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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.7s (25.2%)

Memory

-83.3MiB live, 1 254.5MiB allocated

Samples

621.0ms	2 587×	1	valid
504.0ms	5 174×	0	valid
130.0ms	495×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 678.0ms

ival-pow2: 294.0ms (43.4% of total)

ival-<=: 135.0ms (19.9% of total)

ival-add: 82.0ms (12.1% of total)

adjust: 72.0ms (10.6% of total)

ival-sub: 54.0ms (8% of total)

ival-and: 21.0ms (3.1% of total)

exact: 17.0ms (2.5% of total)

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

Bogosity

explain101.0ms (1.5%)

Memory

14.6MiB live, 173.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
73	1	(7.741849344654024e-87 -4.230502069594615e-238)	-	`(-.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	74	0

Confusion

	Predicted +	Predicted -
+	73	0
-	1	182

Precision

0.9864864864864865

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	0	0
-	1	0	182

Precision?

0.9864864864864865

Recall?

1.0

Freqs

test

number	freq
0	182
1	74

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms	338×	0	valid
16.0ms	140×	1	valid
8.0ms	34×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-pow2: 16.0ms (57.5% of total)

adjust: 4.0ms (14.4% of total)

ival-add: 4.0ms (14.4% of total)

ival-sub: 3.0ms (10.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess349.0ms (5.2%)

Memory

-5.5MiB live, 227.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	45	47
2	149	45
3	549	35
4	1721	35
5	3972	35
6	5466	35
7	6180	35
8	6408	35
9	6514	35
10	6535	35
11	6535	35
12	6535	35
13	6535	35
14	6626	35
15	6954	35
16	7748	35
0	7	9
0	11	9
1	16	9
2	36	9
3	91	9
4	271	7
5	855	7
6	2424	7
7	4630	7
8	6290	7
9	7277	7
10	7703	7
11	7971	7
12	7977	7
13	7977	7
0	8284	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

simplify219.0ms (3.2%)

Memory

-26.6MiB live, 200.1MiB 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	36	23
3	91	23
4	271	21
5	855	21
6	2424	21
7	4630	21
8	6290	21
9	7277	21
10	7703	21
11	7971	21
12	7977	21
13	7977	21
0	8284	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)

localize28.0ms (0.4%)

Memory

-2.7MiB live, 35.9MiB 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	0.05078125	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.180539718820423	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

10.0ms	70×	1	valid
9.0ms	169×	0	valid
3.0ms	17×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-pow2: 9.0ms (63.3% of total)

adjust: 2.0ms (14.1% of total)

ival-add: 2.0ms (14.1% of total)

ival-sub: 2.0ms (14.1% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB 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	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))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))

simplify156.0ms (2.3%)

Memory

-10.5MiB live, 106.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	214	151
2	572	151
3	1829	143
4	4154	143
5	7321	143
0	8166	124

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

rewrite168.0ms (2.5%)

Memory

17.1MiB live, 175.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5134	20
0	8154	20

Stop Event

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

Counts

4 → 370

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 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 eps x) #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
(*.f64 (+.f64 (+.f64 eps x) x) (-.f64 (+.f64 eps x) x))
(*.f64 (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(*.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 8 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 4 binary64)) (pow.f64 x #s(literal 8 binary64))) (pow.f64 (+.f64 eps x) #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 18 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 4 binary64))) #s(literal -1 binary64))) (+.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 12 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (*.f64 (+.f64 eps x) x) #s(literal 6 binary64))))
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(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (pow.f64 (-.f64 eps x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (.f64 (-.f64 x eps) (+.f64 eps x)))
(.f64 (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (neg.f64 (.f64 (-.f64 x eps) (+.f64 eps x))) (pow.f64 (neg.f64 (-.f64 x eps)) #s(literal -1 binary64)))
(.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (+.f64 eps x))
(.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (/.f64 (+.f64 eps x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (.f64 (+.f64 eps x) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))))
(.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)))
(*.f64 (+.f64 eps x) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 eps x) (.f64 (-.f64 x eps) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 eps eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (-.f64 x eps) #s(literal -1 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x eps)) (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 3 binary64)) (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (-.f64 x eps))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (.f64 (.f64 (-.f64 x eps) (+.f64 eps x)) #s(literal 1 binary64)) (-.f64 x eps))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 eps x) eps (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 x eps)))
(/.f64 (.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps eps (*.f64 x x)) (-.f64 x eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x eps)) (.f64 (-.f64 x eps) (.f64 eps eps))) (pow.f64 (-.f64 x eps) #s(literal 2 binary64)))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)))) (exp.f64 (log.f64 (-.f64 x eps))))
(/.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (exp.f64 (log.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (-.f64 x eps) (fma.f64 eps eps (.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (-.f64 x eps) (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) (-.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (*.f64 eps x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (+.f64 eps x) (-.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 eps x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 eps x) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (+.f64 eps x) eps (.f64 x x)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x eps))) (.f64 eps (/.f64 eps (-.f64 x eps))))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 eps x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 eps x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 eps x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (+.f64 eps x)))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 eps x)
(+.f64 x eps)
(*.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 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 x x)
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (sqrt.f64 x) #s(literal 4 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))
(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 (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)))

eval44.0ms (0.7%)

