Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

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

analyze17.0ms (0.6%)

Memory

-11.9MiB live, 33.1MiB allocated; 8ms 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)

sample1.5s (54.3%)

Memory

-22.2MiB live, 1 539.8MiB allocated; 1.0s collecting garbage

Samples

365.0ms	2 733×	1	valid
288.0ms	4 817×	0	valid
205.0ms	706×	2	valid
6.0ms	150×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 616.0ms

ival-sub!: 211.0ms (34.2% of total)

adjust: 171.0ms (27.7% of total)

ival-sqrt: 123.0ms (20% of total)

ival-mult!: 111.0ms (18% of total)

Bogosity

preprocess132.0ms (4.9%)

Memory

-39.7MiB live, 66.6MiB allocated; 52ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	44	54
2	80	54
3	132	54
4	352	54
5	1951	54
6	4598	54

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 12 to 12 computations (0% saved)

series9.0ms (0.3%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

6 → 50

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 (+ 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) (+ 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 (* -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 (* 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)
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
1.0ms	eps	@	-inf	((- 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)

rewrite68.0ms (2.5%)

Memory

21.5MiB live, 70.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	315	1513
0	320	1391
0	1743	1340

Stop Event

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

Counts

56 → 66

Calls

Call 1

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

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

eval20.0ms (0.8%)

Memory: -30.5MiB live, 14.1MiB allocated; 4ms collecting garbage
Compiler: Compiled 941 to 362 computations (61.5% saved)

prune7.0ms (0.3%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	48	12	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	13	61

Accuracy

99.5%

Counts

61 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.7%	(/.f64 (-.f64 (.f64 (.f64 x x) x) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	63.8%	(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	63.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	63.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
	29.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (+.f64 (/.f64 (neg.f64 eps) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))))
▶	59.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	34.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/16 binary64)) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
▶	3.3%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
	29.4%	#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) (.f64 (*.f64 x x) x))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	37.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
	42.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
▶	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))))))
	59.5%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 354 to 312 computations (11.9% saved)

series37.0ms (1.4%)

Memory

-8.3MiB live, 35.6MiB allocated; 8ms collecting garbage

Counts

31 → 80

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
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
(+.f64 x 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))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))))))
(.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))))
(-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))))
(/.f64 (neg.f64 x) eps)
(neg.f64 x)
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) eps)
#s(literal 1 binary64)
#s(literal -1 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
(.f64 (fma.f64 (/.f64 eps (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 eps (.f64 (.f64 x x) x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (.f64 (.f64 x x) x))
(.f64 (.f64 x x) x)
(*.f64 x x)
#s(literal 1/8 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) #s(hole binary64 (* 2 x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (+ x (* (sqrt eps) (sqrt -1)))))
#s(approx (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) #s(hole binary64 (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
#s(approx (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) #s(hole binary64 (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
#s(approx (/ (neg x) eps) #s(hole binary64 (* -1 (/ x eps))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (* (+ (* (/ eps (* (* x 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) x)) 1/8) (/ 1/2 x)) #s(hole binary64 (* 1/8 (/ eps (pow x 3)))))
#s(approx (+ (* (/ eps (* (* x 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) x)) #s(hole binary64 (/ eps (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ 1/2 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 (+ 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) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))))
#s(approx (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) #s(hole binary64 (* x (- (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) x))) (/ 1 eps)))))
#s(approx (* (+ (* (/ eps (* (* x 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) x)) 1/8) (/ 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 (* -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 (+ 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 (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))))
#s(approx (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) #s(hole binary64 (* -1 (* x (+ (* (sqrt (/ 1 eps)) (/ (sqrt -1) x)) (/ 1 eps))))))
#s(approx (* (+ (* (/ eps (* (* x 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) x)) 1/8) (/ 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 eps #s(hole binary64 eps))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (* -1 (- (* -1 x) (* (sqrt eps) (sqrt -1))))))
#s(approx (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) #s(hole binary64 (/ (- (* -1 x) (* (sqrt eps) (sqrt -1))) eps)))
#s(approx (sqrt (* (/ 1 eps) -1)) #s(hole binary64 (* (sqrt (/ 1 eps)) (sqrt -1))))
#s(approx (* (/ 1 eps) -1) #s(hole binary64 (/ -1 eps)))
#s(approx (/ 1 eps) #s(hole binary64 (/ 1 eps)))
#s(approx (+ (* (/ eps (* (* x x) x)) 1/8) (/ 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 (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
#s(approx (* (+ (* (/ eps (* (* x 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) x)) 1/8) (/ 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 (* -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 (* 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 (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))))
#s(approx (+ (* (/ eps (* (* x x) x)) 1/8) (/ 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
14.0ms	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))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) (/ (neg x) eps) (neg x) (sqrt (* (/ 1 eps) -1)) (* (/ 1 eps) -1) (/ 1 eps) 1 -1 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ eps (* (* x x) x)) (* (* x x) x) (* x x) 1/8 (/ 1/2 x) 1/2)
6.0ms	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))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) (/ (neg x) eps) (neg x) (sqrt (* (/ 1 eps) -1)) (* (/ 1 eps) -1) (/ 1 eps) 1 -1 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ eps (* (* x x) x)) (* (* x x) x) (* x x) 1/8 (/ 1/2 x) 1/2)
5.0ms	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))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) (/ (neg x) eps) (neg x) (sqrt (* (/ 1 eps) -1)) (* (/ 1 eps) -1) (/ 1 eps) 1 -1 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ eps (* (* x x) x)) (* (* x x) x) (* x x) 1/8 (/ 1/2 x) 1/2)
4.0ms	eps	@	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))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) (/ (neg x) eps) (neg x) (sqrt (* (/ 1 eps) -1)) (* (/ 1 eps) -1) (/ 1 eps) 1 -1 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ eps (* (* x x) x)) (* (* x x) x) (* x x) 1/8 (/ 1/2 x) 1/2)
4.0ms	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))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1))) (/ (neg x) eps) (neg x) (sqrt (* (/ 1 eps) -1)) (* (/ 1 eps) -1) (/ 1 eps) 1 -1 (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ eps (* (* x x) x)) (* (* x x) x) (* x x) 1/8 (/ 1/2 x) 1/2)

