Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

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

analyze10.0ms (0.4%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.2s (44.7%)

Memory

14.1MiB live, 1 694.9MiB allocated; 503ms collecting garbage

Samples

321.0ms	4 868×	0	valid
308.0ms	2 699×	1	valid
230.0ms	689×	2	valid
30.0ms	150×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 490.0ms

adjust: 164.0ms (33.5% of total)

ival-mult!: 116.0ms (23.7% of total)

ival-sqrt: 106.0ms (21.6% of total)

ival-sub!: 103.0ms (21% of total)

Bogosity

preprocess130.0ms (4.8%)

Memory

2.8MiB live, 60.8MiB allocated; 49ms 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
▶	62.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 12 to 12 computations (0% saved)

series8.0ms (0.3%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Counts

6 → 54

Calls

Call 1

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

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (neg eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#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 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#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 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#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)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#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	x	@	inf	((- 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	@	0	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
1.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)
1.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) x (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x) eps)

rewrite234.0ms (8.6%)

Memory

7.4MiB live, 191.9MiB allocated; 87ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	293	1501
0	298	1433
1	1621	1377
0	8815	1331

Stop Event

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

Counts

60 → 99

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

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

eval10.0ms (0.4%)

Memory: 13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 232 to 464 computations (62.3% saved)

prune7.0ms (0.3%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	11	94

Accuracy

99.7%

Counts

94 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.1%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	62.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	57.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	4.2%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
▶	41.7%	#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))
	35.3%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 eps eps) eps)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
	26.5%	#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))
▶	3.7%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	43.6%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
	57.6%	#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)))))
	58.3%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 298 to 270 computations (9.4% saved)

series32.0ms (1.2%)

Memory

-17.7MiB live, 27.8MiB allocated; 4ms collecting garbage

Counts

24 → 108

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (fabs x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps))
6.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (fabs x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps))
4.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (fabs x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps))
3.0ms	eps	@	0	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (fabs x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps))
3.0ms	x	@	0	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (+ x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (fabs x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) 1/2 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps))

rewrite262.0ms (9.7%)

Memory

7.0MiB live, 196.9MiB allocated; 123ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	631	3949
0	657	3539
1	3705	3189
0	8526	3091

Stop Event

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

Counts

132 → 278

Calls

Call 1

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

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

eval46.0ms (1.7%)

Memory: -10.0MiB live, 46.3MiB allocated; 9ms collecting garbage
Compiler: Compiled 4 283 to 1 466 computations (65.8% saved)

prune8.0ms (0.3%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	281	5	286
Fresh	4	1	5
Picked	2	3	5
Done	0	1	1
Total	287	10	297

Accuracy

100.0%

Counts

297 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	62.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	57.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	4.2%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
▶	57.9%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
▶	1.7%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (sqrt.f64 (neg.f64 eps)))
▶	58.3%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
	41.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
✓	3.7%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓	43.6%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))

Compiler

Compiled 206 to 184 computations (10.7% saved)

series14.0ms (0.5%)

Memory

-28.2MiB live, 15.7MiB allocated; 5ms collecting garbage

Counts

18 → 97

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite202.0ms (7.4%)

Memory

49.6MiB live, 190.2MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	583	3684
0	600	3413
1	3447	2934
0	9319	2845

Stop Event

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

Counts

115 → 223

Calls

Call 1

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

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

eval29.0ms (1.1%)

Memory: 3.6MiB live, 49.0MiB allocated; 4ms collecting garbage
Compiler: Compiled 3 444 to 1 177 computations (65.8% saved)

prune10.0ms (0.4%)

Memory

-29.5MiB live, 13.6MiB allocated; 7ms collecting garbage

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	280	3	283
Fresh	1	0	1
Picked	1	4	5
Done	1	3	4
Total	283	10	293

Accuracy

100.0%

Counts

293 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	60.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
▶	43.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
▶	44.0%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
✓	62.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	57.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	4.2%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
✓	1.7%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (sqrt.f64 (neg.f64 eps)))
✓	58.3%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
✓	3.7%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))

Compiler

Compiled 120 to 104 computations (13.3% saved)

series13.0ms (0.5%)

