Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze29.0ms (0.7%)

Memory

-13.3MiB live, 31.5MiB allocated; 28ms 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)

sample1.8s (41.2%)

Memory

1.1MiB live, 2 213.0MiB allocated; 526ms collecting garbage

Samples

670.0ms	2 769×	1	valid
476.0ms	4 808×	0	valid
128.0ms	679×	2	valid
10.0ms	154×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 957.0ms

ival-<=: 214.0ms (22.4% of total)

ival-sub: 186.0ms (19.4% of total)

ival-mult: 183.0ms (19.1% of total)

adjust: 166.0ms (17.3% of total)

ival-sqrt: 165.0ms (17.2% of total)

ival-and: 23.0ms (2.4% of total)

exact: 18.0ms (1.9% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain152.0ms (3.5%)

Memory

-28.4MiB live, 129.6MiB allocated; 34ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
113	-	-	`(-.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	113	1

Confusion

	Predicted +	Predicted -
+	113	1
-	0	142

Precision

1.0

Recall

0.9912280701754386

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	113	1	0
-	0	0	142

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	143
1	113

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

51.0ms	190×	1	valid
15.0ms	290×	0	valid
5.0ms	32×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-sub: 36.0ms (66% of total)

adjust: 7.0ms (12.8% of total)

ival-sqrt: 6.0ms (11% of total)

ival-mult: 6.0ms (11% of total)

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

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

preprocess15.0ms (0.3%)

Memory

22.8MiB live, 22.8MiB 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
0	6	8
0	10	8
1	14	8
2	27	8
3	46	8
4	58	8
0	58	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

series10.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated; 0ms 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
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)
2.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
2.0ms	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)

simplify180.0ms (4.1%)

Memory

-0.3MiB live, 288.5MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	1485
1	871	1471
2	3638	1456
0	8099	1395

Stop Event

1×	iter limit
1×	node limit

Counts

54 → 54

Calls

Call 1

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

rewrite50.0ms (1.1%)

Memory

-29.9MiB live, 108.2MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	42	24
0	320	24

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

6 → 43

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

eval46.0ms (1%)

Memory: -2.3MiB live, 46.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 2 114 to 462 computations (78.1% saved)

prune7.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Accuracy

99.5%

Counts

99 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.8%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	60.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
▶	54.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	7.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
	25.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	39.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 298 to 200 computations (32.9% saved)

series19.0ms (0.4%)

Memory

23.0MiB live, 23.0MiB allocated; 0ms collecting garbage

Counts

26 → 88

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
#s(approx (sqrt (- (* x x) eps)) x)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(-.f64 x #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 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(literal 1/2 binary64) x)
#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 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) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1/2 (/ eps x))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (/ (+ (* -1/2 eps) (pow x 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (/ 1/8 (pow x 3)) #s(hole binary64 (/ 1/8 (pow x 3))))
#s(approx (pow x 3) #s(hole binary64 (pow x 3)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#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 x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 x))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#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 (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) 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 (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 (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (+ (* 1/8 (/ eps (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 (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 x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* eps (- (/ x eps) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#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)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) 1/8 (pow x 3) 3 (/ 1/2 x) 1/2)
3.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) 1/8 (pow x 3) 3 (/ 1/2 x) 1/2)
3.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) 1/8 (pow x 3) 3 (/ 1/2 x) 1/2)
3.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) 1/8 (pow x 3) 3 (/ 1/2 x) 1/2)
3.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) 1/8 (pow x 3) 3 (/ 1/2 x) 1/2)

simplify246.0ms (5.6%)

Memory

-28.0MiB live, 251.7MiB allocated; 69ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	399	2095
1	1058	2074
2	4159	2067
0	8244	1969

Stop Event

1×	iter limit
1×	node limit

Counts

88 → 88

Calls

Call 1

Inputs
#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) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1/2 (/ eps x))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (/ (+ (* -1/2 eps) (pow x 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (/ 1/8 (pow x 3)) #s(hole binary64 (/ 1/8 (pow x 3))))
#s(approx (pow x 3) #s(hole binary64 (pow x 3)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#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 x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 x))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#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 (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) 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 (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 (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (+ (* 1/8 (/ eps (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 (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 x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* eps (- (/ x eps) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#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)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))))

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

rewrite73.0ms (1.7%)

Memory

6.3MiB live, 101.0MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	187
0	47	187
1	176	187
0	1348	187

