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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample3.5s (45.1%)

Memory

58.6MiB live, 1 451.6MiB allocated

Samples

1.2s	5 263×	0	valid
1.2s	2 487×	1	valid
530.0ms	506×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-<=: 572.0ms (31.3% of total)

ival-add: 543.0ms (29.7% of total)

adjust: 379.0ms (20.7% of total)

ival-pow2: 241.0ms (13.2% of total)

ival-sub: 52.0ms (2.8% of total)

ival-and: 21.0ms (1.1% of total)

exact: 16.0ms (0.9% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain162.0ms (2.1%)

Memory

-14.1MiB live, 147.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
67	35	(-1.6774426313205692e-93 -3.8739354950775933e-275)	1	(-5.50280618667882e-91 -3.3939623280652998e-93)	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	0	-	`(+.f64 x eps)`
0	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	1

Confusion

	Predicted +	Predicted -
+	66	2
-	35	153

Precision

0.6534653465346535

Recall

0.9705882352941176

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	66	1	1
-	35	0	153

Precision?

0.6568627450980392

Recall?

0.9852941176470589

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

19.0ms	322×	0	valid
17.0ms	142×	1	valid
8.0ms	48×	2	valid

Compiler

Compiled 105 to 45 computations (57.1% saved)

Precisions

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

ival-pow2: 14.0ms (52.3% of total)

adjust: 4.0ms (14.9% of total)

ival-add: 4.0ms (14.9% of total)

ival-sub: 3.0ms (11.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess400.0ms (5.2%)

Memory

19.6MiB live, 211.6MiB 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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.0%	(-.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)

simplify244.0ms (3.2%)

Memory

-6.6MiB live, 198.2MiB 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)

localize37.0ms (0.5%)

Memory

0.4MiB live, 39.8MiB 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	14.07948090982703	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

13.0ms	24×	2	valid
9.0ms	161×	0	valid
8.0ms	71×	1	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

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

ival-pow2: 16.0ms (73.1% of total)

adjust: 2.0ms (9.1% of total)

ival-add: 2.0ms (9.1% of total)

ival-sub: 2.0ms (9.1% 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

9.2MiB live, 9.2MiB 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))

simplify118.0ms (1.5%)

Memory

6.8MiB live, 124.5MiB 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)

rewrite167.0ms (2.2%)

Memory

-1.9MiB live, 153.2MiB 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))))
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(exp.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(+.f64 (.f64 (+.f64 eps x) eps) (.f64 (+.f64 eps x) x))
(+.f64 (.f64 (+.f64 eps x) x) (.f64 (+.f64 eps x) eps))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 eps x) eps (*.f64 x x)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 eps x) eps)))
(.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 eps x) eps) (-.f64 (.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x))
(.f64 (pow.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 (+.f64 eps x)))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (exp.f64 (log.f64 (-.f64 x eps))))
(/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (log.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 eps x) eps (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(sqrt.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (+.f64 eps x)))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)

eval60.0ms (0.8%)

Memory: -3.9MiB live, 81.7MiB allocated
Compiler: Compiled 9 307 to 1 150 computations (87.6% saved)

prune8.0ms (0.1%)

Memory

-10.5MiB live, 28.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	373	5	378
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	374	5	379

Accuracy

100.0%

Counts

379 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.6%	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps) (-.f64 (.f64 (+.f64 eps x) x) (.f64 x x)))
▶	78.0%	(*.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))
▶	62.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	75.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 158 to 98 computations (38% saved)

simplify213.0ms (2.8%)

Memory

-16.3MiB live, 174.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (-.f64 x eps) (+.f64 eps x))
cost-diff	704	(-.f64 (.f64 (+.f64 eps x) x) (.f64 x x))
cost-diff	1600	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps) (-.f64 (.f64 (+.f64 eps x) x) (.f64 x x)))
cost-diff	6080	(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps)
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	28	167
0	47	133
1	99	130
2	250	122
3	844	122
4	5141	122
0	8809	122

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

localize116.0ms (1.5%)

Memory

-6.5MiB live, 113.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(fma.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps) (-.f64 (.f64 (+.f64 eps x) x) (.f64 x x)))
accuracy	0.03515625	(pow.f64 (-.f64 x eps) #s(literal -1 binary64))
accuracy	0.2421875	(*.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) eps)
accuracy	14.09877603665143	(-.f64 (.f64 (+.f64 eps x) x) (.f64 x x))
accuracy	0	(+.f64 eps x)
accuracy	0.01171875	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
accuracy	0.04296875	(+.f64 (+.f64 eps x) x)
accuracy	26.959118464426037	(-.f64 (+.f64 eps x) x)
accuracy	0	(*.f64 eps x)
accuracy	0.01953125	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	23.97542203518598	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	15.828070593819202	#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	0.01171875	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

