Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

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

analyze11.0ms (0.2%)

Memory

24.0MiB live, 24.0MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.0s (14.8%)

Memory

28.6MiB live, 747.5MiB allocated; 880ms collecting garbage

Samples

515.0ms	4 890×	0	valid
223.0ms	2 714×	1	valid
75.0ms	652×	2	valid
6.0ms	159×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 333.0ms

ival-sqrt: 105.0ms (31.5% of total)

ival-sub!: 95.0ms (28.5% of total)

adjust: 74.0ms (22.2% of total)

ival-mult!: 59.0ms (17.7% of total)

Bogosity

preprocess64.0ms (0.9%)

Memory

-28.7MiB live, 23.2MiB allocated; 10ms 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
▶	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 12 to 12 computations (0% saved)

series175.0ms (2.5%)

Memory

27.5MiB live, 118.8MiB allocated; 14ms collecting garbage

Counts

6 → 54

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite1.1s (16%)

Memory

13.1MiB live, 526.5MiB allocated; 144ms collecting garbage

Counts

6 → 57

Calls

Call 1

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

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

eval13.0ms (0.2%)

Memory: 17.5MiB live, 17.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 148 to 504 computations (56.1% saved)

prune15.0ms (0.2%)

Memory

-34.8MiB live, 9.5MiB allocated; 9ms collecting garbage

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Accuracy

99.2%

Counts

106 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.2%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	32.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 2 binary64)) (.f64 (pow.f64 eps #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))))))
	56.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	42.4%	#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))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	56.0%	#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))))))
▶	57.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 204 to 200 computations (2% saved)

series329.0ms (4.7%)

Memory

23.9MiB live, 164.0MiB allocated; 52ms collecting garbage

Counts

32 → 98

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((- x (sqrt (+ (* x x) (neg eps)))) x (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* 2 x) 2 (- x (sqrt (- (* x x) eps))) (* -1 (sqrt (neg eps))) -1 (sqrt (neg eps)) (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (* -1 (/ x eps)) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))) (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))) (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))) (pow eps 2))
5.0ms	x	@	0	((- x (sqrt (+ (* x x) (neg eps)))) x (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* 2 x) 2 (- x (sqrt (- (* x x) eps))) (* -1 (sqrt (neg eps))) -1 (sqrt (neg eps)) (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (* -1 (/ x eps)) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))) (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))) (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))) (pow eps 2))
5.0ms	x	@	inf	((- x (sqrt (+ (* x x) (neg eps)))) x (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* 2 x) 2 (- x (sqrt (- (* x x) eps))) (* -1 (sqrt (neg eps))) -1 (sqrt (neg eps)) (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (* -1 (/ x eps)) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))) (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))) (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))) (pow eps 2))
4.0ms	eps	@	-inf	((- x (sqrt (+ (* x x) (neg eps)))) x (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* 2 x) 2 (- x (sqrt (- (* x x) eps))) (* -1 (sqrt (neg eps))) -1 (sqrt (neg eps)) (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (* -1 (/ x eps)) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))) (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))) (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))) (pow eps 2))
4.0ms	eps	@	inf	((- x (sqrt (+ (* x x) (neg eps)))) x (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* 2 x) 2 (- x (sqrt (- (* x x) eps))) (* -1 (sqrt (neg eps))) -1 (sqrt (neg eps)) (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (- (* -1 (/ x eps)) (sqrt (/ -1 eps))) (* -1 (/ x eps)) (/ x eps) (sqrt (/ -1 eps)) (/ -1 eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))) (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))) (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))) (pow eps 2))

rewrite1.0s (14.8%)

Memory

20.4MiB live, 355.7MiB allocated; 82ms collecting garbage

Counts

32 → 742

Calls

Call 1

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

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

eval166.0ms (2.4%)

Memory: -29.0MiB live, 104.1MiB allocated; 23ms collecting garbage
Compiler: Compiled 11 027 to 4 916 computations (55.4% saved)

prune45.0ms (0.6%)

Memory

26.1MiB live, 26.1MiB allocated; 0ms collecting garbage

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	923	6	929
Fresh	0	3	3
Picked	4	1	5
Done	0	1	1
Total	927	11	938

Accuracy

99.2%

Counts

938 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.2%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	33.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (fma.f64 x (.f64 (/.f64 x (.f64 (*.f64 eps eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))))
▶	56.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	42.4%	#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))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
	56.0%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)) eps))
▶	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
▶	57.8%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fabs.f64 eps))))
	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))))
	57.2%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 244 to 240 computations (1.6% saved)

series281.0ms (4%)