Stop Event

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

Counts

26 → 172

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
#s(approx (sqrt (- (* x x) eps)) x)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(-.f64 x #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 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

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

eval34.0ms (0.8%)

Memory: 27.4MiB live, 71.7MiB allocated; 8ms collecting garbage
Compiler: Compiled 7 064 to 1 074 computations (84.8% saved)

prune24.0ms (0.6%)

Memory

8.8MiB live, 54.2MiB allocated; 6ms collecting garbage

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	255	15	270
Fresh	0	4	4
Picked	1	4	5
Done	0	0	0
Total	256	23	279

Accuracy

99.9%

Counts

279 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.3%	(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
▶	59.8%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	54.5%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	59.8%	(-.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (/.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
✓	60.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	54.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
▶	39.7%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)))
	27.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x))
	39.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) (/.f64 #s(literal 1/2 binary64) x))))
	38.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 3 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)) (pow.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 2 binary64)))))
	25.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	39.7%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	44.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
	34.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) eps) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64))) eps))
	38.9%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 3 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)) (pow.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) #s(literal 2 binary64)))) eps))
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	40.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))) eps))
	32.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)) eps))
	27.8%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))))
	14.5%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 eps eps))))

Compiler

Compiled 1 284 to 742 computations (42.2% saved)

series85.0ms (1.9%)

Memory

-1.7MiB live, 187.6MiB allocated; 26ms collecting garbage

Counts

37 → 255

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ (/ eps x) x) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (* (/ 1/8 (pow x 3)) eps) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ 1/8 (pow x 3)) eps) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ 1/8 (pow x 3)) #s(hole binary64 (/ 1/8 (pow x 3))))
#s(approx (pow x 3) #s(hole binary64 (pow x 3)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* (pow x 2) (- x (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* (pow x 2) (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (sqrt (pow eps 3)) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (sqrt -1)))))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* (sqrt eps) (* x (sqrt -1))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* x (+ (* x (+ 2 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* (sqrt eps) (* x (sqrt -1))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* x (+ x (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* x (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (- (* 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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x)))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1/2 (* x (+ (* -2 eps) (* -1 eps))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/2 (+ (* -2 eps) (* -1 eps)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* 1/2 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (pow x 3)))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* 3 (pow x 2))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (* 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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 2)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* 2 (pow x 3))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) 2)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))) (+ 2 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (+ 2 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (* 1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* 1/2 eps) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) 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 (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* -1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* eps (- (* 1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* eps (- (* eps (- (* 1/2 (/ (* eps (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6))))) (pow x 3))) (* -1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (pow x 2))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2)))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (+ (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)) (pow x 2)))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (+ (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)) (pow x 2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* -3/2 eps) (* 2 (pow x 2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* 2 (pow x 2)) (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* 2 (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)))) 1))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))

Calls

6 calls:

Time	Variable		Point	Expression
20.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ eps x) x) (/ eps x) 1/8 1/2 (- x (sqrt (- (* x x) eps))) (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) (/ 1/2 x) (* (* (/ 1/8 (pow x 3)) eps) eps) (* (/ 1/8 (pow x 3)) eps) (/ 1/8 (pow x 3)) (pow x 3) 3 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (- (pow x 3) (pow (- (* x x) eps) 3/2)) (pow (- (* x x) eps) 3/2) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) 3/2 (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (sqrt (- (* x x) eps)))
14.0ms	x	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ eps x) x) (/ eps x) 1/8 1/2 (- x (sqrt (- (* x x) eps))) (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) (/ 1/2 x) (* (* (/ 1/8 (pow x 3)) eps) eps) (* (/ 1/8 (pow x 3)) eps) (/ 1/8 (pow x 3)) (pow x 3) 3 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (- (pow x 3) (pow (- (* x x) eps) 3/2)) (pow (- (* x x) eps) 3/2) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) 3/2 (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (sqrt (- (* x x) eps)))
13.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ eps x) x) (/ eps x) 1/8 1/2 (- x (sqrt (- (* x x) eps))) (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) (/ 1/2 x) (* (* (/ 1/8 (pow x 3)) eps) eps) (* (/ 1/8 (pow x 3)) eps) (/ 1/8 (pow x 3)) (pow x 3) 3 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (- (pow x 3) (pow (- (* x x) eps) 3/2)) (pow (- (* x x) eps) 3/2) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) 3/2 (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (sqrt (- (* x x) eps)))
11.0ms	eps	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ eps x) x) (/ eps x) 1/8 1/2 (- x (sqrt (- (* x x) eps))) (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) (/ 1/2 x) (* (* (/ 1/8 (pow x 3)) eps) eps) (* (/ 1/8 (pow x 3)) eps) (/ 1/8 (pow x 3)) (pow x 3) 3 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (- (pow x 3) (pow (- (* x x) eps) 3/2)) (pow (- (* x x) eps) 3/2) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) 3/2 (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (sqrt (- (* x x) eps)))
10.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ eps x) x) (/ eps x) 1/8 1/2 (- x (sqrt (- (* x x) eps))) (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) (/ 1/2 x) (* (* (/ 1/8 (pow x 3)) eps) eps) (* (/ 1/8 (pow x 3)) eps) (/ 1/8 (pow x 3)) (pow x 3) 3 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (- (pow x 3) (pow (- (* x x) eps) 3/2)) (pow (- (* x x) eps) 3/2) (- (* x x) eps) (+ (* x x) (neg eps)) (neg eps) 3/2 (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (sqrt (- (* x x) eps)))