Memory: -12.7MiB live, 101.6MiB allocated
Compiler: Compiled 9 295 to 1 147 computations (87.7% saved)

prune7.0ms (0.1%)

Memory

22.0MiB live, 22.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	372	5	377
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	373	5	378

Accuracy

100.0%

Counts

378 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.1%	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
▶	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))
▶	63.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	72.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 138 to 88 computations (36.2% saved)

simplify269.0ms (4%)

Memory

-19.9MiB live, 221.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	1	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
cost-diff	7	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 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: 0 (0.0ms)

Iter	Nodes	Cost
0	23	132
0	39	114
1	77	111
2	160	105
3	408	105
4	1736	105
5	4735	105
6	7355	105
0	8369	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)
(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
(+.f64 eps x)
eps
x
(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) x)
(neg.f64 x)

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

localize81.0ms (1.2%)

Memory

15.4MiB live, 91.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 (neg.f64 x) x)
accuracy	0.0	(neg.f64 x)
accuracy	0.03125	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
accuracy	20.38091959539621	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
accuracy	0.0	(+.f64 eps x)
accuracy	0.02734375	(*.f64 (-.f64 (+.f64 eps x) x) (+.f64 (+.f64 eps x) x))
accuracy	0.0546875	(+.f64 (+.f64 eps x) x)
accuracy	27.17075783408776	(-.f64 (+.f64 eps x) x)
accuracy	0.0	(*.f64 eps x)
accuracy	0.02734375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	23.506066732295945	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	17.80320484458012	#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	0.02734375	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

32.0ms	97×	1	valid
23.0ms	140×	0	valid
9.0ms	19×	2	valid

Compiler

Compiled 122 to 25 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 16.0ms (35.4% of total)

ival-add: 10.0ms (22.1% of total)

adjust: 7.0ms (15.5% of total)

ival-pow2: 7.0ms (15.5% of total)

ival-sub: 3.0ms (6.6% of total)

ival-neg: 1.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series17.0ms (0.2%)

Memory

-28.8MiB live, 15.7MiB allocated

Counts

16 → 38

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

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

Calls

6 calls:

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

simplify115.0ms (1.7%)

Memory

29.8MiB live, 103.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	101	232
1	309	206
2	833	206
3	2672	198
4	7333	198
0	8022	179

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 36

Calls

Call 1

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

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

rewrite277.0ms (4.1%)

Memory

-1.6MiB live, 236.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	118
0	39	114
1	172	103
2	1507	103
0	8348	103

Stop Event

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

Counts

16 → 1 372

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

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

eval120.0ms (1.8%)

Memory: 4.0MiB live, 191.8MiB allocated
Compiler: Compiled 40 828 to 2 853 computations (93% saved)

prune18.0ms (0.3%)

Memory

-6.8MiB live, 70.1MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	965	4	969
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	968	6	974

Accuracy

100.0%

Counts

974 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	63.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	38.2%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 97 to 65 computations (33% saved)

simplify350.0ms (5.2%)

Memory

17.8MiB live, 255.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	114
0	34	112
1	60	105
2	103	105
3	229	97
4	540	97
5	1862	97
6	3417	97
7	4848	97
8	5510	97
9	5907	97
10	6094	97
11	6166	97
12	6185	97
13	6188	97
14	6190	97
15	6190	97
16	6190	97
17	7846	97
0	8666	88

Stop Event

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

Calls

Call 1

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

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

localize85.0ms (1.3%)

Memory

-17.6MiB live, 108.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
accuracy	0.00390625	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps 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	0.02734375	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.0546875	(+.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	23.506066732295945	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	39.535617488640504	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Samples

32.0ms	169×	0	valid
21.0ms	70×	1	valid
7.0ms	17×	2	valid

Compiler

Compiled 92 to 23 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-mult: 17.0ms (40.9% of total)

ival-add: 10.0ms (24% of total)

ival-pow2: 6.0ms (14.4% of total)

adjust: 5.0ms (12% of total)

ival-sub: 2.0ms (4.8% of total)

ival-neg: 1.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

11 → 26

Calls

Call 1

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

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

Calls

6 calls:

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

simplify182.0ms (2.7%)

Memory

11.0MiB live, 167.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	138
1	224	118
2	607	118
3	1959	118
4	5128	118
0	8073	105

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 24

Calls

Call 1

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

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

rewrite210.0ms (3.1%)

Memory

11.6MiB live, 205.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	102
0	34	100
1	152	93
2	1263	93
0	8139	88

Stop Event

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

Counts

11 → 229

Calls

Call 1

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

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

eval127.0ms (1.9%)

Memory: -21.8MiB live, 53.6MiB allocated
Compiler: Compiled 5 761 to 816 computations (85.8% saved)

prune10.0ms (0.2%)