50.0ms	89×	1	valid
32.0ms	143×	0	valid
12.0ms	24×	2	valid

Compiler

Compiled 322 to 58 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-mult: 23.0ms (30.7% of total)

ival-sub: 18.0ms (24% of total)

ival-pow: 10.0ms (13.3% of total)

ival-add: 8.0ms (10.7% of total)

adjust: 8.0ms (10.7% of total)

ival-pow2: 7.0ms (9.3% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.3%)

Memory

-10.5MiB live, 27.4MiB allocated

Counts

17 → 72

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

Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
eps
(+ eps (* 2 x))
(* 2 (* eps x))
(* eps x)
(+ eps x)
-1
(- (* -1 (/ x eps)) 1)
(- (* x (- (* -1 (/ x (pow eps 2))) (/ 1 eps))) 1)
(- (* x (- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))) 1)
(* -1 (pow eps 2))
(+ (* -1 (pow eps 2)) (* x (+ eps (* -1 eps))))
(+ (* -1 (pow eps 2)) (* x (+ eps (+ x (* -1 eps)))))
(/ -1 eps)
(- (* -1 (/ x (pow eps 2))) (/ 1 eps))
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 x)
(* x (+ 2 (/ eps x)))
x
(* x (+ 1 (/ eps x)))
(/ eps x)
(/ (+ eps (/ (pow eps 2) x)) x)
(/ (- (+ eps (/ (pow eps 3) (pow x 2))) (* -1 (/ (pow eps 2) x))) x)
(/ (- (+ eps (/ (pow eps 4) (pow x 3))) (+ (* -1 (/ (pow eps 2) x)) (* -1 (/ (pow eps 3) (pow x 2))))) x)
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (/ eps x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ eps x)) (+ (* -1 (/ (pow eps 2) (pow x 2))) (/ eps x)))))
(/ 1 x)
(/ (+ 1 (/ eps x)) x)
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x))
(* -1 (/ (+ (* -1 eps) (* -1 (/ (+ (/ (pow eps 3) x) (pow eps 2)) x))) x))
(* -1 (/ (+ (* -1 eps) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow eps 4) x)) (* -1 (pow eps 3))) x)) (pow eps 2)) x))) x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ eps (* -1 eps))) (/ (pow eps 2) x)) x))))
(* -1 (/ (- (* -1 (/ eps x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))
(* eps (+ eps (* 2 x)))
(* eps (+ (/ 1 x) (/ eps (pow x 2))))
(* eps (+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x)))
(* eps (+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x)))
(+ (* eps (+ x (* -1 x))) (pow x 2))
(+ (* eps (+ x (+ (* -1 eps) (* -1 x)))) (pow x 2))
(+ (/ 1 x) (/ eps (pow x 2)))
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (/ x eps)))
(- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps)))
(- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (/ x eps)) 1))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (+ (/ x eps) (/ (pow x 2) (pow eps 2)))) 1))
(/ (- (* -1 (/ x eps)) 1) eps)
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (* -1 (/ (- (/ (pow x 2) eps) (* -1 x)) eps)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) eps)) (pow x 2)) eps)) (* -1 x)) eps)) 1)
(* (pow eps 2) (- (* -1 (/ (+ x (* -1 x)) eps)) 1))
(* (pow eps 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) eps)))) eps)) 1))
(* -1 (/ (+ 1 (/ x eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	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) (* (pow (- x eps) -1) eps) (+ (* (* (- x eps) (+ eps x)) (* (pow (- x eps) -1) eps)) (- (* (+ eps x) x) (* x x))) (- (* (+ eps x) x) (* x x)) (* (- x eps) (+ eps x)) (pow (- x eps) -1))
4.0ms	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) (* (pow (- x eps) -1) eps) (+ (* (* (- x eps) (+ eps x)) (* (pow (- x eps) -1) eps)) (- (* (+ eps x) x) (* x x))) (- (* (+ eps x) x) (* x x)) (* (- x eps) (+ eps x)) (pow (- x eps) -1))
3.0ms	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) (* (pow (- x eps) -1) eps) (+ (* (* (- x eps) (+ eps x)) (* (pow (- x eps) -1) eps)) (- (* (+ eps x) x) (* x x))) (- (* (+ eps x) x) (* x x)) (* (- x eps) (+ eps x)) (pow (- x eps) -1))
3.0ms	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) (* (pow (- x eps) -1) eps) (+ (* (* (- x eps) (+ eps x)) (* (pow (- x eps) -1) eps)) (- (* (+ eps x) x) (* x x))) (- (* (+ eps x) x) (* x x)) (* (- x eps) (+ eps x)) (pow (- x eps) -1))
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) (* (pow (- x eps) -1) eps) (+ (* (* (- x eps) (+ eps x)) (* (pow (- x eps) -1) eps)) (- (* (+ eps x) x) (* x x))) (- (* (+ eps x) x) (* x x)) (* (- x eps) (+ eps x)) (pow (- x eps) -1))

