Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze11.0ms (0.6%)

Memory

21.3MiB live, 21.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 24 to 18 computations (25% saved)

sample802.0ms (40%)

Memory

-8.2MiB live, 1 195.5MiB allocated; 80ms collecting garbage

Samples

249.0ms	2 680×	1	valid
205.0ms	4 835×	0	valid
86.0ms	741×	2	valid
9.0ms	182×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 318.0ms

ival-sqrt: 119.0ms (37.4% of total)

adjust: 73.0ms (22.9% of total)

ival-mult!: 65.0ms (20.4% of total)

ival-sub!: 61.0ms (19.2% of total)

Bogosity

explain84.0ms (4.2%)

Memory

6.8MiB live, 101.8MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
104	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`eps`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	104	1

Confusion

	Predicted +	Predicted -
+	104	0
-	0	152

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	104	0	0
-	0	1	151

Precision?

0.9904761904761905

Recall?

1.0

Freqs

test

number	freq
0	152
1	104

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

15.0ms	172×	1	valid
14.0ms	306×	0	valid
4.0ms	34×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sqrt: 6.0ms (33% of total)

adjust: 4.0ms (22% of total)

ival-sub!: 4.0ms (22% of total)

ival-mult!: 4.0ms (22% of total)

preprocess7.0ms (0.3%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	35	54
2	64	54
3	91	54
4	115	54

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 16 to 12 computations (25% saved)

series12.0ms (0.6%)

Memory

-30.2MiB live, 16.8MiB allocated; 2ms collecting garbage

Counts

6 → 54

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
2.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
2.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
1.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)

rewrite78.0ms (3.9%)

Memory

22.8MiB live, 82.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	319	1558
0	325	1431
0	1747	1380

Stop Event

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

Counts

60 → 70

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Outputs
(/.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x x) x) (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
x
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (fma.f64 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) x) eps))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (fma.f64 eps eps (.f64 (*.f64 x x) eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
eps
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) x (.f64 (neg.f64 (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx x x)
#s(approx (sqrt (- (* x x) eps)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (.f64 x x) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 5 binary64))))) (.f64 x x))) (.f64 x x) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)))))
#s(approx (- (* x x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (* x x) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
#s(approx (sqrt (- (* x x) eps)) x)
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (+.f64 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) x))
#s(approx (- (* x x) eps) (*.f64 x x))
#s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 (-.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) x) #s(literal -1 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) #s(literal -1 binary64)))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) x) (+.f64 (+.f64 (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64))) eps (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64))) eps (.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/8 binary64))) eps (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) eps x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)))) eps (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) eps x))
#s(approx (- (* x x) eps) (fma.f64 #s(literal -1 binary64) eps (*.f64 x x)))
#s(approx eps eps)
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (/.f64 x eps) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (-.f64 (/.f64 x eps) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (-.f64 (/.f64 x eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))) eps))
#s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -1 binary64)) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) x) eps) #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps) #s(literal -1 binary64) x) eps) #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))))
#s(approx (- (* x x) eps) (.f64 (.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))

eval10.0ms (0.5%)

Memory: -29.7MiB live, 17.6MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 939 to 378 computations (80.5% saved)

prune8.0ms (0.4%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	5	75

Accuracy

99.9%

Counts

75 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.6%	(/.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
✓	62.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	41.4%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
▶	21.3%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
▶	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))

Compiler

Compiled 130 to 80 computations (38.5% saved)

series63.0ms (3.1%)