simplify198.0ms (4.5%)

Memory

-6.2MiB live, 225.8MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1434	11835
1	4298	11662
0	8151	11088

Stop Event

1×	iter limit
1×	node limit

Counts

255 → 255

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ (/ eps x) x) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (* (/ 1/8 (pow x 3)) eps) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ 1/8 (pow x 3)) eps) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ 1/8 (pow x 3)) #s(hole binary64 (/ 1/8 (pow x 3))))
#s(approx (pow x 3) #s(hole binary64 (pow x 3)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* (pow x 2) (- x (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (- (* (pow x 2) (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (sqrt (pow eps 3)) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (sqrt -1)))))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* (sqrt eps) (* x (sqrt -1))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* x (+ (* x (+ 2 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* (sqrt eps) (* x (sqrt -1))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* x (+ x (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* x (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (- (* 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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x)))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1/2 (* x (+ (* -2 eps) (* -1 eps))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/2 (+ (* -2 eps) (* -1 eps)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* x (- (* 1/2 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (pow x 3)))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* 3 (pow x 2))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (* 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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 2)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* 2 (pow x 3))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) 2)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))) (+ 2 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1 (* (pow x 3) (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (+ 2 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (* 1/2 (/ eps (pow x 2)))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (/ eps (pow x 2))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* (pow x 2) (- (+ 1 (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))) (/ eps (pow x 2))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (* 1/2 eps) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) eps)))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) 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 (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
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#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3)))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* -1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* eps (- (* 1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* eps (- (* eps (- (* eps (- (* 1/2 (/ (* eps (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6))))) (pow x 3))) (* -1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (pow x 2))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2)))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (+ (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)) (pow x 2)))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (+ (* 2 (pow x 2)) (+ (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)) (pow x 2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* -3/2 eps) (* 2 (pow x 2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* 2 (pow x 2)) (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (+ (* 2 (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (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 (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ 1/2 x) eps) (* (* (/ 1/8 (pow x 3)) eps) eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) 1))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps))) 1))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)))) 1))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.f64 x #s(literal 1 binary64))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) x) #s(literal -1 binary64)) x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (fma.f64 (-.f64 (.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (.f64 (neg.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))) #s(literal -1/2 binary64))) x) #s(literal -1 binary64)) x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))
#s(approx (- (* x x) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (- (* x x) (- (* x x) eps)) eps)
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))
#s(approx x #s(hole binary64 x))
#s(approx x x)
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
#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)) (fma.f64 (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
#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)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (.f64 x x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
#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 (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x))
#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))) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))
#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 (sqrt (- (* x x) eps))) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (neg x) (neg.f64 x))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)))
#s(approx (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
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#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) (*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64)))
#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
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#s(approx (/ (/ eps x) x) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ (/ eps x) x) (/.f64 (/.f64 eps x) x))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (/ eps x) (/.f64 eps x))
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#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ 1/2 x) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (* (* (/ 1/8 (pow x 3)) eps) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (* (/ 1/8 (pow x 3)) eps) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))))
