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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.6s (35.8%)

Memory

-66.8MiB live, 2 104.7MiB allocated

Samples

1.4s	5 188×	0	valid
552.0ms	2 536×	1	valid
185.0ms	532×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-<=: 901.0ms (51.8% of total)

ival-pow2: 438.0ms (25.2% of total)

ival-add: 180.0ms (10.3% of total)

adjust: 117.0ms (6.7% of total)

ival-sub: 62.0ms (3.6% of total)

ival-and: 22.0ms (1.3% of total)

exact: 16.0ms (0.9% of total)

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

Bogosity

explain138.0ms (1.9%)

Memory

6.9MiB live, 252.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
73	-	1	(-2.3371904240712576e-97 -1.966027689036346e-99)	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`eps`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	72	1

Confusion

	Predicted +	Predicted -
+	72	1
-	0	183

Precision

1.0

Recall

0.9863013698630136

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	1	0
-	0	0	183

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	184
1	72

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms	332×	0	valid
19.0ms	144×	1	valid
6.0ms	36×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-pow2: 18.0ms (59.9% of total)

adjust: 4.0ms (13.3% of total)

ival-add: 4.0ms (13.3% of total)

ival-sub: 3.0ms (10% of total)

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

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

exact: 0.0ms (0% of total)

preprocess300.0ms (4.1%)

Memory

-19.7MiB live, 263.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	30	51
2	97	51
3	472	49
4	1479	37
5	4095	35
0	7	9
0	11	9
1	16	9
2	39	9
3	147	9
4	538	7
5	1669	7
6	5414	7
0	8068	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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.1%	(-.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)

simplify211.0ms (2.9%)

Memory

-5.2MiB live, 228.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 2 binary64))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	3	(-.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	39	23
3	147	23
4	538	21
5	1669	21
6	5414	21
0	8068	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)

localize29.0ms (0.4%)

Memory

11.5MiB live, 57.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0	(+.f64 x eps)
accuracy	0.0390625	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.259358645265785	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

10.0ms	72×	1	valid
10.0ms	166×	0	valid
3.0ms	18×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow2: 7.0ms (47.5% of total)

adjust: 4.0ms (27.1% of total)

ival-add: 2.0ms (13.6% of total)

ival-sub: 2.0ms (13.6% 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

14.1MiB live, 14.1MiB allocated

Counts

4 → 23

Calls

Call 1

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

Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(pow x 2)
(* 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 eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))

simplify171.0ms (2.3%)

Memory

6.8MiB live, 144.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

rewrite193.0ms (2.6%)

Memory

14.6MiB live, 161.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	51	20
2	364	20
3	5050	20
0	8368	20

Stop Event

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

Counts

4 → 311

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)
(pow.f64 x #s(literal 2 binary64))

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

eval41.0ms (0.6%)

Memory: -31.5MiB live, 58.6MiB allocated
Compiler: Compiled 7 675 to 1 120 computations (85.4% saved)

prune6.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	322	5	327
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	5	328

Accuracy

100.0%

Counts

328 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.1%	(-.f64 (fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x)) (pow.f64 x #s(literal 2 binary64)))
▶	76.1%	(*.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))
▶	62.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	72.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 138 to 90 computations (34.8% saved)

simplify243.0ms (3.3%)

Memory

3.1MiB live, 157.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 eps x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	3	(-.f64 (fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x)) (pow.f64 x #s(literal 2 binary64)))
cost-diff	5	(fma.f64 (+.f64 eps x) eps (*.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	1	(+.f64 (+.f64 eps x) x)
cost-diff	4	(-.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	23	136
0	38	113
1	76	110
2	181	104
3	673	104
4	2622	104
5	6756	104
0	8280	104

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

localize124.0ms (1.7%)

Memory

-29.9MiB live, 111.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 eps x)
accuracy	0.0078125	(*.f64 (+.f64 eps x) x)
accuracy	0.0234375	(fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x))
accuracy	15.259358645265785	(-.f64 (fma.f64 (+.f64 eps x) eps (*.f64 (+.f64 eps x) x)) (pow.f64 x #s(literal 2 binary64)))
accuracy	0.0	(+.f64 eps x)
accuracy	0.0078125	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
accuracy	0.0390625	(+.f64 (+.f64 eps x) x)
accuracy	27.781960901358975	(-.f64 (+.f64 eps x) x)
accuracy	0.0	(*.f64 eps x)
accuracy	0.0078125	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	23.790216197512407	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	17.436720353175726	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