Memory

19.1MiB live, 19.1MiB allocated; 0ms collecting garbage

Counts

19 → 66

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) eps (+ x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* x x)) -1/2) 2) x) (+ (* (/ eps (* x x)) -1/2) 2) (/ eps (* x x)) (* x x) x -1/2 2 (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ x x) (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ (sqrt (neg eps)) x) (sqrt (neg eps)) (neg eps))
2.0ms	eps	@	0	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) eps (+ x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* x x)) -1/2) 2) x) (+ (* (/ eps (* x x)) -1/2) 2) (/ eps (* x x)) (* x x) x -1/2 2 (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ x x) (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ (sqrt (neg eps)) x) (sqrt (neg eps)) (neg eps))
2.0ms	x	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) eps (+ x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* x x)) -1/2) 2) x) (+ (* (/ eps (* x x)) -1/2) 2) (/ eps (* x x)) (* x x) x -1/2 2 (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ x x) (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ (sqrt (neg eps)) x) (sqrt (neg eps)) (neg eps))
2.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) eps (+ x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* x x)) -1/2) 2) x) (+ (* (/ eps (* x x)) -1/2) 2) (/ eps (* x x)) (* x x) x -1/2 2 (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ x x) (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ (sqrt (neg eps)) x) (sqrt (neg eps)) (neg eps))
2.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) eps (+ x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (* x x)) -1/2) 2) x) (+ (* (/ eps (* x x)) -1/2) 2) (/ eps (* x x)) (* x x) x -1/2 2 (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ x x) (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+ x (sqrt (- (* x x) eps))) (+ (sqrt (neg eps)) x) (sqrt (neg eps)) (neg eps))

rewrite175.0ms (6.4%)

Memory

3.0MiB live, 148.3MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	459	2585
0	474	2332
1	2726	2209
0	8255	2164

Stop Event

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

Counts

85 → 191

Calls

Call 1

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

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

eval33.0ms (1.2%)

Memory: -16.8MiB live, 28.6MiB allocated; 3ms collecting garbage
Compiler: Compiled 2 283 to 1 019 computations (55.4% saved)

prune8.0ms (0.3%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	0	0
Picked	1	2	3
Done	0	7	7
Total	170	10	180

Accuracy

100.0%

Counts

180 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	60.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
✓	43.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
	44.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ eps (* x x)) -1/2) 2) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (+.f64 x x)))))
✓	62.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	57.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	4.2%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
✓	1.7%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (sqrt.f64 (neg.f64 eps)))
✓	58.3%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
✓	3.7%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))

Compiler

Compiled 354 to 223 computations (37% saved)

regimes22.0ms (0.8%)

Memory

-16.8MiB live, 27.0MiB allocated; 6ms collecting garbage

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	x
6.0ms	eps
5.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

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

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes11.0ms (0.4%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Counts

11 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
90.8%	2	`x`
85.4%	2	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Counts

10 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* 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
97.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes18.0ms (0.7%)

Memory

-41.8MiB live, 12.2MiB allocated; 27ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
59.9%	2	`eps`
58.3%	1	`x`
58.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.2%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms collecting garbage

Accuracy

Total -1.3b remaining (-2.1%)

Threshold costs -1.3b (-2.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	eps
1.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
3.7%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.7%	1	`x`
3.7%	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	-1.740384650512072e-151	0.0

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.862565340258909e-151	-1.740384650512072e-151

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch20.0ms (0.7%)

Memory

33.3MiB live, 33.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	-1.6081405656089787e-306	7.052374794153965e-307

Samples

5.0ms	50×	2	valid
4.0ms	47×	1	valid
2.0ms	59×	0	invalid
1.0ms	31×	0	valid

Compiler

Compiled 155 to 171 computations (-10.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 3.0ms (37.5% of total)

adjust: 2.0ms (25% of total)

ival-sub!: 2.0ms (25% of total)

ival-mult!: 1.0ms (12.5% of total)

derivations148.0ms (5.5%)

Memory

-34.1MiB live, 102.9MiB allocated; 13ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 52 to 35 computations (32.7% saved)

preprocess40.0ms (1.5%)

Memory: 3.2MiB live, 97.7MiB allocated; 15ms collecting garbage
Compiler: Compiled 65 to 48 computations (26.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze10.0ms (0.4%)

sample1.2s (44.7%)

preprocess130.0ms (4.8%)

series8.0ms (0.3%)

rewrite234.0ms (8.6%)

eval10.0ms (0.4%)

prune7.0ms (0.3%)

series32.0ms (1.2%)

rewrite262.0ms (9.7%)

eval46.0ms (1.7%)

prune8.0ms (0.3%)

series14.0ms (0.5%)

rewrite202.0ms (7.4%)

eval29.0ms (1.1%)

prune10.0ms (0.4%)

series13.0ms (0.5%)

rewrite175.0ms (6.4%)

eval33.0ms (1.2%)

prune8.0ms (0.3%)

regimes22.0ms (0.8%)

regimes11.0ms (0.4%)

regimes4.0ms (0.1%)

regimes18.0ms (0.7%)

regimes6.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch20.0ms (0.7%)

derivations148.0ms (5.5%)

preprocess40.0ms (1.5%)

end0.0ms (0%)

Profiling