Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

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

analyze28.0ms (1.4%)

Memory

-33.6MiB live, 22.5MiB allocated; 19ms 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)

sample1.3s (62.2%)

Memory

92.2MiB live, 1 502.3MiB allocated; 388ms collecting garbage

Samples

389.0ms	4 838×	0	valid
373.0ms	2 696×	1	valid
181.0ms	722×	2	valid
7.0ms	163×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 580.0ms

adjust: 199.0ms (34.3% of total)

ival-sqrt: 190.0ms (32.7% of total)

ival-mult!: 132.0ms (22.7% of total)

ival-sub!: 59.0ms (10.2% of total)

Bogosity

explain88.0ms (4.4%)

Memory

-11.9MiB live, 133.3MiB allocated; 15ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
103	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`eps`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	103	0

Confusion

	Predicted +	Predicted -
+	103	0
-	0	153

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	103	0	0
-	0	0	153

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	153
1	103

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

14.0ms	148×	1	valid
13.0ms	306×	0	valid
7.0ms	58×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sqrt: 6.0ms (33.1% of total)

adjust: 5.0ms (27.6% of total)

ival-sub!: 4.0ms (22.1% of total)

ival-mult!: 4.0ms (22.1% of total)

preprocess7.0ms (0.3%)

Memory

11.6MiB live, 11.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	35	54
2	64	54
3	91	54
4	115	54

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.6%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 16 to 12 computations (25% saved)

series10.0ms (0.5%)

Memory

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

Counts

6 → 54

Calls

Call 1

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

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Calls

6 calls:

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

rewrite82.0ms (4.1%)

Memory

0.1MiB live, 92.8MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	319	1558
0	325	1431
0	1747	1380

Stop Event

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

Counts

60 → 70

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Outputs
(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 eps eps (.f64 (*.f64 x x) eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
eps
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))))) x #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx x x)
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (*.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -3 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))))) (.f64 x x))) (.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (* x x) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (.f64 #s(literal -1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x))))) x))
#s(approx (sqrt (- (* x x) eps)) x)
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) x))
#s(approx (- (* x x) eps) (*.f64 x x))
#s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64))) eps (*.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3 binary64)))) eps) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
#s(approx eps eps)
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) #s(literal 1/8 binary64) (/.f64 x eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))) eps))
#s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) eps) #s(literal -1 binary64) x) eps)) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* x x) eps) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))))

eval7.0ms (0.4%)

Memory: 10.1MiB live, 10.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 622 to 374 computations (76.9% saved)

prune18.0ms (0.9%)

Memory

-38.0MiB live, 8.3MiB allocated; 3ms collecting garbage

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	56	10	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	10	67

Accuracy

99.7%

Counts

67 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.5%	(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	62.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
	59.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	6.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
	3.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
▶	40.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
	38.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	43.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
▶	59.6%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 316 to 202 computations (36.1% saved)

series19.0ms (1%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Counts

24 → 84

Calls

Call 1

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

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* (/ eps x) 1/2) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (/ (* eps eps) (* x x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))

Calls

6 calls:

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

rewrite88.0ms (4.4%)

Memory

1.2MiB live, 89.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	400	2247
0	420	2088
0	2049	2032

Stop Event

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

Counts

108 → 163

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
#s(approx (sqrt (- (* x x) eps)) x)
#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))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 eps x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (.f64 eps eps) (.f64 x x))
(*.f64 eps eps)
(*.f64 x x)
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 eps)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* (/ eps x) 1/2) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (/ (* eps eps) (* x x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (pow x 2)))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* 1/2 eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ (* x x) (neg eps)) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))

