Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0.0%)

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

analyze15.0ms (0.5%)

Memory

-14.4MiB live, 32.8MiB allocated; 3ms 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)

sample1.1s (37.5%)

Memory

37.7MiB live, 2 072.4MiB allocated; 296ms collecting garbage

Samples

302.0ms	2 828×	1	valid
275.0ms	4 736×	0	valid
148.0ms	692×	2	valid
37.0ms	170×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 458.0ms

ival-sqrt: 133.0ms (29.0% of total)

adjust: 131.0ms (28.6% of total)

ival-mult!: 100.0ms (21.8% of total)

ival-sub!: 94.0ms (20.5% of total)

Bogosity

preprocess41.0ms (1.4%)

Memory

-6.6MiB live, 38.5MiB allocated; 8ms 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
▶	59.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 16 to 12 computations (25.0% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

Inputs

Outputs

series25.0ms (0.8%)

Memory

34.1MiB live, 79.0MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	1452

Stop Event

1×	iter-limit

Counts

6 → 54

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
2.0ms	x	inf
2.0ms	eps	inf
1.0ms	x	0
1.0ms	eps	-inf
1.0ms	x	-inf

rewrite211.0ms (7.2%)

Memory

4.4MiB live, 298.0MiB allocated; 126ms 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 → 275

Calls

Call 1

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

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

eval63.0ms (2.2%)

Memory: -12.5MiB live, 84.5MiB allocated; 9ms collecting garbage
Compiler: Compiled 7 085 to 1 534 computations (78.3% saved)

prune27.0ms (0.9%)

Memory

-6.7MiB live, 40.0MiB allocated; 2ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	313	10	323
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	313	11	324

Accuracy

99.6%

Counts

324 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.8%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	59.5%	(-.f64 x (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	59.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	55.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
▶	59.8%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
	44.5%	#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))
	34.4%	#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)))) (fma.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))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
	46.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	55.2%	#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))))))
▶	55.9%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 366 to 246 computations (32.8% saved)

sample0.0ms (0.0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Calls

Call 1

Inputs
1
2
-1

Outputs
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(literal -1 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 5 to 5 computations (0.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series78.0ms (2.7%)

Memory

17.5MiB live, 149.7MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	825	5974