46.0ms	93×	1	valid
22.0ms	143×	0	valid
9.0ms	20×	2	valid

Compiler

Compiled 125 to 23 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-add: 21.0ms (38.7% of total)

ival-mult: 13.0ms (24% of total)

ival-pow2: 7.0ms (12.9% of total)

adjust: 6.0ms (11.1% of total)

ival-sub: 5.0ms (9.2% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

20.1MiB live, 20.1MiB allocated

Counts

15 → 35

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

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

Calls

6 calls:

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

simplify169.0ms (2.3%)

Memory

29.3MiB live, 214.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	298
1	306	286
2	1029	274
3	4062	274
0	8257	254

Stop Event

1×	iter limit
1×	node limit

Counts

35 → 33

Calls

Call 1

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

rewrite267.0ms (3.6%)

Memory

-17.0MiB live, 260.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	118
0	38	107
1	171	98
2	1442	98
0	8684	98

Stop Event

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

Counts

15 → 1 516

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

eval246.0ms (3.3%)

Memory: -40.1MiB live, 234.1MiB allocated
Compiler: Compiled 48 216 to 3 517 computations (92.7% saved)

prune52.0ms (0.7%)

Memory

10.5MiB live, 57.8MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 149	3	1 152
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 152	5	1 157

Accuracy

100.0%

Counts

1 157 → 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 eps eps (.f64 (.f64 #s(literal 2 binary64) x) 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))
▶	62.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 54 computations (31.6% saved)

simplify262.0ms (3.6%)

Memory

-1.7MiB live, 223.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps)))
cost-diff	2	(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
cost-diff	0	(+.f64 eps 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	1	(+.f64 (+.f64 eps x) x)
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	97
0	27	95
1	53	95
2	134	95
3	327	95
4	772	89
5	1909	89
6	5982	89
0	8297	81

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

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

localize58.0ms (0.8%)

Memory

-6.1MiB live, 99.9MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps)))
accuracy	0.00390625	(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
accuracy	0.0	(+.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.0078125	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.0390625	(+.f64 (+.f64 eps x) x)
accuracy	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	23.790216197512407	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

20.0ms	166×	0	valid
18.0ms	72×	1	valid
5.0ms	18×	2	valid

Compiler

Compiled 77 to 18 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 11.0ms (37% of total)

ival-pow2: 7.0ms (23.5% of total)

ival-add: 6.0ms (20.2% of total)

adjust: 4.0ms (13.5% of total)

ival-sub: 2.0ms (6.7% 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

10.3MiB live, 10.4MiB allocated

Counts

11 → 21

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

Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
eps
(+ eps (* 2 x))
(+ eps x)
(* 2 x)
(* x (+ (* 2 eps) (/ (pow eps 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
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))

simplify128.0ms (1.7%)

Memory

-0.9MiB live, 91.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	101
1	164	91
2	438	91
3	1372	91
4	3913	91
5	6502	91
0	8135	81

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 19

Calls

Call 1

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

rewrite199.0ms (2.7%)

Memory

13.5MiB live, 161.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	89
0	27	87
1	120	87
2	923	87
0	8717	82

Stop Event

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

Counts

11 → 496

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

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

eval65.0ms (0.9%)

Memory: -16.1MiB live, 71.4MiB allocated
Compiler: Compiled 10 594 to 1 357 computations (87.2% saved)

prune6.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	340	5	345

Accuracy

100.0%

Counts

345 → 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 eps eps (*.f64 (+.f64 x x) 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))
▶	62.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	72.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 52 computations (34.2% saved)

simplify293.0ms (4%)

Memory

-26.7MiB live, 265.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
0	20	59
1	39	59
2	111	59
3	314	59
4	764	55
5	1889	55
6	5879	55
0	8185	51

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

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

localize79.0ms (1.1%)

Memory

11.8MiB live, 56.0MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(*.f64 (+.f64 x x) eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
accuracy	0.00390625	(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	23.790216197512407	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

15.0ms	166×	0	valid
13.0ms	72×	1	valid
4.0ms	18×	2	valid

Compiler

Compiled 49 to 14 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-pow2: 7.0ms (30.9% of total)

ival-add: 5.0ms (22.1% of total)

ival-mult: 5.0ms (22.1% of total)

adjust: 3.0ms (13.2% of total)

ival-sub: 2.0ms (8.8% of total)