Memory

20.4MiB live, 20.4MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	0	4	4
Done	0	2	2
Total	188	7	195

Accuracy

100.0%

Counts

195 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	63.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	38.2%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 115 to 76 computations (33.9% saved)

simplify238.0ms (3.5%)

Memory

4.0MiB live, 167.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	15	34
1	25	34
2	50	34
3	112	34
4	298	32
5	854	32
6	2810	32
7	4419	32
8	6130	32
9	6939	32
10	7282	32
11	7460	32
12	7462	32
13	7462	32
0	8046	29

Stop Event

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

Calls

Call 1

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

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

localize114.0ms (1.7%)

Memory

-38.2MiB live, 111.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
accuracy	0.015625	(*.f64 (+.f64 x eps) eps)
accuracy	0.0234375	(fma.f64 x eps (*.f64 (+.f64 x eps) eps))

Samples

53.0ms	169×	0	valid
51.0ms	70×	1	valid
4.0ms	17×	2	valid

Compiler

Compiled 30 to 11 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-pow2: 43.0ms (72.7% of total)

ival-mult: 9.0ms (15.2% of total)

ival-add: 3.0ms (5.1% of total)

adjust: 2.0ms (3.4% of total)

ival-sub: 2.0ms (3.4% of total)

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

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

series4.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

4 → 20

Calls

Call 1

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

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

Calls

6 calls:

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

simplify120.0ms (1.8%)

Memory

-9.7MiB live, 115.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	98
1	158	88
2	386	88
3	1052	88
4	2669	88
5	4272	88
6	6480	88
0	8061	83

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 18

Calls

Call 1

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

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

rewrite252.0ms (3.7%)

Memory

23.6MiB live, 211.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	15	32
1	72	32
2	549	32
3	7737	32
0	8372	30

Stop Event

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

Counts

4 → 216

Calls

Call 1

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

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

eval46.0ms (0.7%)

Memory: -14.2MiB live, 24.9MiB allocated
Compiler: Compiled 7 618 to 947 computations (87.6% saved)

prune6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	222	7	229

Accuracy

100.0%

Counts

229 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 x eps) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	63.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	38.2%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 279 to 123 computations (55.9% saved)

regimes16.0ms (0.2%)

Memory

-44.0MiB live, 9.9MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	eps
4.0ms	x
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes8.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
91.5%	3	`x`
85.6%	3	`eps`
94.5%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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
72.2%	1	`eps`
72.2%	1	`x`
72.2%	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)

regimes21.0ms (0.3%)

Memory

-30.4MiB live, 8.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	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
38.2%	1	`eps`
38.2%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
38.2%	1	`x`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	7.762577e-318

Compiler

Compiled 12 to 12 computations (0% saved)

simplify121.0ms (1.8%)

Memory

3.3MiB live, 40.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	122
1	55	115
2	86	115
3	216	101
4	545	101
5	1847	101
6	3434	101
7	4941	101
8	5945	101
9	6412	101
10	6668	101
11	6792	101
12	6859	101
13	6956	101
14	7148	101
15	7532	101

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness1.1s (16%)

Memory

33.6MiB live, 387.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5134	20
0	8154	20
0	101	232
1	309	206
2	833	206
3	2672	198
4	7333	198
0	8022	179
0	23	118
0	39	114
1	172	103
2	1507	103
0	8348	103
0	69	161
1	214	151
2	572	151
3	1829	143
4	4154	143
5	7321	143
0	8166	124

Stop Event

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

Compiler

Compiled 183 to 90 computations (50.8% saved)

preprocess67.0ms (1%)

Memory: -20.2MiB live, 63.3MiB allocated
Compiler: Compiled 248 to 74 computations (70.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.7s (25.2%)

explain101.0ms (1.5%)

preprocess349.0ms (5.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify219.0ms (3.2%)

localize28.0ms (0.4%)

series5.0ms (0.1%)

simplify156.0ms (2.3%)

rewrite168.0ms (2.5%)

eval44.0ms (0.7%)

prune7.0ms (0.1%)

simplify269.0ms (4%)

localize81.0ms (1.2%)

series17.0ms (0.2%)

simplify115.0ms (1.7%)

rewrite277.0ms (4.1%)

eval120.0ms (1.8%)

prune18.0ms (0.3%)

simplify350.0ms (5.2%)

localize85.0ms (1.3%)

series8.0ms (0.1%)

simplify182.0ms (2.7%)

rewrite210.0ms (3.1%)

eval127.0ms (1.9%)

prune10.0ms (0.2%)

simplify238.0ms (3.5%)

localize114.0ms (1.7%)

series4.0ms (0.1%)

simplify120.0ms (1.8%)

rewrite252.0ms (3.7%)

eval46.0ms (0.7%)

prune6.0ms (0.1%)

regimes16.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes21.0ms (0.3%)

bsearch0.0ms (0%)

simplify121.0ms (1.8%)

soundness1.1s (16%)

preprocess67.0ms (1%)

end0.0ms (0%)

Profiling