Stop Event

1×	iter-limit

Counts

28 → 179

Calls

Call 1

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

Outputs
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps))))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (+.f64 x (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps)))))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (fma.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 (/ (sqrt (- (* x x) eps)) x)) x) (fma.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 (- 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 (/ (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)) (fma.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)) (fma.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 (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)) (fma.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)) (fma.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 x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (pow.f64 x #s(literal 2 binary64)) eps))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx x 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 (* 2 x) (*.f64 #s(literal 2 binary64) x))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (+.f64 x (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* -1 (/ x eps)) (*.f64 #s(literal -1 binary64) (/.f64 x eps)))
#s(approx (/ x eps) (/.f64 x 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)))) (fma.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)))) (fma.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.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)))) (fma.f64 x (-.f64 (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.f64 #s(literal -1 binary64) (/.f64 (fma.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))))))) (fma.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)) 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 (fma.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 (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (/.f64 (fma.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 (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.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 (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) eps (.f64 #s(literal 1/2 binary64) (/.f64 (fma.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))))))) x))
#s(approx (- 1 (/ (sqrt (- (* x x) eps)) x)) (*.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 (.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)) (pow.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (/ (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 4 binary64)))) (fma.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)))))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (- 1 (/ (sqrt (- (* x x) eps)) x)) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (fma.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)))) (fma.f64 #s(literal -1/2 binary64) eps (fma.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))))))) (pow.f64 x #s(literal 2 binary64))))
#s(approx (/ (sqrt (- (* x x) eps)) x) #s(literal 1 binary64))
#s(approx (/ (sqrt (- (* x x) eps)) 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)) x) (+.f64 #s(literal 1 binary64) (fma.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 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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) 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 (- 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)))) (fma.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 (fma.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)))) (fma.f64 #s(literal -1/2 binary64) eps (fma.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 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)) #s(literal 1 binary64))))
#s(approx (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) x)) (/.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (-.f64 (fma.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))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (pow.f64 eps #s(literal 4 binary64)) (.f64 #s(literal -1/128 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) eps)) (fma.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 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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (* (- 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 (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (fma.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 (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.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)) #s(literal 2 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))))) (fma.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 (/ (sqrt (- (* x x) eps)) x) #s(literal -1 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 (fma.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 (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.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)) (.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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 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) (fma.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 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)) #s(literal 1 binary64)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)))))
#s(approx (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) 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 (fma.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 (fma.f64 #s(literal -2 binary64) (/.f64 (fma.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) (fma.f64 #s(literal -1/4 binary64) (.f64 eps (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (/.f64 (fma.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 (fma.f64 #s(literal -1/2 binary64) eps (fma.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 (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.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))) (fma.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 (* (- 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) (fma.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) (fma.f64 eps (fma.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) (fma.f64 eps (fma.f64 eps (fma.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 (- 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 (fma.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 (fma.f64 eps (fma.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 (/ (sqrt (- (* x x) eps)) x) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) x))
#s(approx (/ (sqrt (- (* x x) eps)) x) (fma.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) (fma.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) (fma.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 (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 x) eps) (fma.f64 #s(literal -1 binary64) eps (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 (fma.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 (fma.f64 eps (fma.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 (sqrt (neg eps))) (.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal -1 binary64) eps))))
#s(approx (sqrt (neg eps)) (sqrt.f64 (*.f64 #s(literal -1 binary64) eps)))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 #s(literal -1 binary64) (-.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (-.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (.f64 #s(literal -1 binary64) eps))))
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#s(approx (/ -1 eps) (/.f64 #s(literal -1 binary64) eps))
#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))))))
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#s(approx (- 1 (/ (sqrt (- (* x x) eps)) x)) (.f64 eps (-.f64 (fma.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 #s(literal 1 binary64) eps)) (/.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) x))))
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#s(approx (/ (sqrt (- (* x x) eps)) x) (/.f64 (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x))
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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))))
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#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 #s(literal -1 binary64) (.f64 eps (fma.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))))))
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#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)))))
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#s(approx (/ (sqrt (- (* x x) eps)) x) (.f64 #s(literal -1 binary64) (.f64 eps (fma.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)))) (fma.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 (fma.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)))) (fma.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)))) (fma.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)) (.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)) (fma.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)) (fma.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)))) (fma.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 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 (- 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 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (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))))
#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 (fma.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 (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 x (fma.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)))))) (fma.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 (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 (fma.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))))))

Calls

6 calls:

Time	Variable	Point
21.0ms	x	-inf
7.0ms	eps	inf
4.0ms	x	0
4.0ms	eps	0
4.0ms	eps	-inf

rewrite149.0ms (5.1%)

Memory

23.5MiB live, 255.7MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	197
0	52	176
1	218	166
2	800	164
3	3809	164
0	4012	153

Stop Event

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

Counts

28 → 843

Calls

Call 1

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

Outputs
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 0 binary64))) #s(literal 0 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x))) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) x))
(.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 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 eps))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x))) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) x))
(.f64 (fma.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 eps (.f64 x x))) (/.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 (/.f64 #s(literal 1 binary64) x) x))
(.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1 binary64))
(.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) (.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) #s(literal 1 binary64)) (neg.f64 x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) eps)
(.f64 (neg.f64 x) (-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 1 binary64)))
(.f64 (neg.f64 eps) (/.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 x #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
(.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 x (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (/.f64 (-.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 (/.f64 (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) x) #s(literal 1 binary64)) x)
(/.f64 (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) x) (neg.f64 x))
(/.f64 (.f64 x (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 x))
(/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 eps (.f64 x x))) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (fma.f64 (.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (-.f64 eps (.f64 x x)) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (fma.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x) (.f64 (-.f64 eps (.f64 x 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 (-.f64 (.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)) (.f64 (/.f64 (-.f64 eps (.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 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x) (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x))) (-.f64 x (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x)))
(/.f64 (+.f64 (pow.f64 #s(literal 0 binary64) #s(literal 3 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64))) (fma.f64 #s(literal 0 binary64) #s(literal 0 binary64) (-.f64 (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) #s(literal 3 binary64)) (pow.f64 (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (-.f64 (.f64 (/.f64 (-.f64 eps (.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 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))))
(/.f64 (+.f64 (pow.f64 (neg.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 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x) (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x)) (.f64 x (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x)))))
(/.f64 (fma.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)))
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(+.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (.f64 (/.f64 x (+.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)) (-.f64 eps (*.f64 x x))))
(+.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x) (/.f64 (-.f64 eps (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 x (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 x)) x))
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
eps
(.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 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)) (neg.f64 x))) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
(/.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 (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 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64))) (fma.f64 x x (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(/.f64 (neg.f64 eps) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(neg.f64 (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
(fma.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))) x)
(fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64) x)
(fma.f64 #s(literal 1 binary64) (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)) x)
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

eval149.0ms (5.1%)