Memory

26.8MiB live, 119.6MiB allocated; 4ms collecting garbage

Counts

48 → 197

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
(.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps)
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64))
(/.f64 eps (.f64 (.f64 x x) x))
eps
(.f64 (.f64 x x) x)
(*.f64 x x)
#s(literal 1/8 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x)
(-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x))))
(-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))
(pow.f64 eps #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal 5/64 binary64)
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x)))
#s(literal -1/16 binary64)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 eps #s(literal 3 binary64))
#s(literal 3 binary64)
(pow.f64 x #s(literal 4 binary64))
(/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x))
(.f64 #s(literal -1/8 binary64) (.f64 eps eps))
#s(literal -1/8 binary64)
(*.f64 eps eps)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (.f64 eps eps) (.f64 x x))
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 x x) eps)
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ eps (* (* x x) x)) 1/8) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ eps (* (* x x) x)) #s(hole binary64 (/ eps (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* 5/128 (/ (pow eps 4) (pow x 7)))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* 1/16 (* (pow eps 3) (pow x 2)))) (pow x 7))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))))) (pow x 7))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))))) (pow x 7))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* 5/128 (/ (pow eps 4) (pow x 6)))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* 1/16 (* (pow eps 3) (pow x 2)))) (pow x 6))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (- (* 1/8 (* (pow eps 2) (pow x 2))) (* -1/16 (pow eps 3))))) (pow x 6))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2)))) (* -1/16 (pow eps 3))))) (pow x 6))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* 5/128 (/ (pow eps 4) (pow x 6)))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (/ (+ (* 5/128 (pow eps 4)) (* 1/2 (* eps (pow x 6)))) (pow x 6))))
#s(approx (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) #s(hole binary64 (* 5/128 (/ (pow eps 4) (pow x 6)))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1/16 (/ (pow eps 3) (pow x 4)))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (/ (+ (* -1/8 (* (pow eps 2) (pow x 2))) (* -1/16 (pow eps 3))) (pow x 4))))
#s(approx (/ (pow eps 3) (pow x 4)) #s(hole binary64 (/ (pow eps 3) (pow x 4))))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (/ (* -1/8 (* eps eps)) (* x x)) #s(hole binary64 (* -1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (/ (* eps eps) (* x x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) #s(hole binary64 eps))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 eps)))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (/ (+ (* 5/128 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x)))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (- (* 5/128 (/ (pow eps 4) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (- (* 5/128 (/ (pow eps 4) (pow x 6))) (* -1/2 eps))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (/ (+ (* -1/8 (pow eps 2)) (* -1/16 (/ (pow eps 3) (pow x 2)))) (pow x 2))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (pow x 2)))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 x))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 2 x)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (* -5/128 (/ (pow eps 4) (pow x 6)))))) x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 x)))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2)))))))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 5/128 (/ (pow eps 3) (pow x 6)))))))
#s(approx (* 1/2 (* (pow eps 4) 5/64)) #s(hole binary64 (* 5/128 (pow eps 4))))
#s(approx (* (pow eps 4) 5/64) #s(hole binary64 (* 5/64 (pow eps 4))))
#s(approx (pow eps 4) #s(hole binary64 (pow eps 4)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* (pow eps 2) (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (pow eps 3) #s(hole binary64 (pow eps 3)))
#s(approx (* -1/8 (* eps eps)) #s(hole binary64 (* -1/8 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 5)))) (* 5/128 (/ 1 (pow x 7)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (/ 1/8 (* (pow eps 2) (pow x 3))) (* 5/128 (/ 1 (pow x 7))))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 3)))) (+ (* 1/2 (/ 1 (* (pow eps 3) x))) (* 5/128 (/ 1 (pow x 7)))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 4)))) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (/ 1/8 (* (pow eps 2) (pow x 2))) (* 5/128 (/ 1 (pow x 6))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 2)))) (+ (* 1/2 (/ 1 (pow eps 3))) (* 5/128 (/ 1 (pow x 6)))))))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* (pow eps 4) (+ (* 1/2 (/ 1 (pow eps 3))) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2)))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5)))) eps)) (* 5/128 (/ 1 (pow x 7)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4)))) eps)) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (pow x -1) x -1 1/2 (* (/ eps (* (* x x) x)) 1/8) (/ eps (* (* x x) x)) eps (* (* x x) x) (* x x) 1/8 (- x (sqrt (- (* x x) eps))) (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* 1/2 (* (pow eps 4) 5/64)) (* (pow eps 4) 5/64) (pow eps 4) 4 5/64 (pow x 6) 6 (* -1/2 eps) -1/2 (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) -1/16 (/ (pow eps 3) (pow x 4)) (pow eps 3) 3 (pow x 4) (/ (* -1/8 (* eps eps)) (* x x)) (* -1/8 (* eps eps)) -1/8 (* eps eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
10.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (pow x -1) x -1 1/2 (* (/ eps (* (* x x) x)) 1/8) (/ eps (* (* x x) x)) eps (* (* x x) x) (* x x) 1/8 (- x (sqrt (- (* x x) eps))) (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* 1/2 (* (pow eps 4) 5/64)) (* (pow eps 4) 5/64) (pow eps 4) 4 5/64 (pow x 6) 6 (* -1/2 eps) -1/2 (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) -1/16 (/ (pow eps 3) (pow x 4)) (pow eps 3) 3 (pow x 4) (/ (* -1/8 (* eps eps)) (* x x)) (* -1/8 (* eps eps)) -1/8 (* eps eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
10.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (pow x -1) x -1 1/2 (* (/ eps (* (* x x) x)) 1/8) (/ eps (* (* x x) x)) eps (* (* x x) x) (* x x) 1/8 (- x (sqrt (- (* x x) eps))) (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* 1/2 (* (pow eps 4) 5/64)) (* (pow eps 4) 5/64) (pow eps 4) 4 5/64 (pow x 6) 6 (* -1/2 eps) -1/2 (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) -1/16 (/ (pow eps 3) (pow x 4)) (pow eps 3) 3 (pow x 4) (/ (* -1/8 (* eps eps)) (* x x)) (* -1/8 (* eps eps)) -1/8 (* eps eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
9.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (pow x -1) x -1 1/2 (* (/ eps (* (* x x) x)) 1/8) (/ eps (* (* x x) x)) eps (* (* x x) x) (* x x) 1/8 (- x (sqrt (- (* x x) eps))) (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* 1/2 (* (pow eps 4) 5/64)) (* (pow eps 4) 5/64) (pow eps 4) 4 5/64 (pow x 6) 6 (* -1/2 eps) -1/2 (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) -1/16 (/ (pow eps 3) (pow x 4)) (pow eps 3) 3 (pow x 4) (/ (* -1/8 (* eps eps)) (* x x)) (* -1/8 (* eps eps)) -1/8 (* eps eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))
8.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (pow x -1) x -1 1/2 (* (/ eps (* (* x x) x)) 1/8) (/ eps (* (* x x) x)) eps (* (* x x) x) (* x x) 1/8 (- x (sqrt (- (* x x) eps))) (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* 1/2 (* (pow eps 4) 5/64)) (* (pow eps 4) 5/64) (pow eps 4) 4 5/64 (pow x 6) 6 (* -1/2 eps) -1/2 (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) -1/16 (/ (pow eps 3) (pow x 4)) (pow eps 3) 3 (pow x 4) (/ (* -1/8 (* eps eps)) (* x x)) (* -1/8 (* eps eps)) -1/8 (* eps eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps) (+ x (pow (- (* x x) eps) 1/2)))