simplify154.0ms (2%)

Memory

18.7MiB live, 135.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	251	858
1	797	776
2	2150	700
3	7633	700
0	8184	648

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 70

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

rewrite166.0ms (2.2%)

Memory

-1.3MiB live, 192.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	141
0	47	125
1	204	110
2	1824	110
0	8316	110

Stop Event

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

Counts

17 → 763

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

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

eval133.0ms (1.7%)

Memory: 0.4MiB live, 156.5MiB allocated
Compiler: Compiled 22 787 to 2 301 computations (89.9% saved)

prune13.0ms (0.2%)

Memory

-1.1MiB live, 37.9MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	782	3	785
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	785	5	790

Accuracy

100.0%

Counts

790 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #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))
▶	62.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	75.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 54 computations (31.6% saved)

simplify230.0ms (3%)

Memory

-3.0MiB live, 150.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	95
0	27	93
1	46	93
2	80	93
3	126	93
4	265	87
5	819	87
6	2361	87
7	4371	87
8	6045	87
9	7053	87
10	7481	87
11	7750	87
12	7756	87
13	7756	87
0	8072	79

Stop Event

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

Calls

Call 1

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

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

localize73.0ms (1%)

Memory

24.6MiB live, 63.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 eps x)
accuracy	0	(*.f64 eps eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
accuracy	0.0078125	(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
accuracy	0	(+.f64 eps x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.01171875	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.04296875	(+.f64 (+.f64 eps x) x)
accuracy	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	23.97542203518598	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

36.0ms	71×	1	valid
19.0ms	161×	0	valid
7.0ms	24×	2	valid

Compiler

Compiled 170 to 37 computations (78.2% saved)

Precisions

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

ival-mult: 10.0ms (35.4% of total)

ival-pow2: 7.0ms (24.8% of total)

ival-add: 6.0ms (21.2% of total)

adjust: 4.0ms (14.2% of total)

ival-sub: 2.0ms (7.1% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

11 → 22

Calls

Call 1

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

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

Calls

6 calls:

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

simplify115.0ms (1.5%)

Memory

-14.0MiB live, 69.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	104
1	159	94
2	376	94
3	1065	94
4	2689	94
5	4375	94
6	6830	94
0	8134	84

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 20

Calls

Call 1

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

rewrite194.0ms (2.5%)

Memory

19.5MiB live, 245.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	87
0	27	85
1	114	85
2	834	85
0	8970	77

Stop Event

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

Counts

11 → 475

Calls

Call 1

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

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

eval107.0ms (1.4%)

Memory: -18.4MiB live, 72.6MiB allocated
Compiler: Compiled 10 128 to 1 363 computations (86.5% saved)

prune9.0ms (0.1%)

Memory

-16.7MiB live, 21.1MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	350	1	351
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	351	5	356

Accuracy

100.0%

Counts

356 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #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))
✓	62.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	75.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 53 computations (32.9% saved)

simplify258.0ms (3.3%)

Memory

32.3MiB live, 189.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	15	34
1	24	32
2	48	32
3	108	32
4	304	30
5	872	30
6	2711	30
7	4256	30
8	5923	30
9	6730	30
10	7073	30
11	7251	30
12	7253	30
13	7253	30
14	7884	30
15	7948	30
16	7948	30
17	7948	30
0	8237	27

Stop Event

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

Calls

Call 1

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

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

localize37.0ms (0.5%)

Memory

7.3MiB live, 46.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps x)
accuracy	0	(*.f64 eps x)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
accuracy	0.01171875	(fma.f64 (+.f64 eps x) eps (*.f64 eps x))