#s(approx (* (/ 1/8 (pow x 3)) eps) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (* (/ 1/8 (pow x 3)) eps) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)))
#s(approx (/ 1/8 (pow x 3)) #s(hole binary64 (/ 1/8 (pow x 3))))
#s(approx (/ 1/8 (pow x 3)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
#s(approx (pow x 3) #s(hole binary64 (pow x 3)))
#s(approx (pow x 3) (pow.f64 x #s(literal 3 binary64)))
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#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1)))))
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#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))))
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#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (sqrt (pow eps 3)) (sqrt -1))))
#s(approx (pow (- (* x x) eps) 3/2) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1)))))
#s(approx (pow (- (* x x) eps) 3/2) (fma.f64 (.f64 (.f64 (.f64 x x) (/.f64 (.f64 #s(literal 3 binary64) (.f64 eps eps)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))))))
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#s(approx (pow (- (* x x) eps) 3/2) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (-.f64 (.f64 eps #s(literal -3 binary64)) (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (.f64 #s(literal 3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (.f64 #s(literal 3 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (.f64 eps #s(literal -3 binary64)) (.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 (.f64 #s(literal 3 binary64) (.f64 eps eps)) #s(literal 2 binary64)) (pow.f64 eps #s(literal 3 binary64))))))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (.f64 #s(literal 3 binary64) (.f64 eps eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 x x) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) (neg.f64 eps))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* x x) (neg eps)) (-.f64 (*.f64 x x) eps))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (neg.f64 eps))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* (sqrt eps) (* x (sqrt -1))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (-.f64 (.f64 (.f64 (sqrt.f64 eps) x) (sqrt.f64 #s(literal -1 binary64))) eps))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (.f64 #s(literal 2 binary64) x)) x) eps))
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#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) #s(hole binary64 (* -1 eps)))
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#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (-.f64 (.f64 (.f64 (sqrt.f64 eps) x) (sqrt.f64 #s(literal -1 binary64))) eps))
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#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (-.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x) x) eps))
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#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
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#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) (*.f64 x x))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1 binary64) #s(literal 1 binary64)) (.f64 x x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
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#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) (.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps eps)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps eps)))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps eps)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- (pow x 3) (pow (- (* x x) eps) 3/2)) (.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal 9 binary64) (pow.f64 x #s(literal 4 binary64))) eps) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps eps)) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (pow (- (* x x) eps) 3/2) (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps eps)))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps eps)))
#s(approx (pow (- (* x x) eps) 3/2) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (pow (- (* x x) eps) 3/2) (.f64 (fma.f64 (/.f64 (fma.f64 (.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (.f64 (.f64 #s(literal 9 binary64) (pow.f64 x #s(literal 4 binary64))) eps) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 (.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* x x) (neg eps)) (.f64 (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) (neg.f64 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) (neg.f64 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) #s(literal 1 binary64)) (neg.f64 eps)))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))
#s(approx (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 2 binary64))) (neg.f64 eps))) #s(literal 1 binary64)) (neg.f64 eps)))
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#s(approx (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x)) (neg.f64 eps))) #s(literal 1 binary64)) (neg.f64 eps)))
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rewrite137.0ms (3.1%)

Memory

-23.8MiB live, 120.2MiB allocated; 66ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	359
0	73	355
1	271	339
0	2117	337

Stop Event

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

Counts

37 → 388

Calls

Call 1

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

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

eval192.0ms (4.4%)

Memory: -14.7MiB live, 121.3MiB allocated; 23ms collecting garbage
Compiler: Compiled 36 357 to 3 329 computations (90.8% saved)

prune32.0ms (0.7%)

Memory

4.8MiB live, 51.6MiB allocated; 3ms collecting garbage

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	792	6	798
Fresh	13	1	14
Picked	4	1	5
Done	0	4	4
Total	809	12	821

Accuracy

100.0%

Counts

821 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	59.8%	(-.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (/.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
✓	60.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	54.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
▶	46.0%	#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (.f64 (/.f64 (.f64 eps #s(literal -3 binary64)) x) #s(literal -1/6 binary64)))
▶	46.2%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
▶	44.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64)) eps) x))
▶	44.4%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
	44.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) eps)) eps)) x) eps))

Compiler

Compiled 467 to 256 computations (45.2% saved)

series49.0ms (1.1%)

