Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze14.0ms (0.1%)

Memory

23.8MiB live, 23.8MiB allocated

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)

sample1.5s (16.1%)

Memory

21.9MiB live, 1 353.1MiB allocated

Samples

537.0ms	2 730×	1	valid
461.0ms	4 910×	0	valid
133.0ms	616×	2	valid
10.0ms	172×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 825.0ms

ival-mult: 257.0ms (31.1% of total)

ival-<=: 202.0ms (24.5% of total)

ival-sub: 122.0ms (14.8% of total)

adjust: 116.0ms (14.1% of total)

ival-sqrt: 89.0ms (10.8% of total)

ival-and: 21.0ms (2.5% of total)

exact: 16.0ms (1.9% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain119.0ms (1.3%)

Memory

-20.1MiB live, 146.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
114	-	-	`(-.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	114	0

Confusion

	Predicted +	Predicted -
+	114	0
-	0	142

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	114	0	0
-	0	0	142

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	142
1	114

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms	184×	1	valid
14.0ms	296×	0	valid
7.0ms	32×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sub: 10.0ms (40.1% of total)

ival-mult: 5.0ms (20.1% of total)

ival-sqrt: 5.0ms (20.1% of total)

adjust: 4.0ms (16% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess45.0ms (0.5%)

Memory

-2.9MiB live, 47.4MiB allocated

Algorithm

1×	egg-herbie

Rules

176×	`lower-fma.f64`
176×	`lower-fma.f32`
136×	`sub-neg`
104×	`lower-*.f32`
102×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify10.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Rules

176×	`lower-fma.f64`
176×	`lower-fma.f32`
104×	`lower-*.f32`
102×	`lower-*.f64`
64×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(-.f64 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

localize41.0ms (0.4%)

Memory

7.0MiB live, 45.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.015625	(-.f64 (*.f64 x x) eps)
accuracy	25.300289234331544	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

24.0ms	148×	0	valid
9.0ms	92×	1	valid
2.0ms	16×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sub: 4.0ms (36.8% of total)

ival-mult: 3.0ms (27.6% of total)

ival-sqrt: 3.0ms (27.6% of total)

adjust: 2.0ms (18.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series12.0ms (0.1%)

Memory

-19.2MiB live, 17.1MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ eps x))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt eps) (sqrt -1))) (taylor inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) (taylor inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) (taylor inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* 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))))) (taylor inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt eps) (sqrt -1)) (taylor inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) (taylor inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 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))))) (taylor inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 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)))))) (taylor inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (/ (pow x 2) eps) 1)) (taylor inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (/ (pow x 2) eps) 1)) (taylor inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (- (/ (pow x 2) eps) 1)) (taylor inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (sqrt eps) (sqrt -1)) (taylor -inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) (taylor -inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) (taylor -inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -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))))) (taylor -inf eps) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt eps) (sqrt -1))) (taylor -inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) (taylor -inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -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)))))) (taylor -inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor -inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) (taylor -inf eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt eps) (sqrt -1))) (taylor 0 x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (- x (* (sqrt eps) (sqrt -1))) (taylor 0 x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) (taylor 0 x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (- (* 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))) (taylor 0 x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt eps) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) eps) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) eps) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) eps) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) (taylor inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) (taylor inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 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) (taylor inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) (taylor -inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) (taylor -inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
2.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify153.0ms (1.6%)

Memory

30.1MiB live, 216.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 222×	`lower-fma.f64`
11 222×	`lower-fma.f32`
4 906×	`lower-*.f64`
4 906×	`lower-*.f32`
3 416×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1253
1	784	1238
2	2588	1200
3	6920	1197
0	8069	1129

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* 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))))))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -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)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -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))))))
(* -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)))))))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* 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)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (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)))))))
(+ (* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite168.0ms (1.8%)

Memory

4.0MiB live, 239.8MiB allocated

Rules

4 146×	`lower-fma.f64`
4 146×	`lower-fma.f32`
3 310×	`lower-*.f32`
3 308×	`lower-*.f64`
2 470×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22