Samples

15.0ms	161×	0	valid
10.0ms	71×	1	valid
5.0ms	24×	2	valid

Compiler

Compiled 62 to 23 computations (62.9% saved)

Precisions

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

ival-pow2: 7.0ms (32.8% of total)

ival-add: 6.0ms (28.1% of total)

adjust: 3.0ms (14.1% of total)

ival-mult: 3.0ms (14.1% of total)

ival-sub: 2.0ms (9.4% of total)

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

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

series54.0ms (0.7%)

Memory

-32.8MiB live, 15.2MiB allocated

Counts

4 → 15

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	eps	@	inf	((+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)) (+ eps x) (* eps x))
25.0ms	x	@	-inf	((+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)) (+ eps x) (* eps x))
1.0ms	eps	@	-inf	((+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)) (+ eps x) (* eps x))
1.0ms	x	@	inf	((+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)) (+ eps x) (* eps x))
0.0ms	eps	@	0	((+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)) (+ eps x) (* eps x))

simplify181.0ms (2.4%)

Memory

12.4MiB live, 85.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	73
1	125	63
2	296	63
3	870	63
4	2233	63
5	4110	63
6	6722	63
0	8045	58

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 13

Calls

Call 1

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

rewrite165.0ms (2.1%)

Memory

-3.6MiB live, 151.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
0	15	32
1	79	30
2	674	30
0	8305	30

Stop Event

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

Counts

4 → 202

Calls

Call 1

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

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

eval25.0ms (0.3%)

Memory: 17.2MiB live, 52.5MiB allocated
Compiler: Compiled 7 420 to 861 computations (88.4% saved)

prune11.0ms (0.1%)

Memory

-32.6MiB live, 20.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	207	5	212

Accuracy

100.0%

Counts

212 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #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))
✓	62.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	75.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 235 to 95 computations (59.6% saved)

regimes35.0ms (0.5%)

Memory

27.2MiB live, 62.9MiB allocated

Counts

10 → 1

Calls

Call 1

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

Calls

3 calls:

23.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
8.0ms	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)

regimes10.0ms (0.1%)

Memory

-4.8MiB live, 32.0MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	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)

regimes6.0ms (0.1%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

Results

Accuracy	Segments	Branch
94.5%	3	`x`
87.2%	3	`eps`
96.7%	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)

regimes6.0ms (0.1%)

Memory

-27.1MiB live, 11.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	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
75.3%	1	`eps`
75.3%	1	`x`
75.3%	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)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.846e-321

Compiler

Compiled 12 to 12 computations (0% saved)

simplify26.0ms (0.3%)

Memory

9.4MiB live, 54.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	88
1	34	88
2	38	88
3	40	88
4	41	88

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness632.0ms (8.2%)

Memory

-18.1MiB live, 301.2MiB allocated

Iterations

Useful iterations: 1 (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
0	28	141
0	47	125
1	204	110
2	1824	110
0	8316	110

Stop Event

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

Compiler

Compiled 146 to 74 computations (49.3% saved)

preprocess25.0ms (0.3%)

Memory: 19.5MiB live, 19.5MiB allocated
Compiler: Compiled 194 to 66 computations (66% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample3.5s (45.1%)

explain162.0ms (2.1%)

preprocess400.0ms (5.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify244.0ms (3.2%)

localize37.0ms (0.5%)

series5.0ms (0.1%)

simplify118.0ms (1.5%)

rewrite167.0ms (2.2%)

eval60.0ms (0.8%)

prune8.0ms (0.1%)

simplify213.0ms (2.8%)

localize116.0ms (1.5%)

series20.0ms (0.3%)

simplify154.0ms (2%)

rewrite166.0ms (2.2%)

eval133.0ms (1.7%)

prune13.0ms (0.2%)

simplify230.0ms (3%)

localize73.0ms (1%)

series7.0ms (0.1%)

simplify115.0ms (1.5%)

rewrite194.0ms (2.5%)

eval107.0ms (1.4%)

prune9.0ms (0.1%)

simplify258.0ms (3.3%)

localize37.0ms (0.5%)

series54.0ms (0.7%)

simplify181.0ms (2.4%)

rewrite165.0ms (2.1%)

eval25.0ms (0.3%)

prune11.0ms (0.1%)

regimes35.0ms (0.5%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

simplify26.0ms (0.3%)

soundness632.0ms (8.2%)

preprocess25.0ms (0.3%)

end0.0ms (0%)

Profiling