Memory: -3.6MiB live, 232.2MiB allocated; 83ms collecting garbage
Compiler: Compiled 27 056 to 4 068 computations (85.0% saved)

prune24.0ms (0.8%)

Memory

6.7MiB live, 55.6MiB allocated; 5ms collecting garbage

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	994	9	1 003
Fresh	3	2	5
Picked	5	0	5
Done	0	1	1
Total	1 002	12	1 014

Accuracy

100.0%

Counts

1 014 → 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))))
✓	59.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	55.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) eps)
	4.2%	(.f64 (-.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (- ( x x) eps)) x) #s(literal 1 binary64))) x)
	55.6%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
	41.2%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.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))))))))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	46.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))))
	55.9%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
	55.2%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (+.f64 x (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))

Compiler

Compiled 460 to 284 computations (38.3% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

Inputs
-1
1/2

Outputs
#s(literal -1 binary64)
#s(literal 1/2 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 4 to 4 computations (0.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series43.0ms (1.5%)

Memory

-39.1MiB live, 53.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	593	3700

Stop Event

1×	iter-limit

Counts

23 → 107

Calls

Call 1

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

Outputs
#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)))) (fma.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)))) (fma.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.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)))) (fma.f64 x (-.f64 (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.f64 #s(literal -1 binary64) (/.f64 (fma.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))))))) (fma.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)) eps)
#s(approx (+ x (sqrt (- (* x x) eps))) (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 (fma.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)
#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)) (fma.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)) (fma.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 x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (pow.f64 x #s(literal 2 binary64)) eps))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#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) (*.f64 #s(literal 2 binary64) x))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (+.f64 x (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (* -1 x) (*.f64 #s(literal -1 binary64) x))
#s(approx (* 1/2 (/ eps x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (/ eps x) (/.f64 eps x))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.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 (fma.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))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (pow.f64 eps #s(literal 4 binary64)) (.f64 #s(literal -1/128 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) eps)) (fma.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 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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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) 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 (- 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)))) (fma.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 (fma.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)))) (fma.f64 #s(literal -1/2 binary64) eps (fma.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 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)) #s(literal 1 binary64))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))) #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 (fma.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 (fma.f64 #s(literal -2 binary64) (/.f64 (fma.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) (fma.f64 #s(literal -1/4 binary64) (.f64 eps (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (/.f64 (fma.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 (fma.f64 #s(literal -1/2 binary64) eps (fma.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 (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.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))) (fma.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) (.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) (fma.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) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 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) (fma.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 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)) #s(literal 1 binary64)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) x)))))
#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 (fma.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 (fma.f64 eps (fma.f64 eps (fma.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 (fma.f64 eps (fma.f64 eps (fma.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)))) (fma.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 (fma.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 (fma.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 (+ 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 (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 x) eps) (fma.f64 #s(literal -1 binary64) eps (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 (fma.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 (fma.f64 eps (fma.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 (neg eps)) (sqrt.f64 (*.f64 #s(literal -1 binary64) eps)))
#s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 #s(literal -1 binary64) (-.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (*.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (-.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (.f64 #s(literal -1 binary64) 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)))) (fma.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 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.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))))) (pow.f64 eps #s(literal 2 binary64))) (/.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))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 x (fma.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)))) (fma.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)))) (fma.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 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)) (fma.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)) (fma.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)))) (fma.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)) (.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)) (fma.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)) (fma.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)))) (fma.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 x) eps) (*.f64 eps (-.f64 (/.f64 (pow.f64 x #s(literal 2 binary64)) eps) #s(literal 1 binary64))))
#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 (fma.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 (fma.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 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 eps (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) (/.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))))
#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 (fma.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 (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 x (fma.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)))))) (fma.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 (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 (fma.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 (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)) (fma.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)) (fma.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)))) (fma.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 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 (- 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 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 #s(literal -1 binary64) (/.f64 x eps))))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)))))

Calls

6 calls:

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

rewrite121.0ms (4.1%)

Memory

16.7MiB live, 157.8MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	185
0	50	176
1	213	164
2	656	160
3	2590	154
0	4227	143

Stop Event

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

Counts

23 → 632

Calls

Call 1

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

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

eval108.0ms (3.7%)