Stop Event

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

Counts

4 → 224

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 2 binary64)))) (-.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (-.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
(.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))
(.f64 (neg.f64 (-.f64 (fma.f64 x x eps) (.f64 x x))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))) (fma.f64 x x (-.f64 (.f64 x x) eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))) (fma.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 9/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64))) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
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(neg.f64 (neg.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) eps)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (fma.f64 x x eps) eps) (-.f64 (*.f64 (fma.f64 x x eps) eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64)))) (-.f64 (.f64 x x) eps) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 x x) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (*.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps)
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval45.0ms (0.5%)

Memory: -20.8MiB live, 95.9MiB allocated
Compiler: Compiled 7 073 to 1 088 computations (84.6% saved)

prune16.0ms (0.2%)

Memory

10.1MiB live, 49.0MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	294	12	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	294	13	307

Accuracy

99.6%

Counts

307 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.2%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
	60.2%	(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
▶	60.0%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	55.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	8.3%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
▶	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	60.3%	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
	3.8%	(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64))) #s(literal -1 binary64)))
	24.4%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps x)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
	30.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.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))
▶	38.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 436 to 260 computations (40.4% saved)

simplify123.0ms (1.3%)

Memory

17.0MiB live, 206.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
cost-diff	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))
cost-diff	6080	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))

Rules

8 596×	`lower-fma.f32`
8 592×	`lower-fma.f64`
2 562×	`lower-*.f32`
2 554×	`lower-*.f64`
1 742×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	215
0	51	208
1	86	208
2	162	201
3	367	199
4	717	199
5	2106	199
6	6074	199
0	8290	199

Stop Event

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

Calls

Call 1

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

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

localize96.0ms (1%)

Memory

12.1MiB live, 131.4MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.14726734264898864	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	9.59283227945656	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	11.155143790481509	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	35.12049041099633	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.015625	(-.f64 (*.f64 x x) eps)
accuracy	0.33203125	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
accuracy	25.300289234331544	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.2578125	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	34.17442332287445	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0	(neg.f64 x)
accuracy	25.300289234331544	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.422944035055075	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.1484375	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
accuracy	0.234375	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
accuracy	24.913852199237134	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Samples

36.0ms	92×	1	valid
32.0ms	148×	0	valid
8.0ms	16×	2	valid

Compiler

Compiled 197 to 27 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-add: 11.0ms (20% of total)

ival-pow: 10.0ms (18.2% of total)

ival-mult: 10.0ms (18.2% of total)

adjust: 7.0ms (12.8% of total)

ival-sub: 7.0ms (12.8% of total)

ival-div: 6.0ms (10.9% of total)

ival-sqrt: 3.0ms (5.5% of total)

ival-neg: 1.0ms (1.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series46.0ms (0.5%)

Memory

3.3MiB live, 75.9MiB allocated

Counts

19 → 408

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (-.f64 (fma.f64 x x eps) (.f64 x x)) (patch (-.f64 (fma.f64 x x eps) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (-.f64 (fma.f64 x x eps) (.f64 x x)) (patch (-.f64 (fma.f64 x x eps) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (-.f64 (fma.f64 x x eps) (.f64 x x)) (patch (-.f64 (fma.f64 x x eps) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (-.f64 (fma.f64 x x eps) (.f64 x x)) (patch (-.f64 (fma.f64 x x eps) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ eps x)) (* 2 x)) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) (patch (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) (patch (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) (patch (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) (patch (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (patch #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ eps x))) (taylor 0 eps) (#s(alt #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (patch #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (patch #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) (patch #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ eps x))) (taylor 0 eps) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 eps) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (patch (.f64 (/.f64 #s(literal 1/2 binary64) x) eps) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) (patch (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	0	((* (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (+ (* x x) eps) (* x x))) (- (+ (* x x) eps) (* x x)) (pow (+ (sqrt (- (* x x) eps)) x) -1) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (sqrt (- (* x x) eps)))
7.0ms	x	@	-inf	((* (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (+ (* x x) eps) (* x x))) (- (+ (* x x) eps) (* x x)) (pow (+ (sqrt (- (* x x) eps)) x) -1) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (sqrt (- (* x x) eps)))
6.0ms	x	@	inf	((* (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (+ (* x x) eps) (* x x))) (- (+ (* x x) eps) (* x x)) (pow (+ (sqrt (- (* x x) eps)) x) -1) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (sqrt (- (* x x) eps)))
4.0ms	eps	@	inf	((* (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (+ (* x x) eps) (* x x))) (- (+ (* x x) eps) (* x x)) (pow (+ (sqrt (- (* x x) eps)) x) -1) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (sqrt (- (* x x) eps)))
4.0ms	x	@	0	((* (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (+ (* x x) eps) (* x x))) (- (+ (* x x) eps) (* x x)) (pow (+ (sqrt (- (* x x) eps)) x) -1) (+ (sqrt (- (* x x) eps)) x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (sqrt (- (* x x) eps)))

