Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0.0%)

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

analyze16.0ms (0.1%)

Memory

-18.7MiB live, 26.7MiB allocated; 6ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0.0%	0.0%	12.8%	87.2%	0.0%	0.0%	0.0%	0
0.0%	0.0%	12.8%	87.2%	0.0%	0.0%	0.0%	1
0.0%	0.0%	12.8%	87.2%	0.0%	0.0%	0.0%	2
50.0%	6.4%	6.4%	87.2%	0.0%	0.0%	0.0%	3
57.1%	6.4%	4.8%	87.2%	0.0%	1.6%	0.0%	4
69.2%	7.2%	3.2%	87.2%	0.0%	2.4%	0.0%	5
75.0%	7.2%	2.4%	87.2%	0.0%	3.2%	0.0%	6
82.6%	7.6%	1.6%	87.2%	0.0%	3.6%	0.0%	7
86.4%	7.6%	1.2%	87.2%	0.0%	4.0%	0.0%	8
90.7%	7.8%	0.8%	87.2%	0.0%	4.2%	0.0%	9
92.6%	7.8%	0.6%	87.2%	0.0%	4.4%	0.0%	10
95.0%	7.9%	0.4%	87.2%	0.0%	4.5%	0.0%	11
96.3%	8.0%	0.3%	87.2%	0.0%	4.5%	0.0%	12

Compiler

Compiled 24 to 18 computations (25.0% saved)

sample1.0s (6.7%)

Memory

50.7MiB live, 1 995.3MiB allocated; 252ms collecting garbage

Samples

355.0ms	2 777×	1	valid
263.0ms	4 739×	0	valid
125.0ms	740×	2	valid
11.0ms	178×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 439.0ms

ival-sqrt: 139.0ms (31.6% of total)

adjust: 132.0ms (30.0% of total)

ival-sub!: 91.0ms (20.7% of total)

ival-mult!: 77.0ms (17.5% of total)

Bogosity

preprocess78.0ms (0.5%)

Memory

-1.0MiB live, 122.7MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	77	49
2	187	49
3	372	49
4	785	49
5	3592	49

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 16 to 12 computations (25.0% saved)

series60.0ms (0.4%)

Memory

17.8MiB live, 127.9MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	1465

Stop Event

1×	iter-limit

Counts

6 → 54

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
3.0ms	x	inf
3.0ms	eps	inf
2.0ms	x	0
2.0ms	x	-inf
2.0ms	eps	-inf

rewrite190.0ms (1.2%)

Memory

-17.6MiB live, 262.7MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	59	24
2	158	24
3	460	24
4	882	24
5	3369	24
0	4949	24

Stop Event

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

Counts

6 → 271

Calls

Call 1

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

Outputs
x
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (*.f64 (fabs.f64 x) x) (neg.f64 x))) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (*.f64 (fabs.f64 x) x) x)) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (*.f64 (neg.f64 x) x) x)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (*.f64 x x) x)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (fabs.f64 x) (neg.f64 x))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (fabs.f64 x) (neg.f64 x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (fabs.f64 x) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (fabs.f64 x) x) #s(literal 1/4 binary64)))
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(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) x)
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (-.f64 x (neg.f64 (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) eps) (.f64 x x)) (+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 x)))
(/.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
(/.f64 (-.f64 (.f64 (-.f64 eps (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (.f64 (neg.f64 x) x) x)) (+.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 x)))))
(/.f64 (+.f64 (.f64 (-.f64 eps (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (.f64 x x) x)) (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))))
(/.f64 (+.f64 (.f64 (.f64 x x) x) (.f64 (-.f64 eps (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (neg.f64 (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))) (+.f64 (.f64 x x) (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 x))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

eval39.0ms (0.3%)

Memory: 29.5MiB live, 80.9MiB allocated; 12ms collecting garbage
Compiler: Compiled 7 129 to 1 532 computations (78.5% saved)

prune16.0ms (0.1%)