Memory

-17.2MiB live, 141.7MiB allocated; 42ms collecting garbage

Counts

28 → 77

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (* -1 (sqrt (fabs eps))) -1 (sqrt (fabs eps)) (fabs eps) eps (- x (sqrt (- (* x x) eps))) (+ x x) x (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) 1/2 (/ eps x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))))) (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps)))) (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))) (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2) (/ x (* (* eps eps) (sqrt (/ -1 eps)))) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps) (sqrt (/ -1 eps)) (/ -1 eps))
18.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (* -1 (sqrt (fabs eps))) -1 (sqrt (fabs eps)) (fabs eps) eps (- x (sqrt (- (* x x) eps))) (+ x x) x (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) 1/2 (/ eps x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))))) (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps)))) (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))) (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2) (/ x (* (* eps eps) (sqrt (/ -1 eps)))) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps) (sqrt (/ -1 eps)) (/ -1 eps))
11.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (* -1 (sqrt (fabs eps))) -1 (sqrt (fabs eps)) (fabs eps) eps (- x (sqrt (- (* x x) eps))) (+ x x) x (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) 1/2 (/ eps x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))))) (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps)))) (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))) (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2) (/ x (* (* eps eps) (sqrt (/ -1 eps)))) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps) (sqrt (/ -1 eps)) (/ -1 eps))
9.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) (* -1 (sqrt (fabs eps))) -1 (sqrt (fabs eps)) (fabs eps) eps (- x (sqrt (- (* x x) eps))) (+ x x) x (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) 1/2 (/ eps x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))))) (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps)))) (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))) (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2) (/ x (* (* eps eps) (sqrt (/ -1 eps)))) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps) (sqrt (/ -1 eps)) (/ -1 eps))
4.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (* -1 (sqrt (fabs eps))) -1 (sqrt (fabs eps)) (fabs eps) eps (- x (sqrt (- (* x x) eps))) (+ x x) x (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (* 1/2 (/ eps x)) 1/2 (/ eps x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* -1 (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))))) (* eps (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps)))) (+ (* x (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2)) (sqrt (/ -1 eps))) (* (/ x (* (* eps eps) (sqrt (/ -1 eps)))) 1/2) (/ x (* (* eps eps) (sqrt (/ -1 eps)))) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps) (sqrt (/ -1 eps)) (/ -1 eps))

rewrite948.0ms (13.5%)

Memory

-0.8MiB live, 472.9MiB allocated; 136ms collecting garbage

Counts

28 → 464

Calls

Call 1

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

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

eval106.0ms (1.5%)

Memory: 17.4MiB live, 62.5MiB allocated; 12ms collecting garbage
Compiler: Compiled 6 827 to 2 994 computations (56.1% saved)

prune19.0ms (0.3%)

Memory

15.9MiB live, 15.9MiB allocated; 0ms collecting garbage

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	530	2	532
Fresh	0	4	4
Picked	1	4	5
Done	0	2	2
Total	531	12	543

Accuracy

99.2%

Counts

543 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.2%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	33.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (neg.f64 eps))))
✓	56.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	42.4%	#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))
✓	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶	56.0%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)) eps))
▶	44.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))
✓	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
✓	57.8%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fabs.f64 eps))))
▶	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))))
▶	57.2%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 226 to 222 computations (1.8% saved)

series272.0ms (3.9%)

Memory

-23.4MiB live, 131.9MiB allocated; 38ms collecting garbage

Counts

29 → 87

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (* -1 x) x (- x (sqrt (- (* x x) eps))) (* eps (/ 1/2 x)) (/ 1/2 x) 1/2 (- x (sqrt (- (* x x) eps))) (* (+ (sqrt (/ -1 eps)) (/ x eps)) eps) (+ (sqrt (/ -1 eps)) (/ x eps)) (sqrt (/ -1 eps)) (/ -1 eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (neg eps)) (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps)))) (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps))
6.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (* -1 x) x (- x (sqrt (- (* x x) eps))) (* eps (/ 1/2 x)) (/ 1/2 x) 1/2 (- x (sqrt (- (* x x) eps))) (* (+ (sqrt (/ -1 eps)) (/ x eps)) eps) (+ (sqrt (/ -1 eps)) (/ x eps)) (sqrt (/ -1 eps)) (/ -1 eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (neg eps)) (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps)))) (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps))
4.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (* -1 x) x (- x (sqrt (- (* x x) eps))) (* eps (/ 1/2 x)) (/ 1/2 x) 1/2 (- x (sqrt (- (* x x) eps))) (* (+ (sqrt (/ -1 eps)) (/ x eps)) eps) (+ (sqrt (/ -1 eps)) (/ x eps)) (sqrt (/ -1 eps)) (/ -1 eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (neg eps)) (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps)))) (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps))
4.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (* -1 x) x (- x (sqrt (- (* x x) eps))) (* eps (/ 1/2 x)) (/ 1/2 x) 1/2 (- x (sqrt (- (* x x) eps))) (* (+ (sqrt (/ -1 eps)) (/ x eps)) eps) (+ (sqrt (/ -1 eps)) (/ x eps)) (sqrt (/ -1 eps)) (/ -1 eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (neg eps)) (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps)))) (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps))
4.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) eps (- x (sqrt (- (* x x) eps))) (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps))))) -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (* -1 x) x (- x (sqrt (- (* x x) eps))) (* eps (/ 1/2 x)) (/ 1/2 x) 1/2 (- x (sqrt (- (* x x) eps))) (* (+ (sqrt (/ -1 eps)) (/ x eps)) eps) (+ (sqrt (/ -1 eps)) (/ x eps)) (sqrt (/ -1 eps)) (/ -1 eps) (/ x eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (* (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (neg eps)) (+ (* x (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))))) (sqrt (/ -1 eps))) (/ (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps)))) (* x 1/2) (* (* eps eps) (sqrt (/ -1 eps))) (* eps eps))

