Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0.0%)

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

analyze13.0ms (0.5%)

Memory

5.4MiB live, 52.3MiB allocated; 2ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25.0% saved)

sample1.0s (37.7%)

Memory

30.1MiB live, 2 757.7MiB allocated; 314ms collecting garbage

Samples

369.0ms	4 927×	0	valid
306.0ms	2 654×	1	valid
93.0ms	675×	2	valid
7.0ms	157×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 431.0ms

ival-mult!: 145.0ms (33.6% of total)

ival-sqrt: 131.0ms (30.4% of total)

adjust: 90.0ms (20.9% of total)

ival-sub!: 65.0ms (15.1% of total)

Bogosity

preprocess53.0ms (1.9%)

Memory

-25.2MiB live, 75.0MiB 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
▶	64.1%	(-.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

series24.0ms (0.9%)

Memory

30.7MiB live, 77.7MiB allocated; 2ms 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
x
(*.f64 x x)
eps
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

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

Calls

6 calls:

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

rewrite172.0ms (6.2%)

Memory

-23.4MiB live, 361.0MiB allocated; 42ms 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
x
(*.f64 x x)
eps
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

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

eval47.0ms (1.7%)

Memory: 6.2MiB live, 188.5MiB allocated; 32ms collecting garbage
Compiler: Compiled 6 740 to 1 531 computations (77.3% saved)

prune14.0ms (0.5%)

Memory

18.8MiB live, 65.3MiB allocated; 5ms collecting garbage

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	313	11	324
Fresh	0	0	0
Picked	1	0	1
Done	-1	1	0
Total	313	12	325

Accuracy

99.9%

Counts

325 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.8%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	64.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	64.0%	(-.f64 x (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (neg.f64 eps))) (neg.f64 eps))))
	59.1%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
▶	64.0%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
	24.4%	#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))
	39.9%	#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))
	36.1%	#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))
▶	3.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
	42.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
	58.8%	#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))))))
▶	59.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 334 to 256 computations (23.4% saved)

sample0.0ms (0.0%)

Memory

1.1MiB live, 1.1MiB 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)

series83.0ms (3.0%)

Memory

-10.0MiB live, 270.1MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	841	6091

Stop Event

1×	iter-limit

Counts

25 → 169

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable	Point
9.0ms	eps	inf
9.0ms	x	inf
4.0ms	x	0
4.0ms	eps	0
4.0ms	eps	-inf

rewrite264.0ms (9.5%)

Memory

27.7MiB live, 603.8MiB allocated; 102ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	174
0	47	148
1	226	135
2	892	133
3	3897	133
0	4047	121

Stop Event

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

Counts

25 → 1 225

Calls

Call 1

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

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

eval190.0ms (6.8%)

Memory: -33.0MiB live, 352.7MiB allocated; 92ms collecting garbage
Compiler: Compiled 33 252 to 5 797 computations (82.6% saved)

prune25.0ms (0.9%)

Memory

22.8MiB live, 70.1MiB allocated; 1ms collecting garbage

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1 365	4	1 369
Fresh	4	2	6
Picked	5	0	5
Done	-1	2	1
Total	1 373	8	1 381

Accuracy

100.0%

Counts

1 381 → 8

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))))
✓	64.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	59.1%	(-.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)
✓	64.0%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
▶	3.2%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	42.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	59.3%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 108 to 93 computations (13.9% saved)

sample0.0ms (0.0%)

Memory

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

Calls

Call 1

Inputs
1/2

Outputs
#s(literal 1/2 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)

series33.0ms (1.2%)

Memory

25.5MiB live, 72.3MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	568	3414

Stop Event

1×	iter-limit

Counts

20 → 97

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite132.0ms (4.7%)

Memory

0.6MiB live, 286.2MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	137
0	40	137
1	161	125
2	487	121
3	1794	121
0	4078	113

Stop Event

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

Counts

20 → 694

Calls

Call 1

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

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

eval101.0ms (3.6%)

Memory: 0.1MiB live, 233.0MiB allocated; 18ms collecting garbage
Compiler: Compiled 19 452 to 3 820 computations (80.4% saved)

prune21.0ms (0.7%)

Memory

7.8MiB live, 54.6MiB allocated; 2ms collecting garbage

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	986	6	992
Fresh	1	0	1
Picked	5	0	5
Done	-3	5	2
Total	989	11	1 000

Accuracy

100.0%

Counts

1 000 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	62.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
✓	64.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	60.1%	(-.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))
✓	64.0%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
✓	3.2%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	42.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
✓	42.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	59.8%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps))))