simplify294.0ms (3.1%)

Memory

-75.6MiB live, 214.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 860×	`lower-fma.f64`
12 860×	`lower-fma.f32`
6 436×	`lower-*.f64`
6 436×	`lower-*.f32`
2 740×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	563	6324
1	1786	6101
2	6212	6005
0	8413	5673

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 378

Calls

Call 1

Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
eps
eps
eps
eps
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* 1/2 (/ eps x))
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(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/ 1/2 x)
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x
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eps
eps
eps
eps
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(* 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))))))
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eps
eps
eps
eps
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(* -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)))))))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* (sqrt eps) (sqrt -1))
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eps
eps
eps
eps
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(- (* 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)))
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(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
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(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* 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)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
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(- (* 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)))
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(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
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(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (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)
eps
eps
eps
eps
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/ (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
eps
eps
eps
eps
(* 2 (/ x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(/ 1/8 (pow x 3))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))

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

rewrite519.0ms (5.5%)

Memory

10.9MiB live, 239.4MiB allocated

Rules

4 662×	`lower-/.f32`
4 656×	`lower-/.f64`
4 140×	`lower-*.f32`
4 132×	`lower-*.f64`
3 726×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	177
0	51	183
1	199	181
2	1582	163
0	8305	163

Stop Event

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

Counts

19 → 883

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (pow.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (pow.f64 (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)) (fma.f64 (neg.f64 x) x (fma.f64 x x eps))))
(.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (neg.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (neg.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
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(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x x)) eps)) (.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps)))
(/.f64 (-.f64 (.f64 (neg.f64 x) x) (neg.f64 eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))) (fma.f64 x x eps))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1/2 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) eps)) (+.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(/.f64 (neg.f64 (fma.f64 x x eps)) (neg.f64 (fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (fma.f64 x x eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 x x) eps) #s(literal 1 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) (.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps)) (-.f64 (.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (sqrt.f64 (-.f64 (.f64 x x) (neg.f64 eps))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) (neg.f64 eps))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (fma.f64 x x eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 x x eps) (fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(fma.f64 (/.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) eps)) (fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))))) (/.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 x x) eps)) (fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -3/2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) eps)) (+.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (/.f64 (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64)) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) eps)) (+.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))
(-.f64 (/.f64 (.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) (/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps) (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 x x eps))) (/.f64 (.f64 eps eps) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(-.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

eval301.0ms (3.2%)

Memory: 44.0MiB live, 617.8MiB allocated
Compiler: Compiled 44 742 to 4 975 computations (88.9% saved)

prune62.0ms (0.7%)

Memory

19.8MiB live, 178.0MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	1 724	11	1 735
Fresh	5	2	7
Picked	2	3	5
Done	0	1	1
Total	1 731	17	1 748

Accuracy

100.0%

Counts

1 748 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.9%	(/.f64 (fma.f64 x x (neg.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
▶	60.2%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
✓	60.0%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
	55.3%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	55.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	8.3%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	99.4%	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))))
	60.3%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
	38.8%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) eps) eps)))
	46.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
▶	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	44.9%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
	24.3%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))))