Memory

-1.9MiB live, 44.4MiB allocated; 4ms collecting garbage

Counts

30 → 169

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 #s(hole binary64 x))
#s(approx (* (/ 1/2 x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (* (/ (* eps -3) x) -1/6) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (* eps -3) x) #s(hole binary64 (* -3 (/ eps x))))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ eps (* x x)) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ (/ eps x) x) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x)))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) 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 eps #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (* eps -3) #s(hole binary64 (* -3 eps)))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))))))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) 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 (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	eps	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) x (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* (/ 1/2 x) eps) (/ 1/2 x) 1/2 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (* (/ (* eps -3) x) -1/6) (/ (* eps -3) x) (* eps -3) -3 -1/6 (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) 1/8 (- x (sqrt (- (* x x) eps))) (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) (+ (* 1/8 (/ (/ eps x) x)) 1/2) (/ (/ eps x) x) (/ eps x))
4.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) x (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* (/ 1/2 x) eps) (/ 1/2 x) 1/2 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (* (/ (* eps -3) x) -1/6) (/ (* eps -3) x) (* eps -3) -3 -1/6 (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) 1/8 (- x (sqrt (- (* x x) eps))) (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) (+ (* 1/8 (/ (/ eps x) x)) 1/2) (/ (/ eps x) x) (/ eps x))
4.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) x (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* (/ 1/2 x) eps) (/ 1/2 x) 1/2 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (* (/ (* eps -3) x) -1/6) (/ (* eps -3) x) (* eps -3) -3 -1/6 (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) 1/8 (- x (sqrt (- (* x x) eps))) (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) (+ (* 1/8 (/ (/ eps x) x)) 1/2) (/ (/ eps x) x) (/ eps x))
3.0ms	x	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) x (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* (/ 1/2 x) eps) (/ 1/2 x) 1/2 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (* (/ (* eps -3) x) -1/6) (/ (* eps -3) x) (* eps -3) -3 -1/6 (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) 1/8 (- x (sqrt (- (* x x) eps))) (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) (+ (* 1/8 (/ (/ eps x) x)) 1/2) (/ (/ eps x) x) (/ eps x))
3.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) eps (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) x (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* (/ 1/2 x) eps) (/ 1/2 x) 1/2 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (* (/ (* eps -3) x) -1/6) (/ (* eps -3) x) (* eps -3) -3 -1/6 (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) 1/8 (- x (sqrt (- (* x x) eps))) (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) (+ (* 1/8 (/ (/ eps x) x)) 1/2) (/ (/ eps x) x) (/ eps x))

simplify236.0ms (5.4%)

Memory

3.9MiB live, 327.4MiB allocated; 75ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1006	7664
1	3053	7562
0	8968	7191

Stop Event

1×	iter limit
1×	node limit

Counts

169 → 169

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* (sqrt eps) (/ 1 (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 #s(hole binary64 x))
#s(approx (* (/ 1/2 x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (* (/ (* eps -3) x) -1/6) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (* eps -3) x) #s(hole binary64 (* -3 (/ eps x))))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ eps (* x x)) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ (/ eps x) x) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x)))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* 2 x)))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2)))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) 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 eps #s(hole binary64 eps))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* -1/2 (/ eps x)) (* 2 x))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))))
#s(approx (* eps -3) #s(hole binary64 (* -3 eps)))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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 (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 (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))))))
#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 (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (* (+ (* 1/8 (/ (/ eps x) x)) 1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(hole binary64 (+ x (* -1 (* (sqrt eps) (sqrt -1))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #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 (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) #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 (+ (sqrt (- (* x x) eps)) x) #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)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps)))))))
#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) 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 (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (+ (* 1/8 (/ (/ eps x) x)) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))

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

rewrite226.0ms (5.2%)

Memory

35.8MiB live, 261.6MiB allocated; 67ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	259
0	71	243
1	256	211
2	1758	211
0	9310	211