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

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

series6.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

7 → 9

Calls

Call 1

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

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

Calls

6 calls:

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

simplify121.0ms (1.6%)

Memory

5.3MiB live, 107.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	89	49
2	284	49
3	941	49
4	2845	49
5	5683	49
0	8065	44

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 9

Calls

Call 1

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

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

rewrite141.0ms (1.9%)

Memory

1.8MiB live, 47.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	20	51
1	98	47
0	836	47

Stop Event

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

Counts

7 → 216

Calls

Call 1

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

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

eval27.0ms (0.4%)

Memory: -18.1MiB live, 27.0MiB allocated
Compiler: Compiled 1 908 to 275 computations (85.6% saved)

prune6.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	95	8	103

Accuracy

100.0%

Counts

103 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
	5.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (+.f64 x x))
	6.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (+.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))
✓	62.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	72.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
	5.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 #s(literal -2 binary64) x))

Compiler

Compiled 318 to 128 computations (59.7% saved)

regimes15.0ms (0.2%)

Memory

-7.7MiB live, 36.3MiB allocated

Counts

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

Calls

3 calls:

7.0ms	x
4.0ms	eps
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes9.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes46.0ms (0.6%)

Memory

-26.1MiB live, 77.6MiB allocated

Counts

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

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

Calls

3 calls:

40.0ms	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	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes8.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.6%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
89.8%	3	`x`
87.2%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes136.0ms (1.8%)

Memory

-33.7MiB live, 13.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

132.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
72.8%	1	`eps`
72.8%	1	`x`
72.8%	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)

regimes5.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Accuracy

Total -1.6b remaining (-2.6%)

Threshold costs -1.6b (-2.6%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
6.2%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
6.2%	1	`eps`
6.2%	1	`x`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.32624737e-315	7.828376884697283e-307

Compiler

Compiled 12 to 12 computations (0% saved)

simplify58.0ms (0.8%)

Memory

9.0MiB live, 56.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	117
1	38	117
2	65	117
3	177	117
4	577	103
5	1745	103
6	6779	103

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 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)) (*.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 404804507/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (+.f64 eps eps) x)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (+.f64 eps eps))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 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)) (*.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 404804507/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (+.f64 eps eps) x)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (+.f64 eps eps))

soundness803.0ms (10.9%)

Memory

-30.3MiB live, 405.3MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	20	51
1	98	47
0	836	47
0	18	89
0	27	87
1	120	87
2	923	87
0	8717	82
0	23	118
0	38	107
1	171	98
2	1442	98
0	8684	98
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176

Stop Event

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

Compiler

Compiled 276 to 151 computations (45.3% saved)

preprocess31.0ms (0.4%)

Memory: 34.6MiB live, 34.6MiB allocated
Compiler: Compiled 252 to 78 computations (69% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample2.6s (35.8%)

explain138.0ms (1.9%)

preprocess300.0ms (4.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify211.0ms (2.9%)

localize29.0ms (0.4%)

series5.0ms (0.1%)

simplify171.0ms (2.3%)

rewrite193.0ms (2.6%)

eval41.0ms (0.6%)

prune6.0ms (0.1%)

simplify243.0ms (3.3%)

localize124.0ms (1.7%)

series12.0ms (0.2%)

simplify169.0ms (2.3%)

rewrite267.0ms (3.6%)

eval246.0ms (3.3%)

prune52.0ms (0.7%)

simplify262.0ms (3.6%)

localize58.0ms (0.8%)

series7.0ms (0.1%)

simplify128.0ms (1.7%)

rewrite199.0ms (2.7%)

eval65.0ms (0.9%)

prune6.0ms (0.1%)

simplify293.0ms (4%)

localize79.0ms (1.1%)

series6.0ms (0.1%)

simplify121.0ms (1.6%)

rewrite141.0ms (1.9%)

eval27.0ms (0.4%)

prune6.0ms (0.1%)

regimes15.0ms (0.2%)

regimes9.0ms (0.1%)

regimes46.0ms (0.6%)

regimes8.0ms (0.1%)

regimes136.0ms (1.8%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify58.0ms (0.8%)

soundness803.0ms (10.9%)

preprocess31.0ms (0.4%)

end0.0ms (0%)

Profiling