Compiler

Compiled 395 to 274 computations (30.6% saved)

simplify208.0ms (2.2%)

Memory

-34.8MiB live, 266.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x))
cost-diff	0	(.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
cost-diff	1024	(fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
cost-diff	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(neg.f64 eps)
cost-diff	0	#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff	0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff	0	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
cost-diff	192	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	832	(-.f64 (.f64 x x) (.f64 x x))
cost-diff	6080	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))))

Rules

11 274×	`lower-fma.f32`
11 270×	`lower-fma.f64`
3 602×	`lower-*.f32`
3 590×	`lower-*.f64`
1 510×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	287
0	63	257
1	124	249
2	232	241
3	710	229
4	3357	227
5	6794	227
0	8949	223

Stop Event

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

Calls

Call 1

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

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

localize206.0ms (2.2%)

Memory

-7.9MiB live, 112.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	1.978835136049017	(/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x))
accuracy	8.18391554147115	(fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64)))
accuracy	9.49126977945656	(.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)
accuracy	35.12049041099633	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.015625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.24609375	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	1.0524582255889425	(-.f64 (fma.f64 x x eps) (*.f64 x x))
accuracy	0	(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
accuracy	34.02294078716477	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	1.1037290082241684	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	2.9750902756276107	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.015625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.1328125	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
accuracy	0.1328125	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))))

Samples

155.0ms	152×	0	valid
28.0ms	104×	1	exit

Compiler

Compiled 259 to 32 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-div: 108.0ms (77.8% of total)

ival-mult: 10.0ms (7.2% of total)

adjust: 6.0ms (4.3% of total)

ival-sub: 5.0ms (3.6% of total)

ival-add: 4.0ms (2.9% of total)

ival-pow: 3.0ms (2.2% of total)

ival-sqrt: 2.0ms (1.4% of total)

ival-neg: 1.0ms (0.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series75.0ms (0.8%)

Memory

17.6MiB live, 52.8MiB allocated

Counts

23 → 504

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (patch (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (patch (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) eps) (neg.f64 eps)) (patch #s(approx (- (* x x) eps) (neg.f64 eps)) #<representation binary64>) () ())
#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) (patch (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())
#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps)))) (patch #s(approx (- x (sqrt (- ( x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #<representation binary64>) () ())
#s(alt (/.f64 x (.f64 #s(literal 1/2 binary64) eps)) (patch (/.f64 x (.f64 #s(literal 1/2 binary64) eps)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 x x eps) (.f64 x x)) (patch (-.f64 (fma.f64 x x eps) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x x eps) (patch (fma.f64 x x eps) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (patch (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) (patch #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) (patch (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) (patch (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 eps) (#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (patch (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (patch (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (patch (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (patch (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (patch (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (patch (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ eps x))) (taylor 0 eps) (#s(alt (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (patch (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (patch (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (patch (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt #s(approx (- (* x x) eps) (neg.f64 eps)) (patch #s(approx (- (* x x) eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt #s(approx (- (* x x) eps) (neg.f64 eps)) (patch #s(approx (- (* x x) eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt #s(approx (- (* x x) eps) (neg.f64 eps)) (patch #s(approx (- (* x x) eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt #s(approx (- (* x x) eps) (neg.f64 eps)) (patch #s(approx (- (* x x) eps) (neg.f64 eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* -1 eps) (taylor 0 eps) (#s(alt (neg.f64 eps) (patch (neg.f64 eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) (patch (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) (patch (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) (patch (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) (patch (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 #s(literal 1/2 binary64) eps))) #<representation binary64>) () ())) ())
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#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) (patch #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) (patch (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) (patch (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) (patch (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (/ eps (pow x 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) (patch (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify216.0ms (2.3%)

Memory

19.1MiB live, 247.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 064×	`lower-fma.f64`
13 064×	`lower-fma.f32`
6 632×	`lower-*.f64`
6 632×	`lower-*.f32`
2 806×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	584	6130
1	1861	5831
2	6391	5735
0	8610	5437