rewrite1.0s (14.5%)

Memory

-3.0MiB live, 510.9MiB allocated; 95ms collecting garbage

Counts

29 → 591

Calls

Call 1

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

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

eval154.0ms (2.2%)

Memory: 24.2MiB live, 165.9MiB allocated; 34ms collecting garbage
Compiler: Compiled 7 868 to 3 347 computations (57.5% saved)

prune36.0ms (0.5%)

Memory

9.7MiB live, 51.9MiB allocated; 14ms collecting garbage

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	749	2	751
Fresh	0	1	1
Picked	1	4	5
Done	1	5	6
Total	751	12	763

Accuracy

99.2%

Counts

763 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.2%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	33.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 x (/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (neg.f64 eps))))
✓	56.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps))))
	42.4%	#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))
✓	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓	56.0%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (/.f64 x eps)) eps))
✓	44.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))
✓	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
	3.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( (- (neg (/ x eps)) (sqrt (/ -1 eps))) eps) (neg.f64 x))))
✓	57.2%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
	57.8%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps))))

Compiler

Compiled 302 to 237 computations (21.5% saved)

regimes78.0ms (1.1%)

Memory

-50.6MiB live, 40.1MiB allocated; 101ms collecting garbage

Counts

19 → 2

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

Outputs

(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

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

Calls

3 calls:

66.0ms	eps
5.0ms	x
5.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
98.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
87.3%	2	`x`
78.9%	2	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes12.0ms (0.2%)

Memory

-30.1MiB live, 14.1MiB allocated; 8ms collecting garbage

Counts

17 → 2

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
98.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes4.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Counts

12 → 2

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
98.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes4.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Counts

11 → 2

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
95.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 6 to 6 computations (0% saved)

regimes9.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated; 0ms collecting garbage

Counts

9 → 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))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( (- (neg (/ x eps)) (sqrt (/ -1 eps))) eps) (neg.f64 x))))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (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 binary64) #s(approx ( eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))) (*.f64 #s(literal -1 binary64) x))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fabs.f64 eps))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
57.8%	1	`eps`
57.8%	1	`x`
57.8%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes6.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated; 0ms collecting garbage

Counts

4 → 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))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(literal -1 binary64) #s(approx ( (- (neg (/ x eps)) (sqrt (/ -1 eps))) eps) (neg.f64 x))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
57.2%	1	`x`
57.2%	1	`eps`
57.2%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 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))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.6%	1	`x`
3.6%	1	`eps`

Compiler

Compiled 8 to 10 computations (-25% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.7087646702272546e-155	-1.4794682236572676e-157

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.7087646702272546e-155	-1.4794682236572676e-157

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.7087646702272546e-155	-1.4794682236572676e-157

Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.7087646702272546e-155	-1.4794682236572676e-157

Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations2.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 70 to 46 computations (34.3% saved)

preprocess55.0ms (0.8%)

Memory: -24.7MiB live, 67.9MiB allocated; 8ms collecting garbage
Compiler: Compiled 83 to 59 computations (28.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze11.0ms (0.2%)

sample1.0s (14.8%)

preprocess64.0ms (0.9%)

series175.0ms (2.5%)

rewrite1.1s (16%)

eval13.0ms (0.2%)

prune15.0ms (0.2%)

series329.0ms (4.7%)

rewrite1.0s (14.8%)

eval166.0ms (2.4%)

prune45.0ms (0.6%)

series281.0ms (4%)

rewrite948.0ms (13.5%)

eval106.0ms (1.5%)

prune19.0ms (0.3%)

series272.0ms (3.9%)

rewrite1.0s (14.5%)

eval154.0ms (2.2%)

prune36.0ms (0.5%)

regimes78.0ms (1.1%)

regimes12.0ms (0.2%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

derivations2.0ms (0%)

preprocess55.0ms (0.8%)

end0.0ms (0%)

Profiling