Memory

-11.3MiB live, 34.6MiB allocated; 6ms collecting garbage

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	307	13	320
Fresh	0	0	0
Picked	1	0	1
Done	-1	1	0
Total	307	14	321

Accuracy

99.4%

Counts

321 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.1%	(/.f64 (-.f64 (.f64 (.f64 x x) x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	59.7%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	59.4%	(-.f64 x (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	60.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	24.1%	(-.f64 x (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x))) (*.f64 x x))))
	59.9%	(-.f64 x (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (neg.f64 eps))) (neg.f64 eps))))
	54.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
▶	60.0%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
▶	60.0%	(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	30.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 eps #s(literal 4 binary64))) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))))))) x))
▶	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) eps)) x))
	37.5%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))))) x))
▶	3.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
	46.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

Compiler

Compiled 566 to 352 computations (37.8% saved)

series130.0ms (0.9%)

Memory

-12.4MiB live, 267.8MiB allocated; 66ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1236	10018

Stop Event

1×	iter-limit

Counts

29 → 243

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
12.0ms	eps	inf
10.0ms	x	inf
8.0ms	eps	0
7.0ms	eps	-inf
5.0ms	x	0

rewrite281.0ms (1.8%)

Memory

-2.2MiB live, 744.9MiB allocated; 105ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	223
0	54	210
1	259	195
2	1033	185
0	4068	179

Stop Event

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

Counts

29 → 1 814

Calls

Call 1

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

Outputs
#s(literal 1 binary64)
x
(*.f64 (pow.f64 (fabs.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 (fabs.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (neg.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 (neg.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (fabs.f64 x))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 x))
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eps
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(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (neg.f64 x)) (/.f64 (*.f64 eps eps) x))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x) (/.f64 (*.f64 eps eps) (neg.f64 x)))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (.f64 (neg.f64 eps) eps) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64)))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/8 binary64))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) (.f64 eps eps) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64))))
(134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) eps #s(literal 1/2 binary64) #s(literal 1/8 binary64) (.f64 (neg.f64 eps) (/.f64 eps (.f64 x x))))
(neg.f64 (/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) x) (.f64 x (.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 x) x)))
(neg.f64 (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x))) x))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 (.f64 x x) x)) x) x) (/.f64 (.f64 #s(literal -1/2 binary64) eps) x))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) x) (.f64 x x)) (/.f64 (.f64 x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x)))
(-.f64 (.f64 (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (neg.f64 x)))
(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 (.f64 x x) x)) (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(+.f64 (.f64 (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x)))
(+.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 (.f64 x x) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (.f64 #s(literal -1/2 binary64) eps)) x))

eval9.9s (64.4%)

Memory

370.8MiB live, 19 531.4MiB allocated; 2.6s collecting garbage

Samples

5.4s	90 251×	0	valid
2.0s	19 621×	1	valid
342.0ms	5 840×	0	invalid

Compiler

Compiled 49 062 to 5 567 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-mult!: 2.1s (70.3% of total)

adjust: 443.0ms (15.2% of total)

ival-sub!: 426.0ms (14.6% of total)

prune68.0ms (0.4%)

Memory

21.1MiB live, 113.2MiB allocated; 16ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1 550	7	1 557
Fresh	7	1	8
Picked	5	0	5
Done	0	1	1
Total	1 562	9	1 571

Accuracy

100.0%

Counts

1 571 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.5%	(/.f64 (+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
▶	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64))))
✓	60.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	54.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 eps #s(literal 0 binary64)))
	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) (.f64 eps (/.f64 eps (.f64 x x))) #s(literal 1/8 binary64) eps #s(literal -1/2 binary64)))
▶	46.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
▶	3.5%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))

Samples

20.0ms	328×	0	valid
9.0ms	184×	0	invalid

Compiler

Compiled 332 to 200 computations (39.8% saved)

Precisions

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

ival-mult!: 6.0ms (73.7% of total)

ival-sub!: 1.0ms (12.3% of total)

adjust: 1.0ms (12.3% of total)

series72.0ms (0.5%)