Outputs
(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (fma.f64 x x (neg.f64 eps))))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (neg.f64 eps) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (.f64 x x) (neg.f64 eps)))
(/.f64 (+.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) (neg.f64 eps)))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x x (neg.f64 eps))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(neg.f64 eps)
eps
(/.f64 (-.f64 (.f64 x x) (.f64 #s(approx (sqrt (- (* x x) eps)) x) #s(approx (sqrt (- (* x x) eps)) x))) (+.f64 x #s(approx (sqrt (- (* x x) eps)) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) x) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) x) #s(approx (sqrt (- (* x x) eps)) x) (.f64 x #s(approx (sqrt (- ( x x) eps)) x)))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
#s(approx (sqrt (- (* x x) eps)) x)
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (neg.f64 eps)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps)))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(pow.f64 (neg.f64 eps) #s(literal 1/2 binary64))
(sqrt.f64 (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps)) x)
(-.f64 (/.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) x) (.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(+.f64 (/.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) x) (.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x))) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps))) (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x))) (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps))) (-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) eps) (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) eps)) (.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal 1/2 binary64) eps (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)))
(fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (.f64 #s(literal -1/2 binary64) eps))
(+.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)) (.f64 #s(literal 1/2 binary64) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x)))
(*.f64 (/.f64 eps x) (/.f64 eps x))
(.f64 eps (/.f64 eps (.f64 x x)))
(/.f64 (/.f64 (*.f64 eps eps) x) x)
(/.f64 (neg.f64 (.f64 eps eps)) (neg.f64 (.f64 x x)))
(/.f64 (.f64 eps eps) (.f64 x x))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))))) x #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx x x)
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))))) (*.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -3 binary64)))) (.f64 x x))) (.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (+ (* x x) (neg eps)) (neg.f64 eps))
#s(approx (+ (* x x) (neg eps)) (-.f64 (*.f64 x x) eps))
#s(approx (* (/ eps x) 1/2) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (/ eps x) (/.f64 eps x))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (*.f64 x x)))
#s(approx (/ (* eps eps) (* x x)) (*.f64 (/.f64 eps x) (/.f64 eps x)))
#s(approx (* x x) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (*.f64 #s(literal -1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x))))) x))
#s(approx (sqrt (- (* x x) eps)) x)
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) x))
#s(approx (- (* x x) eps) (*.f64 x x))
#s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (+ (* x x) (neg eps)) (*.f64 x x))
#s(approx (+ (* x x) (neg eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal -1/2 binary64) eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64))) eps (*.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3 binary64)))) eps) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
#s(approx (+ (* x x) (neg eps)) (fma.f64 x x (neg.f64 eps)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx eps eps)
#s(approx (neg (sqrt (neg eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (neg eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* 1/2 eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) #s(literal 1/8 binary64) (/.f64 x eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))) eps))
#s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (+ (* x x) (neg eps)) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) (*.f64 eps eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 eps eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) eps) #s(literal -1 binary64) x) eps)) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))))
#s(approx (- (* x x) eps) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))))
#s(approx (+ (* x x) (neg eps)) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))))
#s(approx (neg (sqrt (neg eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (neg eps)) (neg.f64 (sqrt.f64 (neg.f64 eps))))

eval133.0ms (6.6%)

Memory: -28.4MiB live, 37.9MiB allocated; 139ms collecting garbage
Compiler: Compiled 3 949 to 736 computations (81.4% saved)

prune5.0ms (0.3%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	2	3	5
Picked	1	4	5
Done	0	0	0
Total	151	8	159

Accuracy

99.9%

Counts

159 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
▶	59.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	6.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
▶	40.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
✓	43.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓	59.6%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 123 to 84 computations (31.7% saved)

series26.0ms (1.3%)

Memory

-11.1MiB live, 38.2MiB allocated; 12ms collecting garbage

Counts

23 → 91

Calls

Call 1

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

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ eps (* x x)) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1/2 (/ eps x))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (/ (+ (* -1/2 eps) (pow x 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 x))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* eps (- (/ x eps) (* 1/2 (/ 1 x))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) eps (* x x) x 1/8 1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps))
5.0ms	x	@	-inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) eps (* x x) x 1/8 1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps))
3.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) eps (* x x) x 1/8 1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps))
2.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) eps (* x x) x 1/8 1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps))
2.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ eps (* x x)) eps (* x x) x 1/8 1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) -1/2 (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps))

rewrite86.0ms (4.3%)

Memory

4.3MiB live, 94.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	426	2510
0	442	2346
0	2204	2264

Stop Event

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

Counts

114 → 157

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 eps (*.f64 x x))
eps
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
#s(literal -1/2 binary64)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* 1/8 (/ eps (pow x 2)))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))))
#s(approx (/ eps (* x x)) #s(hole binary64 (/ eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1/2 (/ eps x))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (/ (+ (* -1/2 eps) (pow x 2)) x)))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* 1/2 eps)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ eps (pow x 2))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 x))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (pow x 2)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (+ x (* -1/2 (/ eps x)))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* eps (- (/ x eps) (* 1/2 (/ 1 x))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* (sqrt eps) (sqrt -1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(hole binary64 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* (sqrt eps) (sqrt -1)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))))
#s(approx (+ (* (/ eps x) -1/2) x) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))

Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 (neg.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))) (neg.f64 x))
(/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(.f64 eps (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64)) eps))
(fma.f64 #s(literal 1/2 binary64) eps (.f64 eps (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64)) eps))
(fma.f64 eps #s(literal 1/2 binary64) (.f64 eps (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) eps))
(+.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 eps (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64))) #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64))))))
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x))))
(+.f64 (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)))
(/.f64 (/.f64 eps x) x)
(/.f64 (neg.f64 eps) (neg.f64 (*.f64 x x)))
(/.f64 eps (*.f64 x x))
eps
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(/.f64 (-.f64 (.f64 x x) (.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (.f64 x #s(approx (sqrt (- ( x x) eps)) (neg.f64 x))))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
(/.f64 (-.f64 (.f64 x x) (.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) (.f64 x #s(approx (sqrt (- ( x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (.f64 (/.f64 eps x) #s(literal -1/2 binary64)))) (-.f64 x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (.f64 (/.f64 eps x) #s(literal -1/2 binary64))) (.f64 x x)) (-.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (.f64 (/.f64 eps x) #s(literal -1/2 binary64))) (.f64 x (.f64 (/.f64 eps x) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) (-.f64 (.f64 x x) (.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x))))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(-.f64 x (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) x)
(+.f64 x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
#s(literal -1/2 binary64)
(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(neg.f64 eps)
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))))) x #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (*.f64 x x)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (*.f64 x x)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) eps)) (*.f64 x x)))
#s(approx (/ eps (* x x)) (/.f64 eps (*.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))))) (*.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (.f64 x x) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -3 binary64)))) (.f64 x x))) (.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (neg x) (neg.f64 x))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (/ eps x) -1/2) x) (/.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 x x)) x))
#s(approx (/ eps x) (/.f64 eps x))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (*.f64 #s(literal -1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (*.f64 x x))))) x))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (*.f64 #s(literal 1/2 binary64) eps))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) eps)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
#s(approx (sqrt (- (* x x) eps)) x)
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) x))
#s(approx (+ (* (/ eps x) -1/2) x) x)
#s(approx (+ (* (/ eps x) -1/2) x) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (- (* x x) eps) (*.f64 x x))
#s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(literal 2 binary64) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 #s(literal -1/2 binary64) eps)) x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))))
#s(approx (+ (* (/ eps x) -1/2) x) (.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64))) eps (*.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
#s(approx eps eps)
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3 binary64)))) eps) (/.f64 #s(literal 1/2 binary64) x)) eps x))
#s(approx (+ (* (/ eps x) -1/2) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
#s(approx (neg eps) (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 x eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (-.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) #s(literal 1/8 binary64) (/.f64 x eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (.f64 (fma.f64 (pow.f64 x #s(literal -3 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps x))) (*.f64 eps eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 eps eps)))
#s(approx (* (+ (* (/ eps (* x x)) 1/8) 1/2) eps) (.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) eps)) (.f64 eps eps)))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))) eps))
#s(approx (sqrt (- (* x x) eps)) (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))) eps))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 eps))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) eps) #s(literal -1 binary64) x) eps)) (sqrt.f64 (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) (*.f64 (fma.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) eps)) eps))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64)))))))
#s(approx (sqrt (- (* x x) eps)) (.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 eps #s(literal -5 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 eps #s(literal -7 binary64)))) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal -3 binary64)))) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))))))))
#s(approx (+ (* (/ eps x) -1/2) x) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (- (* x x) eps) (.f64 (neg.f64 eps) (fma.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))))

eval25.0ms (1.2%)

Memory: -7.7MiB live, 41.0MiB allocated; 16ms collecting garbage
Compiler: Compiled 4 399 to 751 computations (82.9% saved)

prune6.0ms (0.3%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	4	4
Done	0	4	4
Total	136	8	144

Accuracy

99.9%

Counts

144 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	62.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓	59.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	6.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	4.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) x))
✓	40.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
✓	43.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓	59.6%	#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 324 to 149 computations (54% saved)

regimes12.0ms (0.6%)

Memory

26.2MiB live, 26.2MiB allocated; 0ms collecting garbage

Counts

12 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
89.8%	2	`x`
82.2%	2	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes5.0ms (0.3%)

Memory

-36.8MiB live, 8.6MiB allocated; 4ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
99.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
97.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes6.0ms (0.3%)

Memory

14.9MiB live, 14.9MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
59.6%	1	`eps`
59.6%	1	`x`
59.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.2%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
4.3%	1	`eps`
4.3%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.398850128096647e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.398850128096647e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-8.398850128096647e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

derivations31.0ms (1.6%)

Memory

-32.9MiB live, 55.3MiB allocated; 11ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 158 to 46 computations (70.9% saved)

preprocess73.0ms (3.6%)

Memory: 3.7MiB live, 58.9MiB allocated; 16ms collecting garbage
Compiler: Compiled 352 to 118 computations (66.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze28.0ms (1.4%)

sample1.3s (62.2%)

explain88.0ms (4.4%)

preprocess7.0ms (0.3%)

series10.0ms (0.5%)

rewrite82.0ms (4.1%)

eval7.0ms (0.4%)

prune18.0ms (0.9%)

series19.0ms (1%)

rewrite88.0ms (4.4%)

eval133.0ms (6.6%)

prune5.0ms (0.3%)

series26.0ms (1.3%)

rewrite86.0ms (4.3%)

eval25.0ms (1.2%)

prune6.0ms (0.3%)

regimes12.0ms (0.6%)

regimes5.0ms (0.3%)

regimes3.0ms (0.1%)

regimes6.0ms (0.3%)

regimes4.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

derivations31.0ms (1.6%)

preprocess73.0ms (3.6%)

end0.0ms (0%)

Profiling