rewrite109.0ms (4.1%)

Memory

37.1MiB live, 126.8MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	437	2404
0	467	2121
0	2301	2064

Stop Event

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

Counts

111 → 184

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

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

eval34.0ms (1.3%)

Memory: -11.2MiB live, 33.5MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 953 to 821 computations (58% saved)

prune10.0ms (0.4%)

Memory

18.8MiB live, 18.8MiB allocated; 0ms collecting garbage

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	0	7	7
Picked	2	3	5
Done	0	1	1
Total	159	14	173

Accuracy

99.7%

Counts

173 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.7%	(/.f64 (-.f64 (.f64 (.f64 x x) x) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	47.7%	(/.f64 (-.f64 (.f64 (.f64 x x) x) (pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 3 binary64))) (fma.f64 x x (fma.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)))) (.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))))))
▶	63.8%	(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	63.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	63.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
▶	29.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (+.f64 (/.f64 (neg.f64 eps) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))))
✓	59.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	34.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/16 binary64)) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
✓	3.3%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	29.4%	#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) (.f64 (*.f64 x x) x))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	42.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
	40.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
▶	59.5%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
▶	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (*.f64 (+.f64 (/.f64 x eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)))

Compiler

Compiled 429 to 349 computations (18.6% saved)

series65.0ms (2.4%)