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 451

Calls

Call 1

Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
eps
eps
eps
eps
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
eps
eps
eps
eps
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(pow x 2)
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
(* 1/2 x)
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
eps
eps
eps
eps
(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* 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))))))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
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(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
0
0
0
0
eps
eps
eps
eps
(* 2 (/ x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
(* 2 (/ x eps))
eps
eps
eps
eps
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 x)
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/8 (/ eps (pow x 2)))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))

Outputs
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.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)
(* 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))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
eps
eps
eps
eps
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(fma.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 (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.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)
(* 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))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.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)
(* 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))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
eps
eps
eps
eps
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.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)
(* 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))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(pow x 2)
(*.f64 x x)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.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)
(* 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))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal 2 binary64) x (*.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) x)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps))) (pow.f64 eps #s(literal 3 binary64))))
eps
eps
eps
eps
(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))
(/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) eps)
(/.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) eps)
(/.f64 (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) eps)
(/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) x)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps))) (pow.f64 eps #s(literal 3 binary64)))) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 eps) x)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) eps)
(* 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)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* 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)))))
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(* 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))))))
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(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 eps) x)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) eps)
(* 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)))))
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(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
eps
eps
eps
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
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eps
(* eps (+ 1 (/ (pow x 2) eps)))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (/ (pow x 2) eps)))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (/ (pow x 2) eps)))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal 1 binary64)) eps)
(* 1/8 (/ eps x))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) eps)
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (*.f64 x #s(literal 1/2 binary64)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 eps) x)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) eps)
(* 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)))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))) eps)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(fma.f64 (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(fma.f64 (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps x)
(* 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)) (/ x eps)))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) eps) (fma.f64 (fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps x))
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (sqrt.f64 eps)) (/.f64 #s(literal -1/2 binary64) eps) x))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (-.f64 (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 x) x))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64))) x)) (neg.f64 eps)) eps) x)))
eps
eps
eps
eps
(* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (/ (+ (* -1 x) (* (sqrt eps) (sqrt -1))) eps))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x) eps)
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1))) eps))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* 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)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 x #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (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)))))))))
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(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* 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)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
eps
eps
eps
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
eps
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ eps (pow x 2))
(fma.f64 x x eps)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/8 (/ eps x))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) x)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) x)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* 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)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/8 binary64) eps) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/8 binary64) eps) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x eps) x) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 1/8 binary64) eps) eps)) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 x #s(literal 1/2 binary64)) x))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))) #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (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)
(/.f64 (fma.f64 (neg.f64 (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 eps #s(literal 1/2 binary64))))) x)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
eps
eps
eps
eps
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)
(/ (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))) x)
(/ (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))) x)
(/.f64 (fma.f64 (neg.f64 (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)))) x)
(* 1/2 (/ eps x))
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(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (* 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)
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 eps #s(literal 1/2 binary64))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
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(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 eps (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) x)

rewrite272.0ms (2.9%)

Memory

-2.0MiB live, 399.0MiB allocated

Rules

4 584×	`lower-fma.f32`
4 580×	`lower-fma.f64`
4 544×	`lower-/.f32`
4 532×	`lower-/.f64`
4 016×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	232
0	63	202
1	260	186
2	1915	178
0	8517	174