Memory

13.9MiB live, 111.3MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	957	6892

Stop Event

1×	iter-limit

Counts

26 → 179

Calls

Call 1

Inputs
x
eps
#s(approx (- (* x x) (- (* x x) eps)) eps)
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(+.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 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
#s(literal 0 binary64)
(-.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64))))
(.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))

Outputs
#s(approx x x)
#s(approx (- (* x x) (- (* x x) eps)) eps)
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx (- (* x x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (pow.f64 x #s(literal 2 binary64)) eps))
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (neg.f64 eps))))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps))))))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (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 (sqrt.f64 (neg.f64 eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (neg.f64 eps))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps))))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 eps x) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64)))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+.f64 (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64))))))) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (+.f64 (.f64 x (-.f64 (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 eps)))) (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 4 binary64))))))) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64))))))) (/.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))))) (/.f64 eps (sqrt.f64 (neg.f64 eps)))))
#s(approx (+ x x) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (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 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 (neg.f64 eps)))))) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps)))))))) (sqrt.f64 (neg.f64 eps))))
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) (*.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))))
#s(approx (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 2 binary64))))) (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (/.f64 (sqrt.f64 (neg.f64 eps)) eps))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (/.f64 x eps) (/.f64 (sqrt.f64 (neg.f64 eps)) eps)))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (*.f64 eps (sqrt.f64 (neg.f64 eps))))) (/.f64 #s(literal 1 binary64) eps))) (/.f64 (sqrt.f64 (neg.f64 eps)) eps)))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (sqrt.f64 (neg.f64 eps))))))) (/.f64 #s(literal 1 binary64) eps))) (/.f64 (sqrt.f64 (neg.f64 eps)) eps)))
#s(approx (* 0 (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (*.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (+.f64 (.f64 eps x) (.f64 eps (sqrt.f64 (neg.f64 eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (+.f64 (.f64 eps (sqrt.f64 (neg.f64 eps))) (.f64 x (+.f64 eps (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps x) (sqrt.f64 (neg.f64 eps))))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (+.f64 (.f64 eps (sqrt.f64 (neg.f64 eps))) (.f64 x (+.f64 eps (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps (pow.f64 x #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 eps (sqrt.f64 (neg.f64 eps))))))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64)))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (+.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 (neg.f64 eps)))) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (+.f64 (.f64 x (+.f64 (.f64 #s(literal 2 binary64) x) (*.f64 #s(literal 2 binary64) (sqrt.f64 (neg.f64 eps))))) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (+.f64 (.f64 x (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (neg.f64 eps))) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 x (sqrt.f64 (neg.f64 eps))))))) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))))
#s(approx (- (* x x) eps) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))) (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (-.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))) x))
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#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 3 binary64))))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))))
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#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (+.f64 x (.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (+.f64 x (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) (.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (/.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) eps))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (/.f64 (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))) eps))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (/.f64 (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))))) eps))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (/.f64 (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 eps (-.f64 (.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))))) eps))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (*.f64 eps (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 eps (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 eps (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 eps (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 eps (-.f64 (.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 eps (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (+.f64 (.f64 eps (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))) (.f64 eps (+.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))))) (pow.f64 (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))))
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#s(approx (- (* x x) eps) (*.f64 eps (-.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) eps) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (sqrt (- (* x x) eps)) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 5 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (*.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 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))))
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#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (-.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 x (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 4 binary64))))) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 eps (-.f64 (/.f64 x eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (-.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (-.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (/.f64 x eps)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))))
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps x))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (/.f64 x eps))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 eps #s(literal 2 binary64)))) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 eps #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))))
#s(approx (/ (+ (* 0 (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) (.f64 #s(literal 2 binary64) (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))))
#s(approx (/ (+ (* 0 (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (-.f64 (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))))))
#s(approx (/ (+ (* 0 (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (-.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (-.f64 (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 2 binary64)) (-.f64 (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 4 binary64))))) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) (+.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 x (-.f64 (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (.f64 #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))))))
#s(approx (- (* x x) eps) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) eps))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 5 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 #s(literal -1 binary64) (/.f64 x eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) 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 #s(literal -1 binary64) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) (/.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 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) 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 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 4 binary64)))))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) eps)) (.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps))) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x eps)))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps))))
#s(approx (/ (+ (sqrt (- (* x x) eps)) x) (- eps 0)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))) eps))) eps))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 #s(literal -1 binary64) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x eps))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))) eps))) eps)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -2 binary64) (/.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) eps)) (.f64 #s(literal 2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))
#s(approx (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) eps)) (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))))