rewrite177.0ms (8.8%)

Memory

7.2MiB live, 188.3MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	869	7699
0	931	6504
0	4900	6283

Stop Event

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

Counts

245 → 395

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
(.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps)
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(literal 1/2 binary64)
(.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64))
(/.f64 eps (.f64 (.f64 x x) x))
eps
(.f64 (.f64 x x) x)
(*.f64 x x)
#s(literal 1/8 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x)
(-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x))))
(-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))
(pow.f64 eps #s(literal 4 binary64))
#s(literal 4 binary64)
#s(literal 5/64 binary64)
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
(fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x)))
#s(literal -1/16 binary64)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
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#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 x)))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* eps (+ 1/2 (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2)))))))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 5/128 (/ (pow eps 3) (pow x 6)))))))
#s(approx (* 1/2 (* (pow eps 4) 5/64)) #s(hole binary64 (* 5/128 (pow eps 4))))
#s(approx (* (pow eps 4) 5/64) #s(hole binary64 (* 5/64 (pow eps 4))))
#s(approx (pow eps 4) #s(hole binary64 (pow eps 4)))
#s(approx (* -1/2 eps) #s(hole binary64 (* -1/2 eps)))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* (pow eps 2) (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (pow eps 3) #s(hole binary64 (pow eps 3)))
#s(approx (* -1/8 (* eps eps)) #s(hole binary64 (* -1/8 (pow eps 2))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (* (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 5)))) (* 5/128 (/ 1 (pow x 7)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (/ 1/8 (* (pow eps 2) (pow x 3))) (* 5/128 (/ 1 (pow x 7))))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 3)))) (+ (* 1/2 (/ 1 (* (pow eps 3) x))) (* 5/128 (/ 1 (pow x 7)))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 4)))) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (/ 1/8 (* (pow eps 2) (pow x 2))) (* 5/128 (/ 1 (pow x 6))))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 2)))) (+ (* 1/2 (/ 1 (pow eps 3))) (* 5/128 (/ 1 (pow x 6)))))))))
#s(approx (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) #s(hole binary64 (* (pow eps 4) (+ (* 1/2 (/ 1 (pow eps 3))) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2)))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5)))) eps)) (* 5/128 (/ 1 (pow x 7)))))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4)))) eps)) (* 5/128 (/ 1 (pow x 6)))))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))

