes13.0ms (0.1%)

Memory

-17.4MiB live, 22.0MiB allocated

Counts

12 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes9.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes26.0ms (0.3%)

Memory

-19.0MiB live, 34.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

20.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes42.0ms (0.5%)

Memory

-28.5MiB live, 10.8MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

37.0ms	x
2.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
93.3%	3	`x`
85.0%	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)

regimes5.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (+ eps x) (+ eps x)) (* (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:

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

Results

Accuracy	Segments	Branch
69.3%	1	`eps`
69.3%	1	`x`
69.3%	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%)

Memory

6.0MiB live, 6.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
31.6%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
31.6%	1	`x`
31.6%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.504e-320

Compiler

Compiled 12 to 12 computations (0% saved)

simplify41.0ms (0.5%)

Memory

-7.5MiB live, 31.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	120
1	42	120
2	46	120
3	48	120
4	49	120

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (13.6%)

Memory

7.6MiB live, 353.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	144
1	226	124
2	606	124
3	1944	124
4	5014	124
0	8224	111
0	7	20
0	11	20
1	52	20
2	371	20
3	5109	20
0	8219	20
0	24	98
0	31	93
1	141	93
2	1103	93
0	8478	84
0	69	161
1	214	151
2	570	151
3	1802	143
4	4139	143
5	7201	143
0	8049	124
0	22	106
0	36	105
1	159	94
2	1357	94
0	9042	94

Stop Event

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

Compiler

Compiled 232 to 120 computations (48.3% saved)

preprocess57.0ms (0.6%)

Memory: -0.4MiB live, 43.2MiB allocated
Compiler: Compiled 258 to 82 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.9s (20.9%)

explain181.0ms (2%)

preprocess957.0ms (10.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify999.0ms (11.3%)

localize653.0ms (7.4%)

series5.0ms (0.1%)

simplify133.0ms (1.5%)

rewrite225.0ms (2.5%)

eval80.0ms (0.9%)

prune61.0ms (0.7%)

simplify178.0ms (2%)

localize99.0ms (1.1%)

series23.0ms (0.3%)

simplify194.0ms (2.2%)

rewrite250.0ms (2.8%)

eval144.0ms (1.6%)

prune37.0ms (0.4%)

simplify209.0ms (2.4%)

localize101.0ms (1.1%)

series8.0ms (0.1%)

simplify135.0ms (1.5%)

rewrite186.0ms (2.1%)

eval32.0ms (0.4%)

prune9.0ms (0.1%)

simplify290.0ms (3.3%)

localize68.0ms (0.8%)

series4.0ms (0%)

simplify126.0ms (1.4%)

rewrite174.0ms (2%)

eval27.0ms (0.3%)

prune6.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes26.0ms (0.3%)

regimes42.0ms (0.5%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

bsearch0.0ms (0%)

simplify41.0ms (0.5%)

soundness1.2s (13.6%)

preprocess57.0ms (0.6%)

end0.0ms (0%)

Profiling