Calls

6 calls:

Time	Variable	Point
13.0ms	eps	inf
3.0ms	x	-inf
3.0ms	x	inf
2.0ms	eps	-inf
2.0ms	eps	0

rewrite188.0ms (1.2%)

Memory

4.5MiB live, 331.0MiB allocated; 54ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	274
0	59	210
1	333	194
2	1460	188
0	4246	184

Stop Event

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

Counts

26 → 896

Calls

Call 1

Inputs
x
eps
#s(approx (- (* x x) (- (* x x) eps)) eps)
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(+.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 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
#s(literal 0 binary64)
(-.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64))))
(.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))

Outputs
x
eps
#s(approx (- (* x x) (- (* x x) eps)) eps)
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1 binary64)) (pow.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1 binary64)) (fabs.f64 x))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (pow.f64 (fabs.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fabs.f64 x)))
(/.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (pow.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (fabs.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (.f64 x x))) (*.f64 x x))
(.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x))) (*.f64 x x))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(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 (-.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64)) (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64))) (+.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (+.f64 (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64)))))
(/.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (-.f64 (*.f64 x x) (neg.f64 eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (+.f64 (*.f64 x x) eps))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) eps))))
(neg.f64 (-.f64 eps (*.f64 x x)))
(-.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64))
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64))
(+.f64 (*.f64 x x) (neg.f64 eps))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64))) (+.f64 (.f64 x x) (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (neg.f64 eps) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x))
(-.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 x)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.f64 x (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
(.f64 (neg.f64 #s(approx (- ( x x) (- (* x x) eps)) eps)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (neg.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps))) (+.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(literal 1 binary64) (/.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 #s(approx (- ( x x) (- (* x x) eps)) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (- ( x x) (- (* x x) eps)) eps)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 (/.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) x)) x)
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x x)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (+.f64 (.f64 x x) (+.f64 (.f64 x x) (*.f64 (neg.f64 x) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (+.f64 x (neg.f64 x)))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) (*.f64 x x))))
(neg.f64 (-.f64 (neg.f64 x) x))
(-.f64 x (neg.f64 x))
(+.f64 x (neg.f64 (neg.f64 x)))
(+.f64 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(literal 1/2 binary64)
(*.f64 (neg.f64 eps) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 #s(literal -1/2 binary64) (neg.f64 eps))
(*.f64 eps #s(literal 1/2 binary64))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (fabs.f64 x) (fabs.f64 x))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 x) (neg.f64 x))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x x)
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (fabs.f64 x) (fabs.f64 x))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x) (neg.f64 x))
(134-z0z1z2z3z4 #s(literal -1/2 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) x x)
(neg.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 eps)))
(neg.f64 (*.f64 (neg.f64 eps) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 #s(literal -1/2 binary64) eps))
(+.f64 (*.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
#s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
(.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (neg.f64 #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) (/.f64 #s(literal -1 binary64) x))
(.f64 #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (.f64 #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (neg.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (neg.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x)
(neg.f64 (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(literal 1 binary64)
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
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(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fabs.f64 x) (fabs.f64 x))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 x) (neg.f64 x))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x x)
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (fabs.f64 x) (fabs.f64 x))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) (neg.f64 x) (neg.f64 x))
(134-z0z1z2z3z4 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x x)
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 eps)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)))
(neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (/.f64 (-.f64 (.f64 x x) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 x x) (neg.f64 (+.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 (/.f64 (.f64 x x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (+.f64 eps (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (/.f64 (.f64 (neg.f64 eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(-.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 0 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)))
(-.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(-.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (.f64 (neg.f64 eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 x (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) #s(literal -1 binary64)))
(+.f64 (/.f64 (-.f64 (.f64 x x) eps) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 (neg.f64 x) x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
(+.f64 (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(+.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(+.f64 (/.f64 (.f64 x x) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (-.f64 (neg.f64 eps) (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
(+.f64 (/.f64 (.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 eps x) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(+.f64 (/.f64 (.f64 eps x) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(+.f64 (/.f64 (.f64 x eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(+.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 x eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(+.f64 (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 0 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)))
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal 0 binary64)))
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(+.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 (.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(+.f64 #s(literal 0 binary64) (/.f64 (.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
(+.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