Stop Event

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

Counts

23 → 1 267

Calls

Call 1

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

Outputs
(.f64 (/.f64 (.f64 eps eps) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (.f64 eps eps) (pow.f64 (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 eps eps)) (/.f64 (.f64 eps eps) (pow.f64 eps #s(literal -1 binary64))))
(.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (*.f64 eps eps) (pow.f64 eps #s(literal -2 binary64))))
(.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) eps))
(.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3 binary64)) eps))
(.f64 (/.f64 (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 eps (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 eps eps)))
(.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (pow.f64 eps #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (/.f64 (pow.f64 (fma.f64 eps (.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 eps eps) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 eps eps) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (/.f64 (pow.f64 eps #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (/.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 eps eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 eps (.f64 eps eps)))
(.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (*.f64 eps eps)) #s(literal -1 binary64)) (pow.f64 eps #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 eps (*.f64 x x) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 eps #s(literal -2 binary64)))
(.f64 (/.f64 eps (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 eps (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 eps (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) #s(literal -1 binary64)) (/.f64 eps (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (/.f64 eps (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (.f64 eps (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (pow.f64 eps #s(literal -2 binary64))))
(.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (.f64 eps eps) (.f64 eps eps)))
(.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 eps eps))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1/2 binary64)) eps))
(.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (neg.f64 eps) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) eps)
(.f64 eps (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (.f64 (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 0 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 (neg.f64 x) x)) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 x x eps)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 x x eps)) (-.f64 (.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 (neg.f64 x) x)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 (neg.f64 x) x))) (.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 x x eps)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 (neg.f64 x) x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 eps (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 x x)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 eps (.f64 x x))) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 eps (.f64 x x)))) (.f64 (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (.f64 x x)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 eps (.f64 x x)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 eps (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (-.f64 eps (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))) (.f64 (-.f64 eps (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))) (.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (-.f64 eps (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))))))
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eval366.0ms (3.9%)

Memory: -8.0MiB live, 781.3MiB allocated
Compiler: Compiled 50 927 to 4 600 computations (91% saved)

prune75.0ms (0.8%)

Memory

-22.6MiB live, 237.0MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	1 961	6	1 967
Fresh	6	2	8
Picked	3	2	5
Done	1	3	4
Total	1 971	13	1 984

Accuracy

100.0%

Counts

1 984 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.9%	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
▶	99.6%	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	8.3%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	99.4%	(.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
▶	46.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
✓	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) eps (.f64 #s(literal 1/2 binary64) x)) (/.f64 eps (*.f64 x x))))
▶	45.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 207 to 165 computations (20.3% saved)

simplify95.0ms (1%)

Memory

31.1MiB live, 187.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	448	(.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
cost-diff	576	(/.f64 eps #s(literal -1 binary64))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
cost-diff	0	(*.f64 eps eps)
cost-diff	640	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Rules

3 810×	`lower-*.f32`
3 796×	`lower-*.f64`
2 892×	`lower-fma.f64`
2 892×	`lower-fma.f32`
2 182×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	264
0	50	256
1	84	248
2	163	248
3	238	239
4	898	239
5	4046	239
6	7928	239
0	8193	235

Stop Event

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

Calls

Call 1

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

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

localize107.0ms (1.1%)

Memory

-10.2MiB live, 358.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.015625	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.14453125	(/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	0.234375	(.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
accuracy	0.015625	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.09765625	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
accuracy	33.721182775527424	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
accuracy	2.103835136049017	(/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
accuracy	9.59283227945656	(.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)
accuracy	35.12049041099633	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
accuracy	35.621411604967385	#s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	34.17442332287445	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.015625	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.25	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

33.0ms	154×	0	valid
31.0ms	86×	1	valid
8.0ms	16×	2	valid

Compiler

Compiled 224 to 29 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-div: 18.0ms (36.6% of total)

ival-mult: 15.0ms (30.5% of total)

ival-sub: 5.0ms (10.2% of total)

adjust: 4.0ms (8.1% of total)

ival-sqrt: 4.0ms (8.1% of total)

ival-add: 3.0ms (6.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series50.0ms (0.5%)