Compiler

Compiled 157 to 123 computations (21.7% 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)

series46.0ms (1.6%)

Memory

-13.4MiB live, 91.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	707	4661

Stop Event

1×	iter-limit

Counts

25 → 125

Calls

Call 1

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

Outputs
#s(approx x x)
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx (- (* x x) eps) (*.f64 #s(literal -1 binary64) eps))
#s(approx (- (* x x) eps) (-.f64 (pow.f64 x #s(literal 2 binary64)) eps))
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (neg.f64 eps)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (neg.f64 eps))))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (neg.f64 eps)) (.f64 (pow.f64 x #s(literal 2 binary64)) (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 (+ (sqrt (- (* x x) eps)) x) (+.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) 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 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (fma.f64 #s(literal -1 binary64) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps)))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps)))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (fma.f64 x (-.f64 (.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 5 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps)))))
#s(approx (- (* x x) (- (* x x) eps)) eps)
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 (neg.f64 eps)))))) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 eps)))))))) (sqrt.f64 (neg.f64 eps))))
#s(approx (/ 1/2 x) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (* (/ 1/2 x) eps) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (- (* x x) eps) (.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 x (+.f64 #s(literal 1 binary64) (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 (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) 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 (+ (sqrt (- (* x x) eps)) 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)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))))) x))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))))) x))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/32 binary64) (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal -1/128 binary64) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))) x))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (-.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 (+ x (sqrt (neg eps))) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (neg.f64 eps)) x))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (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 (+ (sqrt (- (* x x) eps)) x) (.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 (+ (sqrt (- (* x x) eps)) x) (.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 (+ (sqrt (- (* x x) eps)) x) (.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)) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (.f64 x (-.f64 (fma.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)))) (pow.f64 eps #s(literal 2 binary64))) (fma.f64 #s(literal -1/4 binary64) (.f64 eps (fma.f64 #s(literal -1/4 binary64) eps (.f64 #s(literal 1/8 binary64) eps))) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 2 binary64))))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) (fma.f64 #s(literal -1/4 binary64) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) eps))))))))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 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 (+ 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) eps) (fma.f64 #s(literal -1 binary64) eps (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (sqrt (- (* x x) eps)) (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 eps (-.f64 (.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (+.f64 x (+.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) (.f64 eps (-.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 (sqrt.f64 (pow.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (+.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 (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (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 (/ 1 (+ (sqrt (- (* x x) eps)) x)) (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 (/ 1 (+ (sqrt (- (* x x) eps)) x)) (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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps))) (/.f64 eps (+.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64))))))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (fabs eps) (fabs.f64 eps))
#s(approx (sqrt (fabs eps)) (sqrt.f64 (fabs.f64 eps)))
#s(approx (neg (sqrt (fabs eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fabs.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (+.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 eps (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 x #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (+.f64 x (.f64 eps (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 (+ x (sqrt (neg eps))) (+.f64 x (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 (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 (+ (sqrt (- (* x x) eps)) x) (*.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (.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 (+ (sqrt (- (* x x) eps)) x) (.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 (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 1 binary64) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 (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)))) eps))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 (-.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))))) eps))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 (-.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))))))) eps))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 #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 (- (* x x) eps) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) eps))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (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 (+ (sqrt (- (* x x) eps)) x) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 #s(literal -1 binary64) (/.f64 x eps))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps))))))
#s(approx (+ (sqrt (- (* x x) eps)) x) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1 binary64) (/.f64 (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 (/ 1 (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal -1 binary64) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 x (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64))))) eps)))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))) eps) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) eps)))
#s(approx (/ 1 (+ (sqrt (- (* x x) eps)) x)) (.f64 #s(literal -1 binary64) (/.f64 (fma.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 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64)))))) (.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 eps (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 4 binary64)))))) (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)))))) eps)) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 2 binary64)))) eps) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) eps)))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (* (/ 1 (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* 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 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 eps (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (-.f64 (.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (.f64 #s(literal -1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal 3 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps))) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))

Calls

6 calls:

Time	Variable	Point
6.0ms	x	0
2.0ms	x	-inf
2.0ms	eps	-inf
2.0ms	x	inf
1.0ms	eps	inf

rewrite148.0ms (5.3%)

Memory

-1.3MiB live, 329.6MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	185
0	50	185
1	208	165
2	612	159
3	2247	159
0	4511	149