eval804.0ms (5.3%)

Memory

19.7MiB live, 1 140.7MiB allocated; 241ms collecting garbage

Samples

303.0ms	3 122×	1	valid
242.0ms	4 046×	0	valid

Compiler

Compiled 41 401 to 3 734 computations (91.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 262.0ms

ival-mult!: 179.0ms (68.3% of total)

adjust: 47.0ms (17.9% of total)

ival-sub!: 36.0ms (13.7% of total)

prune61.0ms (0.4%)

Memory

-5.8MiB live, 95.6MiB allocated; 18ms collecting garbage

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	918	5	923
Fresh	1	2	3
Picked	5	0	5
Done	-3	4	1
Total	921	11	932

Accuracy

100.0%

Counts

932 → 11

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))))
▶	57.9%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))))
▶	99.5%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (- ( x x) (- (* x x) eps)) eps)))
✓	60.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	54.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) (.f64 eps (/.f64 eps (.f64 x x))) #s(literal 1/8 binary64) eps #s(literal -1/2 binary64)))
✓	46.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
✓	3.5%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))

Samples

17.0ms	328×	0	valid
15.0ms	184×	0	invalid

Compiler

Compiled 382 to 241 computations (36.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult!: 7.0ms (79.3% of total)

ival-sub!: 1.0ms (11.3% of total)

adjust: 1.0ms (11.3% of total)

series65.0ms (0.4%)

Memory

0.6MiB live, 90.7MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	955	7328

Stop Event

1×	iter-limit

Counts

26 → 185

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
3.0ms	x	-inf
3.0ms	eps	0
3.0ms	eps	-inf
2.0ms	eps	inf
2.0ms	x	inf

rewrite180.0ms (1.2%)

Memory

-15.3MiB live, 320.7MiB allocated; 107ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	260
0	61	250
1	280	222
2	946	208
0	4126	208

Stop Event

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

Counts

26 → 666

Calls

Call 1

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

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

eval2.0s (13.0%)

Memory

63.8MiB live, 2 918.0MiB allocated; 569ms collecting garbage

Samples

1.3s	21 042×	0	valid
220.0ms	1 998×	1	valid

Compiler

Compiled 30 170 to 3 659 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 553.0ms

ival-mult!: 387.0ms (70.0% of total)

adjust: 84.0ms (15.2% of total)

ival-sub!: 82.0ms (14.8% of total)

prune23.0ms (0.2%)

Memory

-9.2MiB live, 36.9MiB allocated; 14ms collecting garbage

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	869	6	875
Fresh	2	0	2
Picked	5	0	5
Done	-2	6	4
Total	874	12	886