Memory

-25.9MiB live, 76.0MiB allocated; 12ms collecting garbage

Counts

41 → 129

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	eps	@	-inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (* x x) x (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (* (+ (/ x eps) (sqrt (/ -1 eps))) eps) (+ (/ x eps) (sqrt (/ -1 eps))) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (/ (neg eps) (* x x)) 1) (* x x)) (+ (/ (neg eps) (* x x)) 1) (/ (neg eps) (* x x)) 1 (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ eps (pow x 5)) (pow x 5) 5 1/16 (/ 1/8 (* (* x x) x)) 1/8 (* (* x x) x) (/ 1/2 x) 1/2)
6.0ms	eps	@	inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (* x x) x (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (* (+ (/ x eps) (sqrt (/ -1 eps))) eps) (+ (/ x eps) (sqrt (/ -1 eps))) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (/ (neg eps) (* x x)) 1) (* x x)) (+ (/ (neg eps) (* x x)) 1) (/ (neg eps) (* x x)) 1 (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ eps (pow x 5)) (pow x 5) 5 1/16 (/ 1/8 (* (* x x) x)) 1/8 (* (* x x) x) (/ 1/2 x) 1/2)
6.0ms	x	@	-inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (* x x) x (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (* (+ (/ x eps) (sqrt (/ -1 eps))) eps) (+ (/ x eps) (sqrt (/ -1 eps))) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (/ (neg eps) (* x x)) 1) (* x x)) (+ (/ (neg eps) (* x x)) 1) (/ (neg eps) (* x x)) 1 (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ eps (pow x 5)) (pow x 5) 5 1/16 (/ 1/8 (* (* x x) x)) 1/8 (* (* x x) x) (/ 1/2 x) 1/2)
5.0ms	eps	@	0	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (* x x) x (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (* (+ (/ x eps) (sqrt (/ -1 eps))) eps) (+ (/ x eps) (sqrt (/ -1 eps))) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (/ (neg eps) (* x x)) 1) (* x x)) (+ (/ (neg eps) (* x x)) 1) (/ (neg eps) (* x x)) 1 (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ eps (pow x 5)) (pow x 5) 5 1/16 (/ 1/8 (* (* x x) x)) 1/8 (* (* x x) x) (/ 1/2 x) 1/2)
5.0ms	x	@	0	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (* x x) x (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (* (+ (/ x eps) (sqrt (/ -1 eps))) eps) (+ (/ x eps) (sqrt (/ -1 eps))) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (+ (/ (neg eps) (* x x)) 1) (* x x)) (+ (/ (neg eps) (* x x)) 1) (/ (neg eps) (* x x)) 1 (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ eps (pow x 5)) (pow x 5) 5 1/16 (/ 1/8 (* (* x x) x)) 1/8 (* (* x x) x) (/ 1/2 x) 1/2)

rewrite134.0ms (5%)

Memory

27.3MiB live, 161.3MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	727	5018
0	777	4020
0	4204	3909

Stop Event

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

Counts

170 → 290

Calls

Call 1

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

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

eval44.0ms (1.6%)

Memory: -8.3MiB live, 48.2MiB allocated; 7ms collecting garbage
Compiler: Compiled 5 077 to 1 506 computations (70.3% saved)

prune16.0ms (0.6%)

Memory

-31.8MiB live, 15.1MiB allocated; 2ms collecting garbage

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	4	1	5
Picked	3	2	5
Done	0	4	4
Total	265	11	276

Accuracy

100.0%

Counts

276 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	63.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	63.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	59.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	42.4%	#s(approx (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓	3.3%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 #s(approx (+ ( (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	40.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
✓	59.5%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
▶	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps (*.f64 (/.f64 x eps) eps))))
✓	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (*.f64 (+.f64 (/.f64 x eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)))

Compiler

Compiled 293 to 265 computations (9.6% saved)

series36.0ms (1.3%)

Memory

13.2MiB live, 57.1MiB allocated; 6ms collecting garbage

Counts

36 → 138

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps (+ x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (+ (* (sqrt (/ -1 eps)) eps) (* (/ x eps) eps)) (sqrt (/ -1 eps)) (/ -1 eps) -1 (* (/ x eps) eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ (+ (* (/ 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))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ (+ (* (/ eps (* x x)) 1/16) 1/8) (* (* x x) x)) (+ (* (/ eps (* x x)) 1/16) 1/8) 1/16 (* (* x x) x) (/ 1/2 x))
5.0ms	eps	@	inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps (+ x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (+ (* (sqrt (/ -1 eps)) eps) (* (/ x eps) eps)) (sqrt (/ -1 eps)) (/ -1 eps) -1 (* (/ x eps) eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ (+ (* (/ 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))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ (+ (* (/ eps (* x x)) 1/16) 1/8) (* (* x x) x)) (+ (* (/ eps (* x x)) 1/16) 1/8) 1/16 (* (* x x) x) (/ 1/2 x))
5.0ms	eps	@	0	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps (+ x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (+ (* (sqrt (/ -1 eps)) eps) (* (/ x eps) eps)) (sqrt (/ -1 eps)) (/ -1 eps) -1 (* (/ x eps) eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ (+ (* (/ 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))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ (+ (* (/ eps (* x x)) 1/16) 1/8) (* (* x x) x)) (+ (* (/ eps (* x x)) 1/16) 1/8) 1/16 (* (* x x) x) (/ 1/2 x))
5.0ms	x	@	-inf	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps (+ x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (+ (* (sqrt (/ -1 eps)) eps) (* (/ x eps) eps)) (sqrt (/ -1 eps)) (/ -1 eps) -1 (* (/ x eps) eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ (+ (* (/ 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))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ (+ (* (/ eps (* x x)) 1/16) 1/8) (* (* x x) x)) (+ (* (/ eps (* x x)) 1/16) 1/8) 1/16 (* (* x x) x) (/ 1/2 x))
4.0ms	x	@	0	((/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps (+ x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) (/ (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps)))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (+ (* (sqrt (/ -1 eps)) eps) (* (/ x eps) eps)) (sqrt (/ -1 eps)) (/ -1 eps) -1 (* (/ x eps) eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/ (+ (* (/ 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))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/ (+ (* (/ eps (* x x)) 1/16) 1/8) (* (* x x) x)) (+ (* (/ eps (* x x)) 1/16) 1/8) 1/16 (* (* x x) x) (/ 1/2 x))