Stop Event

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

Counts

30 → 507

Calls

Call 1

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

Outputs
(.f64 (/.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) (-.f64 #s(literal 0 binary64) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(.f64 (/.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) (-.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)))) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(/.f64 (neg.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 (/.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(neg.f64 (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
#s(approx (- (* x x) (- (* x x) eps)) eps)
eps
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(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) #s(literal -1/4 binary64))) (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/16 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))))
(/.f64 (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/16 binary64)))))
(/.f64 (fma.f64 #s(literal 1/512 binary64) (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64)))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 x))) (/.f64 eps (neg.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 x))) (/.f64 eps x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 eps (neg.f64 (neg.f64 x))) (/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (neg.f64 x)) (/.f64 (neg.f64 eps) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 (neg.f64 eps) x) (/.f64 #s(literal 1/8 binary64) (neg.f64 x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x))))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))) (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 3 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))) (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (pow.f64 (/.f64 eps (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/64 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64))))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (*.f64 x x))
(/.f64 (neg.f64 (neg.f64 eps)) (*.f64 x x))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x))
(/.f64 (neg.f64 eps) (*.f64 x x))
(/.f64 (/.f64 eps x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 eps x) x)
(/.f64 eps (*.f64 x x))
(neg.f64 (/.f64 (/.f64 (neg.f64 eps) x) x))
(neg.f64 (/.f64 eps (*.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
(neg.f64 (/.f64 (neg.f64 eps) x))

eval99.0ms (2.3%)

Memory: -26.4MiB live, 158.0MiB allocated; 39ms collecting garbage
Compiler: Compiled 22 596 to 2 770 computations (87.7% saved)

prune24.0ms (0.6%)

Memory

25.6MiB live, 71.8MiB allocated; 7ms collecting garbage

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	597	5	602
Fresh	0	2	2
Picked	3	2	5
Done	0	5	5
Total	600	14	614

Accuracy

100.0%

Counts

614 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	58.3%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	47.3%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x))
	46.3%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))
	59.8%	(-.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps)))) x)) (/.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) x)))
✓	60.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	54.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
	46.1%	#s(approx (/ (- (pow x 3) (pow (- (* x x) eps) 3/2)) (+ (* x x) (+ (* (sqrt (- (* x x) eps)) x) (- (* x x) eps)))) (.f64 (.f64 #s(literal -3 binary64) (/.f64 eps x)) #s(literal -1/6 binary64)))
✓	46.2%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps) x))
	44.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) eps)) eps)) x) eps))

Compiler

Compiled 1 300 to 381 computations (70.7% saved)

regimes42.0ms (1%)

Memory

-32.1MiB live, 70.6MiB allocated; 23ms collecting garbage

Counts

36 → 1

Calls

Call 1

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

Outputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Calls

3 calls:

17.0ms	eps
9.0ms	x
9.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes12.0ms (0.3%)

Memory

31.3MiB live, 31.3MiB allocated; 0ms collecting garbage

Counts

13 → 2

Calls

Call 1

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

Outputs

(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
98.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
88.8%	2	`x`
81.9%	2	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Counts

12 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
98.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes9.0ms (0.2%)

Memory

-35.4MiB live, 9.3MiB allocated; 10ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))

Calls

1 calls:

8.0ms

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

Results

Accuracy	Segments	Branch
96.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))

Outputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
46.3%	1	`eps`
46.3%	1	`x`
46.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
4.3%	1	`eps`
4.3%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.439725765733447e-152	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.439725765733447e-152	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.439725765733447e-152	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

simplify60.0ms (1.4%)

Memory

-15.9MiB live, 85.2MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	195
1	56	165
2	120	155
3	295	155
4	1446	155
5	6347	155

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))

Outputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) (/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) x) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))

derivations224.0ms (5.1%)

Memory

-17.2MiB live, 176.4MiB allocated; 53ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 195 to 36 computations (81.5% saved)

preprocess52.0ms (1.2%)

Memory: 25.5MiB live, 70.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 426 to 98 computations (77% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze29.0ms (0.7%)

sample1.8s (41.2%)

explain152.0ms (3.5%)

preprocess15.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series10.0ms (0.2%)

simplify180.0ms (4.1%)

rewrite50.0ms (1.1%)

eval46.0ms (1%)

prune7.0ms (0.1%)

series19.0ms (0.4%)

simplify246.0ms (5.6%)

rewrite73.0ms (1.7%)

eval34.0ms (0.8%)

prune24.0ms (0.6%)

series85.0ms (1.9%)

simplify198.0ms (4.5%)

rewrite137.0ms (3.1%)

eval192.0ms (4.4%)

prune32.0ms (0.7%)

series49.0ms (1.1%)

simplify236.0ms (5.4%)

rewrite226.0ms (5.2%)

eval99.0ms (2.3%)

prune24.0ms (0.6%)

regimes42.0ms (1%)

regimes12.0ms (0.3%)

regimes4.0ms (0.1%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify60.0ms (1.4%)

derivations224.0ms (5.1%)

preprocess52.0ms (1.2%)

end0.0ms (0%)

Profiling