Accuracy

100.0%

Counts

886 → 12

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))))
✓	57.9%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (- ( x x) (- (* x x) eps)) eps)))
✓	60.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	55.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (fabs.f64 eps))))
	82.2%	(.f64 (/.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) x)
	82.4%	(.f64 (/.f64 x (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) #s(approx (- ( x x) (- (* x x) eps)) eps))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
	79.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) x) #s(approx (- (* x x) (- (* x x) eps)) eps))
	46.5%	(.f64 #s(approx (/ 1 (+ (sqrt (- ( x x) eps)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
✓	46.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
✓	3.5%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))

Compiler

Compiled 248 to 147 computations (40.7% saved)

regimes80.0ms (0.5%)

Memory

-3.5MiB live, 99.9MiB allocated; 10ms collecting garbage

Counts

2 → 1

4 → 1

8 → 2

10 → 2

32 → 1

Calls

Call 1

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

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

Call 2

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

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

Call 3

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

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

Call 4

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

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

Call 5

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (fabs.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps)) x))
(.f64 #s(approx (/ 1 (+ (sqrt (- ( x x) eps)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (- ( 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 eps #s(literal 0 binary64)))
(-.f64 x (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (neg.f64 eps))) (neg.f64 eps))))
(.f64 (/.f64 x (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) #s(approx (- ( x x) (- (* x x) eps)) eps))
(.f64 (/.f64 #s(approx (- ( x x) (- (* x x) eps)) eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) x)
(-.f64 x (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (- ( x x) (- (* x x) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (- ( x x) (- (* x x) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (-.f64 eps #s(literal 0 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x)) x) #s(approx (- (* x x) (- (* x x) eps)) eps))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) 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))) (134-z0z1z2z3z4 (/.f64 #s(literal 1 binary64) x) (.f64 eps (/.f64 eps (.f64 x x))) #s(literal 1/8 binary64) eps #s(literal -1/2 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 x (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (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))) (+.f64 (.f64 x x) (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (+.f64 (.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 eps #s(literal 4 binary64))) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (.f64 #s(literal -1/2 binary64) eps) (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))))))) x))

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

Calls

13 calls:

12.0ms	x
9.0ms	eps
8.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
4.0ms	eps
4.0ms	eps

Results

Accuracy	Segments	Branch
3.5%	1	`x`
3.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.5%	1	`eps`
55.7%	1	`eps`
55.7%	1	`x`
55.7%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
95.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
98.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
88.6%	2	`x`
80.2%	2	`eps`
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.6%	1	`x`
99.6%	1	`eps`

Samples

8.0ms	164×	0	valid
5.0ms	92×	0	invalid

Compiler

Compiled 741 to 199 computations (73.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult!: 3.0ms (72.9% of total)

ival-sub!: 1.0ms (24.3% of total)

adjust: 0.0ms (0.0% of total)

bsearch0.0ms (0.0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.324530470004861e-153	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

bsearch0.0ms (0.0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.324530470004861e-153	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

derivations42.0ms (0.3%)

Memory

34.7MiB live, 34.7MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 114 to 28 computations (75.4% saved)

preprocess30.0ms (0.2%)

Memory: -31.2MiB live, 60.5MiB allocated; 7ms collecting garbage
Compiler: Compiled 122 to 34 computations (72.1% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze16.0ms (0.1%)

sample1.0s (6.7%)

preprocess78.0ms (0.5%)

series60.0ms (0.4%)

rewrite190.0ms (1.2%)

eval39.0ms (0.3%)

prune16.0ms (0.1%)

series130.0ms (0.9%)

rewrite281.0ms (1.8%)

eval9.9s (64.4%)

prune68.0ms (0.4%)

series72.0ms (0.5%)

rewrite188.0ms (1.2%)

eval804.0ms (5.3%)

prune61.0ms (0.4%)

series65.0ms (0.4%)

rewrite180.0ms (1.2%)

eval2.0s (13.0%)

prune23.0ms (0.2%)

regimes80.0ms (0.5%)

bsearch0.0ms (0.0%)

bsearch0.0ms (0.0%)

derivations42.0ms (0.3%)

preprocess30.0ms (0.2%)

end0.0ms (0.0%)

Profiling