rewrite146.0ms (5.5%)

Memory

33.5MiB live, 179.0MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	746	5312
0	785	4335
0	4326	4156

Stop Event

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

Counts

174 → 259

Calls

Call 1

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

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

eval32.0ms (1.2%)

Memory: 2.6MiB live, 47.8MiB allocated; 9ms collecting garbage
Compiler: Compiled 3 631 to 1 396 computations (61.6% saved)

prune33.0ms (1.2%)

Memory

-28.4MiB live, 16.6MiB allocated; 9ms collecting garbage

Pruning

15 alts after pruning (5 fresh and 10 done)

	Pruned	Kept	Total
New	231	5	236
Fresh	0	0	0
Picked	1	4	5
Done	0	6	6
Total	232	15	247

Accuracy

100.0%

Counts

247 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	99.5%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
	62.8%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
	43.3%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))))
	42.4%	(/.f64 #s(approx (- (* x x) (* (sqrt (- (* x x) eps)) (sqrt (- (* x x) eps)))) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
✓	63.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	63.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	59.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.3%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 #s(approx (+ ( (/ eps (pow x 5)) 1/16) (/ 1/8 (* (* x x) x))) (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
✓	40.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
	42.2%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (* (* x x) x)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps))
✓	59.5%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
✓	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps (*.f64 (/.f64 x eps) eps))))
✓	59.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (* (/ 1 eps) -1)))) (*.f64 (+.f64 (/.f64 x eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)))

Compiler

Compiled 572 to 388 computations (32.2% saved)

regimes21.0ms (0.8%)

Memory

23.8MiB live, 23.8MiB allocated; 0ms collecting garbage

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	x
6.0ms	eps
6.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes57.0ms (2.1%)

Memory

-44.4MiB live, 12.3MiB allocated; 9ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

50.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes10.0ms (0.4%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
91.0%	2	`x`
80.8%	2	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
99.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
96.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes3.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
96.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes5.0ms (0.2%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
59.5%	1	`eps`
59.5%	1	`x`
59.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes36.0ms (1.3%)

Memory

-37.9MiB live, 7.0MiB allocated; 5ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

34.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
3.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.3%	1	`x`
3.3%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0975927963749024e-153	-1.0432851604520634e-156

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0975927963749024e-153	-1.0432851604520634e-156

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0975927963749024e-153	-1.0432851604520634e-156

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0975927963749024e-153	-1.0432851604520634e-156

Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations68.0ms (2.5%)

Memory

0.8MiB live, 45.2MiB allocated; 4ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 82 to 41 computations (50% saved)

preprocess68.0ms (2.5%)

Memory: 45.8MiB live, 189.1MiB allocated; 23ms collecting garbage
Compiler: Compiled 95 to 54 computations (43.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze17.0ms (0.6%)

sample1.5s (54.3%)

preprocess132.0ms (4.9%)

series9.0ms (0.3%)

rewrite68.0ms (2.5%)

eval20.0ms (0.8%)

prune7.0ms (0.3%)

series37.0ms (1.4%)

rewrite109.0ms (4.1%)

eval34.0ms (1.3%)

prune10.0ms (0.4%)

series65.0ms (2.4%)

rewrite134.0ms (5%)

eval44.0ms (1.6%)

prune16.0ms (0.6%)

series36.0ms (1.3%)

rewrite146.0ms (5.5%)

eval32.0ms (1.2%)

prune33.0ms (1.2%)

regimes21.0ms (0.8%)

regimes57.0ms (2.1%)

regimes10.0ms (0.4%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes5.0ms (0.2%)

regimes36.0ms (1.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

derivations68.0ms (2.5%)

preprocess68.0ms (2.5%)

end0.0ms (0%)

Profiling