Stop Event

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

Counts

25 → 831

Calls

Call 1

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

Outputs
#s(literal 1 binary64)
x
(*.f64 (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))))
(.f64 (pow.f64 (.f64 x x) (pow.f64 (cosh.f64 (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (.f64 x x) (.f64 (sinh.f64 (.f64 x x)) (sinh.f64 (*.f64 (neg.f64 x) x)))))
(.f64 (pow.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (.f64 x x) (*.f64 (neg.f64 x) x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 0 binary64)) (*.f64 x x))
(*.f64 (pow.f64 (neg.f64 (neg.f64 (fabs.f64 x))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (neg.f64 (fabs.f64 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 (neg.f64 (fabs.f64 x)) #s(literal 1 binary64)) (neg.f64 (fabs.f64 x)))
(*.f64 (pow.f64 (fabs.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 (fabs.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 (neg.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 (neg.f64 x) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1 binary64)) (pow.f64 (fabs.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1 binary64)) (fabs.f64 x))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) x)
(*.f64 (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 x (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) (pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 0 binary64)))
(.f64 (.f64 x x) (pow.f64 (fabs.f64 x) #s(literal 0 binary64)))
(.f64 (.f64 x x) (pow.f64 x #s(literal 0 binary64)))
(.f64 (.f64 x x) (pow.f64 (neg.f64 x) #s(literal 0 binary64)))
(.f64 (.f64 x x) (pow.f64 (*.f64 x x) #s(literal 0 binary64)))
(*.f64 x x)
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (pow.f64 (.f64 x x) (pow.f64 (cosh.f64 (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (.f64 x x) (pow.f64 (sinh.f64 (.f64 x x)) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (.f64 x x) (.f64 x x)))
(/.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)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (pow.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x x) (pow.f64 (.f64 x x) #s(literal 0 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 (*.f64 x x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 (neg.f64 x) (neg.f64 (fabs.f64 x))))
(fabs.f64 (*.f64 x (neg.f64 (fabs.f64 x))))
(fabs.f64 (*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 (fabs.f64 x)) x))
(fabs.f64 (*.f64 (fabs.f64 x) (neg.f64 x)))
(fabs.f64 (*.f64 x (fabs.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) (fabs.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 (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
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) (pow.f64 (cosh.f64 (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (-.f64 (.f64 x x) eps) (.f64 (sinh.f64 (.f64 x x)) (sinh.f64 (*.f64 (neg.f64 x) x)))))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (-.f64 (.f64 x x) eps) (*.f64 (neg.f64 x) x)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 0 binary64)) (-.f64 (*.f64 x x) eps))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (neg.f64 eps))) (neg.f64 eps))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (.f64 x x))) (*.f64 x x))
(.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x))) (*.f64 x x))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (-.f64 (.f64 x x) eps) (pow.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))) #s(literal 0 binary64)))
(.f64 (-.f64 (.f64 x x) eps) (pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 0 binary64)))
(.f64 (-.f64 (.f64 x x) eps) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64)))
(pow.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (pow.f64 (-.f64 (.f64 x x) eps) (pow.f64 (cosh.f64 (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (-.f64 (.f64 x x) eps) (pow.f64 (sinh.f64 (.f64 x x)) #s(literal 2 binary64))))
(/.f64 (pow.f64 (-.f64 (.f64 x x) eps) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (-.f64 (.f64 x x) eps) (.f64 x x)))
(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (neg.f64 eps) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (+.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (neg.f64 eps) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (-.f64 (*.f64 x x) (neg.f64 eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (fma.f64 eps eps (.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(neg.f64 (-.f64 eps (*.f64 x x)))
(fma.f64 (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) (neg.f64 eps))
(fma.f64 (pow.f64 (neg.f64 eps) (pow.f64 (cosh.f64 (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (neg.f64 eps) (.f64 (sinh.f64 (.f64 x x)) (sinh.f64 (.f64 (neg.f64 x) x)))) (*.f64 x x))
(fma.f64 (pow.f64 (neg.f64 eps) (+.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (neg.f64 eps) (.f64 (neg.f64 x) x)) (*.f64 x x))
(fma.f64 (pow.f64 (neg.f64 eps) #s(literal 0 binary64)) (neg.f64 eps) (*.f64 x x))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 1 binary64)) (sqrt.f64 (neg.f64 eps)) (*.f64 x x))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 x) x) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps) (.f64 x x))
(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 eps) (.f64 x x)) (.f64 x x))) (.f64 x x) (.f64 x x))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x eps) (.f64 x x))) (.f64 x x) (*.f64 x x))
(fma.f64 (pow.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (pow.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) #s(literal 2 binary64))) (*.f64 x x))
(fma.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 eps))
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps) (.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (neg.f64 eps))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) (*.f64 x x))
(fma.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) (*.f64 x x))
(fma.f64 (neg.f64 eps) (pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 0 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 eps) (pow.f64 (neg.f64 eps) #s(literal 0 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 eps) (pow.f64 (.f64 eps eps) #s(literal 0 binary64)) (.f64 x x))
(fma.f64 x x (neg.f64 eps))
(-.f64 (neg.f64 eps) (*.f64 (neg.f64 x) x))
(-.f64 (*.f64 x x) eps)
(sqrt.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))))
(fabs.f64 (neg.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fabs.f64 (neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fabs.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fabs.f64 (-.f64 eps (*.f64 x x)))
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(.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 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.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))))
(.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))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 0 binary64)))
(pow.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/2 binary64)))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (neg.f64 (neg.f64 (fabs.f64 x))) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (neg.f64 (fabs.f64 x)) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (fabs.f64 x))))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (fabs.f64 x)))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (fabs.f64 x))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 x))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)
(hypot.f64 (fabs.f64 x) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (fabs.f64 x) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (neg.f64 x) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (neg.f64 (fabs.f64 x)))))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (fabs.f64 x))))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 (fabs.f64 x)))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (fabs.f64 x))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 x))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) x)
(hypot.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 x (sqrt.f64 (neg.f64 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 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
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eval113.0ms (4.1%)