Memory

-34.5MiB live, 83.4MiB allocated

Counts

18 → 384

Calls

Call 1

Inputs
#s(alt (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())
#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 1/2 binary64) eps) x) (patch (/.f64 (.f64 #s(literal 1/2 binary64) eps) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) eps) (patch (.f64 #s(literal 1/2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) (patch #s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) (patch (/.f64 #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (patch (/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) #<representation binary64>) () ())
#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps) (patch (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps) #<representation binary64>) () ())
#s(alt (/.f64 eps #s(literal -1 binary64)) (patch (/.f64 eps #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (patch (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* 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)))) (taylor 0 eps) (#s(alt (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 eps (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ eps x)) (* 2 x)) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (patch (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1/2 (/ eps x))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) (taylor 0 eps) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) eps)) (patch (sqrt.f64 (-.f64 (.f64 x x) eps)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 eps) (pow x 2)) (taylor 0 eps) (#s(alt (-.f64 (.f64 x x) eps) (patch (-.f64 (.f64 x x) eps) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (taylor 0 eps) (#s(alt #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (patch #s(approx (- x (sqrt (- ( x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) #<representation binary64>) () ())) ())
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#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (patch (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (patch (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (patch (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4))))))))) (taylor -inf x) (#s(alt (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (patch (.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) #<representation binary64>) () ())) ())
#s(alt (* -2 (/ x eps)) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (patch (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) (patch (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x 1/2) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (/ eps -1) (* (/ eps -1) (/ -1 (+ (sqrt (- (* x x) eps)) x))) (/ -1 (+ (sqrt (- (* x x) eps)) x)) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps))
3.0ms	eps	@	inf	((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x 1/2) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (/ eps -1) (* (/ eps -1) (/ -1 (+ (sqrt (- (* x x) eps)) x))) (/ -1 (+ (sqrt (- (* x x) eps)) x)) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps))
3.0ms	x	@	-inf	((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x 1/2) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (/ eps -1) (* (/ eps -1) (/ -1 (+ (sqrt (- (* x x) eps)) x))) (/ -1 (+ (sqrt (- (* x x) eps)) x)) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps))
2.0ms	eps	@	-inf	((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x 1/2) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (/ eps -1) (* (/ eps -1) (/ -1 (+ (sqrt (- (* x x) eps)) x))) (/ -1 (+ (sqrt (- (* x x) eps)) x)) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps))
2.0ms	x	@	0	((/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x 1/2) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (/ eps -1) (* (/ eps -1) (/ -1 (+ (sqrt (- (* x x) eps)) x))) (/ -1 (+ (sqrt (- (* x x) eps)) x)) (* (/ (+ (* (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (* x x)) eps))

simplify245.0ms (2.6%)

Memory

27.8MiB live, 180.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 122×	`lower-fma.f64`
10 122×	`lower-fma.f32`
6 386×	`lower-*.f64`
6 386×	`lower-*.f32`
3 976×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	654	6157
1	2131	5755
2	7173	5740
0	8079	5458

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 382

Calls

Call 1

Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/2 x)
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 2 (* eps x))
(* eps (+ (* -1/2 (/ eps x)) (* 2 x)))
(* eps (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(* eps (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 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))))
(/ -1/2 x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(- (* eps (- (* eps (- (* -5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* 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)) (/ x eps)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* 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))))))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* 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)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps x))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* (sqrt (pow eps 3)) (sqrt -1))
(* (pow eps 2) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* (pow eps 2) (+ (* -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)) (/ x eps)))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (* 1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3)))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))))) eps)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -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)))))))
(* -1 eps)
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(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* (sqrt eps) (sqrt -1))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* (sqrt eps) (sqrt -1))
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(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps x))
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(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x)))))
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(* -1 (* (sqrt eps) (sqrt -1)))
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(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))))
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(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 (* (sqrt eps) (sqrt -1)))
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(* (sqrt (/ 1 eps)) (sqrt -1))
(* -1 (/ (+ x (* -1 (* (sqrt eps) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) eps))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* 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)))
(* (sqrt eps) (sqrt -1))
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(+ (* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* 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)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* 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)))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(* 1/8 (/ eps x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* (sqrt (pow eps 3)) (sqrt -1))
(+ (* eps x) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* x (+ (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(* (sqrt eps) (/ 1 (sqrt -1)))
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(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
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(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1)))) (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4))))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (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)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 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)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (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)
(* 2 (* eps x))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 2 eps)))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (* 2 eps))))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (* 2 eps)))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (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)
(/ -1/2 x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x)
(/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x)
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -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))))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -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))))))))
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* 1/2 x)
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (* -1/8 (/ (pow eps 3) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4)))))) x))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -2 (/ x eps))
(* -1 (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))