Memory: 30.0MiB live, 257.8MiB allocated; 61ms collecting garbage
Compiler: Compiled 19 126 to 3 130 computations (83.6% saved)

prune31.0ms (1.1%)

Memory

-4.6MiB live, 47.9MiB allocated; 11ms collecting garbage

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	714	7	721
Fresh	4	2	6
Picked	2	3	5
Done	0	1	1
Total	720	13	733

Accuracy

100.0%

Counts

733 → 13

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))))
▶	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))
▶	58.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
▶	55.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps))))
✓	59.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	57.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (fabs.f64 eps))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
▶	4.2%	(.f64 (-.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (- ( x x) eps)) x) #s(literal 1 binary64))) x)
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
✓	46.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
	55.9%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 #s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (neg.f64 x))))

Compiler

Compiled 402 to 252 computations (37.3% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

Inputs
1

Outputs
#s(literal 1 binary64)

Samples

0.0ms

1×

valid

Compiler

Compiled 3 to 3 computations (0.0% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0.0% of total)

series84.0ms (2.9%)

Memory

2.9MiB live, 93.1MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	956	7369

Stop Event

1×	iter-limit

Counts

25 → 198

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (fma.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)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (fma.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.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)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (fma.f64 x (-.f64 (.f64 x (-.f64 (.f64 #s(literal -1 binary64) (.f64 x (fma.f64 #s(literal -1 binary64) (/.f64 (fma.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))))))) (fma.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)) eps)
#s(approx (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x) (sqrt.f64 (neg.f64 eps)))
#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))))))))
#s(approx (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (fma.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 (+ 1 (/ (sqrt (- (* x x) eps)) x)) (/.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 (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 (fma.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 #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)) (fma.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)) (fma.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 (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)) (fma.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)) (fma.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 x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (pow.f64 x #s(literal 2 binary64)) eps))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx x 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 (neg (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (neg (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (-.f64 x (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (fma.f64 #s(literal -1 binary64) x (.f64 #s(literal -1 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (neg x) (*.f64 #s(literal -1 binary64) x))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (+.f64 x (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps)))))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (fma.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 (/ (sqrt (- (* x x) eps)) x)) x) (fma.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 (- 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)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (/.f64 (fma.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)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (/.f64 (-.f64 (fma.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))
#s(approx (/ (- (* x x) (- (* x x) eps)) (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x)) (/.f64 (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (pow.f64 eps #s(literal 4 binary64)) (.f64 #s(literal -1/128 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) eps)) (fma.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 (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 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)) x) (.f64 x (+.f64 #s(literal 2 binary64) (fma.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 (* (+ 1 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (fma.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 (+ 1 (/ (sqrt (- (* x x) eps)) x)) #s(literal 2 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))))))
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#s(approx (+ x (sqrt (neg eps))) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (neg.f64 eps)) x)) #s(literal 1 binary64)))))
#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)))))
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#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) (fma.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) (fma.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) (fma.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 (+ 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) (fma.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) (fma.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) (fma.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 (/ (sqrt (- (* x x) eps)) x) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) x))
#s(approx (/ (sqrt (- (* x x) eps)) x) (fma.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) (fma.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) (fma.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 (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 x) eps) (fma.f64 #s(literal -1 binary64) eps (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 (fma.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 (fma.f64 eps (fma.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 (neg (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (-.f64 (sqrt.f64 (.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) x)))
#s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (-.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (.f64 #s(literal -1 binary64) eps))))
#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) (fma.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) (fma.f64 eps (fma.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) (fma.f64 eps (fma.f64 eps (fma.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 (- 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 (fma.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 (fma.f64 eps (fma.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 (/ (- (* 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 (fma.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 (fma.f64 eps (fma.f64 eps (fma.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 (fma.f64 eps (fma.f64 eps (fma.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)))) (fma.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 (fma.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 (fma.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 (+ 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 (sqrt (neg eps)) (sqrt.f64 (*.f64 #s(literal -1 binary64) eps)))
#s(approx (+ x (sqrt (neg eps))) (+.f64 x (sqrt.f64 (*.f64 #s(literal -1 binary64) 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 (- 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 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)))))
#s(approx (* (- 1 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 #s(literal -1 binary64) (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 (fma.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 (/ (sqrt (- (* x x) eps)) x)) x) (.f64 #s(literal -1 binary64) (.f64 eps (fma.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 (fma.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 (- 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)))))

Calls

6 calls:

Time	Variable	Point
22.0ms	x	-inf
3.0ms	eps	0
2.0ms	eps	inf
2.0ms	x	inf
2.0ms	eps	-inf

rewrite155.0ms (5.3%)

Memory

11.1MiB live, 252.5MiB allocated; 48ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	262
0	58	251
1	261	227
2	857	219
3	3453	219
0	4153	206

Stop Event

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

Counts

25 → 587

Calls

Call 1

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

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

eval146.0ms (5.0%)

Memory: -24.3MiB live, 313.2MiB allocated; 43ms collecting garbage
Compiler: Compiled 29 892 to 3 983 computations (86.7% saved)

prune45.0ms (1.6%)

Memory

11.2MiB live, 58.2MiB allocated; 2ms collecting garbage

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	870	1	871
Fresh	0	4	4
Picked	1	4	5
Done	0	4	4
Total	871	13	884

Accuracy

100.0%

Counts

884 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (fma.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) x x))
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	58.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
✓	55.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps))))
✓	59.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	57.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (fabs.f64 eps))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(approx (- (* x x) (- (* x x) eps)) eps))
✓	4.2%	(.f64 (-.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (- ( x x) eps)) x) #s(literal 1 binary64))) x)
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
✓	46.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
	55.9%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
✓	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 #s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (neg.f64 x))))

Compiler

Compiled 227 to 142 computations (37.4% saved)

regimes150.0ms (5.1%)

Memory

6.3MiB live, 297.2MiB allocated; 90ms collecting garbage

Counts

3 → 1

6 → 1

11 → 1

13 → 2

14 → 2

16 → 2

28 → 1

Calls

Call 1

Inputs

#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 #s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (neg.f64 x))))

#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))) (neg.f64 #s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (neg.f64 x))))

Call 2

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

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

Call 3

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

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

Call 4

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

Outputs
(-.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)))

Call 5

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

Outputs

(/.f64 #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 #s(literal 1/2 binary64) (/.f64 eps x)))

Call 6

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 #s(approx (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (neg.f64 x))))
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
(.f64 (-.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (- ( x x) eps)) x) #s(literal 1 binary64))) x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (fabs.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 #s(literal -1 binary64) #s(approx ( eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (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 (/.f64 #s(literal 1/2 binary64) x) eps))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (+.f64 x (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) 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 7

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

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

Calls

17 calls:

32.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
19.0ms	eps
14.0ms	x
12.0ms	eps
8.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
3.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.6%	1	`x`
3.6%	1	`eps`
55.9%	1	`x`
55.9%	1	`eps`
55.9%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
57.0%	1	`eps`
57.0%	1	`x`
57.0%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
96.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
96.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
98.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
86.1%	2	`x`
84.1%	2	`eps`
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 623 to 192 computations (69.2% saved)

bsearch0.0ms (0.0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.8404616592232563e-154	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

bsearch0.0ms (0.0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.8404616592232563e-154	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

bsearch0.0ms (0.0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.8404616592232563e-154	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

derivations61.0ms (2.1%)

Memory

-12.2MiB live, 80.8MiB allocated; 4ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 191 to 48 computations (74.9% saved)

preprocess92.0ms (3.2%)

Memory: 1.7MiB live, 145.9MiB allocated; 21ms collecting garbage
Compiler: Compiled 209 to 61 computations (70.8% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze15.0ms (0.5%)

sample1.1s (37.5%)

preprocess41.0ms (1.4%)

sample0.0ms (0.0%)

series25.0ms (0.8%)

rewrite211.0ms (7.2%)

eval63.0ms (2.2%)

prune27.0ms (0.9%)

sample0.0ms (0.0%)

series78.0ms (2.7%)

rewrite149.0ms (5.1%)

eval149.0ms (5.1%)

prune24.0ms (0.8%)

sample0.0ms (0.0%)

series43.0ms (1.5%)

rewrite121.0ms (4.1%)

eval108.0ms (3.7%)

prune31.0ms (1.1%)

sample0.0ms (0.0%)

series84.0ms (2.9%)

rewrite155.0ms (5.3%)

eval146.0ms (5.0%)

prune45.0ms (1.6%)

regimes150.0ms (5.1%)

bsearch0.0ms (0.0%)

bsearch0.0ms (0.0%)

bsearch0.0ms (0.0%)

derivations61.0ms (2.1%)

preprocess92.0ms (3.2%)

end0.0ms (0.0%)

Profiling