Outputs
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps (.f64 x x)) x) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps))
(.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps (.f64 x x)) x) (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps)
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#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (*.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (/.f64 x eps))) eps))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (/.f64 (*.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (/.f64 x eps)))) eps))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -1 binary64)) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) x) eps) #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps) #s(literal -1 binary64) x) eps) #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ (* (pow x -1) 1/2) (* (/ eps (* (* x x) x)) 1/8)) (.f64 (fma.f64 (pow.f64 (.f64 eps x) #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (*.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/8 binary64))) eps))
#s(approx (/ (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) x) (.f64 (fma.f64 (-.f64 (/.f64 (.f64 (/.f64 (fma.f64 (pow.f64 (.f64 eps x) #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/8 binary64))) eps) #s(literal -1 binary64)) eps) (/.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/16 binary64)) eps)) #s(literal -1 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 5/128 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (- (- (/ (* 1/2 (* (pow eps 4) 5/64)) (pow x 6)) (* -1/2 eps)) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x)))) (.f64 (fma.f64 (-.f64 (/.f64 (.f64 (/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) eps) #s(literal -1 binary64)) eps) (/.f64 (.f64 (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal 1/16 binary64)) eps)) #s(literal -1 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal 5/128 binary64))) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (/ (* -1/8 (* eps eps)) (* x x))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal -1 binary64)) #s(literal 1/8 binary64) (*.f64 (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal 1/16 binary64)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1 binary64) eps) x)) eps) #s(literal -1 binary64) (.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) eps) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)))))) eps) #s(literal -1 binary64) (.f64 (.f64 #s(literal -1 binary64) eps) x)) eps) #s(literal -1 binary64) (.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2)) (.f64 (.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))))
#s(approx (- (* x x) eps) (.f64 (.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) x) eps) #s(literal -1 binary64) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps) #s(literal -1 binary64) x) eps) #s(literal -1 binary64) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))

eval76.0ms (3.8%)

Memory: -3.2MiB live, 96.2MiB allocated; 19ms collecting garbage
Compiler: Compiled 25 887 to 2 353 computations (90.9% saved)

prune303.0ms (15.1%)

Memory

4.2MiB live, 388.2MiB allocated; 31ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	570	3	573
Fresh	0	0	0
Picked	3	1	4
Done	0	1	1
Total	573	5	578

Accuracy

100.0%

Counts

578 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
✓	62.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	41.3%	#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
▶	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
✓	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))

Compiler

Compiled 135 to 74 computations (45.2% saved)

series29.0ms (1.4%)

Memory

-1.3MiB live, 46.2MiB allocated; 1ms collecting garbage

Counts

25 → 127

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
(fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps))
(/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (*.f64 x x) x))
(*.f64 #s(literal 1/8 binary64) eps)
#s(literal 1/8 binary64)
eps
(.f64 (.f64 x x) x)
(*.f64 x x)
x
(.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps))
(*.f64 (/.f64 eps x) (/.f64 eps x))
(/.f64 eps x)
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 #s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
#s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps)
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 x x) eps)