Memory: -0.7MiB live, 232.5MiB allocated; 27ms collecting garbage
Compiler: Compiled 18 102 to 3 704 computations (79.5% saved)

prune19.0ms (0.7%)

Memory

3.9MiB live, 50.9MiB allocated; 2ms collecting garbage

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	972	0	972
Fresh	0	1	1
Picked	5	0	5
Done	-5	10	5
Total	972	11	983

Accuracy

100.0%

Counts

983 → 11

Alt Table

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Status	Accuracy	Program
	99.2%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
✓	99.6%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	62.4%	(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
✓	64.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	60.1%	(-.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))
✓	64.0%	(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) x)
✓	3.2%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓	42.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
✓	42.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
✓	59.8%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps))))

Compiler

Compiled 99 to 78 computations (21.2% saved)

regimes77.0ms (2.8%)

Memory

-26.5MiB live, 171.7MiB allocated; 16ms collecting garbage

Counts

2 → 1

4 → 1

7 → 1

9 → 2

10 → 2

11 → 2

22 → 1

Calls

Call 1

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

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

Call 2

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

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

Call 3

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

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

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

Calls

17 calls:

11.0ms	eps
7.0ms	x
6.0ms	x
6.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
4.0ms	eps

Results

Accuracy	Segments	Branch
3.2%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.2%	1	`eps`
3.2%	1	`x`
59.8%	1	`x`
59.8%	1	`eps`
59.8%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
60.1%	1	`eps`
60.1%	1	`x`
60.1%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
95.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
95.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
88.2%	2	`x`
80.1%	2	`eps`
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 327 to 165 computations (49.5% saved)

bsearch0.0ms (0.0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.1947488293203202e-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	-2.1947488293203202e-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	-2.1947488293203202e-154	0.0

Compiler

Compiled 18 to 15 computations (16.7% saved)

derivations80.0ms (2.9%)

Memory

-6.6MiB live, 136.6MiB allocated; 14ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 100 to 31 computations (69.0% saved)

preprocess75.0ms (2.7%)

Memory: 10.0MiB live, 154.2MiB allocated; 14ms collecting garbage
Compiler: Compiled 118 to 44 computations (62.7% saved)

end0.0ms (0.0%)

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

start0.0ms (0.0%)

analyze13.0ms (0.5%)

sample1.0s (37.7%)

preprocess53.0ms (1.9%)

sample0.0ms (0.0%)

series24.0ms (0.9%)

rewrite172.0ms (6.2%)

eval47.0ms (1.7%)

prune14.0ms (0.5%)

sample0.0ms (0.0%)

series83.0ms (3.0%)

rewrite264.0ms (9.5%)

eval190.0ms (6.8%)

prune25.0ms (0.9%)

sample0.0ms (0.0%)

series33.0ms (1.2%)

rewrite132.0ms (4.7%)

eval101.0ms (3.6%)

prune21.0ms (0.7%)

sample0.0ms (0.0%)

series46.0ms (1.6%)

rewrite148.0ms (5.3%)

eval113.0ms (4.1%)

prune19.0ms (0.7%)

regimes77.0ms (2.8%)

bsearch0.0ms (0.0%)

bsearch0.0ms (0.0%)

bsearch0.0ms (0.0%)

derivations80.0ms (2.9%)

preprocess75.0ms (2.7%)

end0.0ms (0.0%)

Profiling