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (* 1/8 eps) (* (* x x) x)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (* (* (pow x -1) 1/2) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (pow x -1) 1/2) #s(hole binary64 (/ 1/2 x)))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (* (/ eps x) (/ eps x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) #s(hole binary64 eps))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 2 x)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 x))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 x)))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (* 1/8 eps) #s(hole binary64 (* 1/8 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) (/ (* 1/8 eps) (* (* x x) x)) (* 1/8 eps) 1/8 eps (* (* x x) x) (* x x) x (* (* (pow x -1) 1/2) eps) (* (pow x -1) 1/2) (pow x -1) -1 1/2 (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) (* (/ eps x) (/ eps x)) (/ eps x) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps))
4.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) (/ (* 1/8 eps) (* (* x x) x)) (* 1/8 eps) 1/8 eps (* (* x x) x) (* x x) x (* (* (pow x -1) 1/2) eps) (* (pow x -1) 1/2) (pow x -1) -1 1/2 (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) (* (/ eps x) (/ eps x)) (/ eps x) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps))
4.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) (/ (* 1/8 eps) (* (* x x) x)) (* 1/8 eps) 1/8 eps (* (* x x) x) (* x x) x (* (* (pow x -1) 1/2) eps) (* (pow x -1) 1/2) (pow x -1) -1 1/2 (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) (* (/ eps x) (/ eps x)) (/ eps x) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps))
4.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) (/ (* 1/8 eps) (* (* x x) x)) (* 1/8 eps) 1/8 eps (* (* x x) x) (* x x) x (* (* (pow x -1) 1/2) eps) (* (pow x -1) 1/2) (pow x -1) -1 1/2 (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) (* (/ eps x) (/ eps x)) (/ eps x) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps))
3.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) (/ (* 1/8 eps) (* (* x x) x)) (* 1/8 eps) 1/8 eps (* (* x x) x) (* x x) x (* (* (pow x -1) 1/2) eps) (* (pow x -1) 1/2) (pow x -1) -1 1/2 (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) (* (/ eps x) (/ eps x)) (/ eps x) (* 1/2 eps) (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2)) (pow (- (* x x) eps) 1/2) (- (* x x) eps))

rewrite115.0ms (5.7%)

Memory

2.3MiB live, 144.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	617	4581
0	650	3496
0	3516	3381

Stop Event

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

Counts

152 → 220

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
(fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps))
(/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (*.f64 x x) x))
(*.f64 #s(literal 1/8 binary64) eps)
#s(literal 1/8 binary64)
eps
(.f64 (.f64 x x) x)
(*.f64 x x)
x
(.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 x #s(literal -1 binary64))
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps))
(*.f64 (/.f64 eps x) (/.f64 eps x))
(/.f64 eps x)
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 #s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
#s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps)
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(-.f64 (*.f64 x x) eps)
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (* 1/8 eps) (* (* x x) x)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (* (* (pow x -1) 1/2) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (pow x -1) 1/2) #s(hole binary64 (/ 1/2 x)))
#s(approx (pow x -1) #s(hole binary64 (/ 1 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (* (/ eps x) (/ eps x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) #s(hole binary64 eps))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 2 x)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 x))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 x)))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (* 1/8 eps) #s(hole binary64 (* 1/8 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (/ (* 1/8 eps) (* (* x x) x)) eps) (* (* (pow x -1) 1/2) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))))
#s(approx (/ (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (* (/ eps x) (/ eps x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) #s(hole binary64 (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 1/2) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Outputs
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (fma.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) eps))
(.f64 (fma.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) eps)
(.f64 eps (fma.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps) (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps)) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps))) (-.f64 (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps)))
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(fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps (.f64 (.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)) eps))
(fma.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps (.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) eps) (.f64 (.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)) eps))
(fma.f64 eps (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) (.f64 (.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)) eps))
(fma.f64 eps (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps))
(-.f64 (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps) (.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) eps))
(+.f64 (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps) (.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64)) eps))
(.f64 (.f64 (pow.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/8 binary64)) (/.f64 eps x))
(.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64))
(.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 (*.f64 x x) x)))
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(/.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) x)
(/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (*.f64 x x) x))
(*.f64 #s(literal 1/8 binary64) eps)
(*.f64 eps #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
eps
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(.f64 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
(.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))) eps)
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(.f64 eps (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
#s(literal -1 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (neg.f64 (fma.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal -1 binary64) x))
(/.f64 (fma.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) eps)) x)
(-.f64 (/.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(+.f64 (/.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) x) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps))) (-.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps) (.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))))
(fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))))
(-.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (.f64 (/.f64 eps x) (.f64 (/.f64 eps x) #s(literal 1/8 binary64))) (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (/.f64 eps x) (*.f64 (/.f64 eps x) #s(literal 1/8 binary64))))
(*.f64 (neg.f64 (/.f64 eps x)) (neg.f64 (/.f64 eps x)))
(*.f64 (fabs.f64 (/.f64 eps x)) (fabs.f64 (/.f64 eps x)))
(*.f64 (/.f64 eps x) (/.f64 eps x))
(pow.f64 (/.f64 eps x) #s(literal 2 binary64))
(/.f64 (*.f64 eps (/.f64 eps x)) x)
(/.f64 (*.f64 (/.f64 eps x) eps) x)
(/.f64 (neg.f64 (.f64 eps eps)) (neg.f64 (.f64 x x)))
(/.f64 (.f64 eps eps) (.f64 x x))
(/.f64 (.f64 #s(literal -1 binary64) eps) (.f64 #s(literal -1 binary64) x))
(/.f64 eps x)
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#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (-.f64 (.f64 (/.f64 x eps) #s(literal -1 binary64)) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) x) eps) #s(literal -1 binary64) (.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps) #s(literal -1 binary64) x) eps) #s(literal -1 binary64) (*.f64 (neg.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1 binary64) eps) x)) eps) #s(literal -1 binary64) (.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) eps) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/2 binary64)))))) eps) #s(literal -1 binary64) (.f64 (.f64 #s(literal -1 binary64) eps) x)) eps) #s(literal -1 binary64) (.f64 (*.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) x) eps) #s(literal -1 binary64) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (+ x (pow (- (* x x) eps) 1/2)) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))) eps) #s(literal -1 binary64) x) eps) #s(literal -1 binary64) (*.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 1/2 binary64))) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))))))
#s(approx (pow (- (* x x) eps) 1/2) (.f64 (.f64 #s(literal -1 binary64) eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))) (.f64 (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))))
#s(approx (- (* x x) eps) (.f64 (.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))

eval30.0ms (1.5%)

Memory: 3.8MiB live, 50.3MiB allocated; 2ms collecting garbage
Compiler: Compiled 11 436 to 1 051 computations (90.8% saved)

prune107.0ms (5.3%)

Memory

-23.4MiB live, 120.7MiB allocated; 5ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	253	5	258

Accuracy

100.0%

Counts

258 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
✓	62.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	41.3%	#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
✓	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
✓	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))

Compiler

Compiled 367 to 147 computations (59.9% saved)

regimes9.0ms (0.4%)

Memory

13.4MiB live, 13.3MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 #s(approx (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))

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

Calls

3 calls:

3.0ms	eps
3.0ms	x
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.4%)

Memory

13.4MiB live, 13.4MiB allocated; 0ms collecting garbage

Counts

6 → 2

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (*.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))

Calls

3 calls:

2.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
98.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
88.3%	2	`x`
85.9%	2	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.4%)

Memory

-36.1MiB live, 11.3MiB allocated; 1ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (.f64 x x)))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 (.f64 x x) x)) eps (.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) eps)))
#s(approx (/ (- (* x x) (* (pow (- (* x x) eps) 1/2) (pow (- (* x x) eps) 1/2))) (+ x (pow (- (* x x) eps) 1/2))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))

Calls

3 calls:

3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
41.4%	1	`eps`
41.4%	1	`x`
41.4%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Accuracy

Total -11.1b remaining (-28%)

Threshold costs -11.1b (-28%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (*.f64 (/.f64 eps (*.f64 (*.f64 x x) x)) #s(literal 1/8 binary64))) eps))

#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x))

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64))) eps))

Calls

3 calls:

1.0ms	eps
1.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
38.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
38.3%	1	`x`
38.3%	1	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.544976484412512e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

derivations33.0ms (1.7%)

Memory

30.3MiB live, 30.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 142 to 44 computations (69% saved)

preprocess35.0ms (1.7%)

Memory: -40.3MiB live, 55.4MiB allocated; 5ms collecting garbage
Compiler: Compiled 300 to 100 computations (66.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze11.0ms (0.6%)

sample802.0ms (40%)

explain84.0ms (4.2%)

preprocess7.0ms (0.3%)

series12.0ms (0.6%)

rewrite78.0ms (3.9%)

eval10.0ms (0.5%)

prune8.0ms (0.4%)

series63.0ms (3.1%)

rewrite177.0ms (8.8%)

eval76.0ms (3.8%)

prune303.0ms (15.1%)

series29.0ms (1.4%)

rewrite115.0ms (5.7%)

eval30.0ms (1.5%)

prune107.0ms (5.3%)

regimes9.0ms (0.4%)

regimes7.0ms (0.4%)

regimes7.0ms (0.4%)

regimes4.0ms (0.2%)

bsearch0.0ms (0%)

derivations33.0ms (1.7%)

preprocess35.0ms (1.7%)

end0.0ms (0%)

Profiling