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

rewrite354.0ms (3.7%)

Memory

-4.4MiB live, 147.7MiB allocated

Rules

10 044×	`lower-fma.f64`
10 044×	`lower-fma.f32`
5 914×	`lower-*.f32`
5 900×	`lower-*.f64`
3 190×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	201
0	50	193
1	184	184
2	1267	176
0	9118	172

Stop Event

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

Counts

18 → 749

Calls

Call 1

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

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

eval1.5s (15.6%)

Memory: 6.4MiB live, 322.8MiB allocated
Compiler: Compiled 35 788 to 3 496 computations (90.2% saved)

prune906.0ms (9.6%)

Memory

15.6MiB live, 102.4MiB allocated

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	1 678	7	1 685
Fresh	1	2	3
Picked	2	3	5
Done	1	4	5
Total	1 682	16	1 698

Accuracy

100.0%

Counts

1 698 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.8%	(/.f64 (.f64 eps eps) (.f64 (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x) eps))
✓	99.6%	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	58.2%	(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	47.9%	(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x))
	47.9%	(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) (*.f64 #s(literal 2 binary64) x))))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
✓	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	8.3%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	99.4%	(.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 eps))
✓	46.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
	46.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
✓	45.6%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 #s(approx (+ ( (* (/ eps x) (/ 1/8 x)) x) (* x 1/2)) (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 673 to 274 computations (59.3% saved)

regimes210.0ms (2.2%)

Memory

7.3MiB live, 126.4MiB allocated

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

112.0ms	eps
78.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
18.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes104.0ms (1.1%)

Memory

-13.0MiB live, 145.9MiB allocated

Counts

13 → 2

Calls

Call 1

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

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

Calls

3 calls:

64.0ms	eps
24.0ms	x
15.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
88.8%	2	`x`
81.5%	2	`eps`
98.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes15.0ms (0.2%)

Memory

3.7MiB live, 43.2MiB allocated

Counts

12 → 2

Calls

Call 1

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

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

Calls

1 calls:

14.0ms

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

Results

Accuracy	Segments	Branch
97.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes42.0ms (0.4%)

Memory

-12.6MiB live, 27.2MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

42.0ms

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

Results

Accuracy	Segments	Branch
95.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes7.0ms (0.1%)

Memory

22.2MiB live, 22.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

6.0ms

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

Results

Accuracy	Segments	Branch
95.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes35.0ms (0.4%)

Memory

0.9MiB live, 40.5MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

28.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
55.0%	1	`eps`
55.0%	1	`x`
55.0%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes19.0ms (0.2%)

Memory

-35.2MiB live, 25.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

13.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	x
3.0ms	eps

Results

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

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.04676746532045e-154	-5.826828696250162e-157

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.04676746532045e-154	-5.826828696250162e-157

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.04676746532045e-154	-5.826828696250162e-157

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.04676746532045e-154	-5.826828696250162e-157

Compiler

Compiled 11 to 11 computations (0% saved)

simplify34.0ms (0.4%)

Memory

-12.9MiB live, 66.6MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`+-commutative-binary64-+.f64`
18×	`sub-neg-binary64-neg.f64-+.f64--.f64`
14×	`-commutative-binary64-.f64`
10×	`neg-sub0-binary64--.f64-neg.f64`
10×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	173
1	55	173
2	69	173
3	77	173
4	80	173

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness677.0ms (7.2%)

Memory

12.8MiB live, 845.7MiB allocated

Rules

11 222×	`lower-fma.f64`
11 222×	`lower-fma.f32`
10 122×	`lower-fma.f64`
10 122×	`lower-fma.f32`
6 386×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	37	232
0	63	202
1	260	186
2	1915	178
0	8517	174
0	654	6157
1	2131	5755
2	7173	5740
0	8079	5458
0	31	177
0	51	183
1	199	181
2	1582	163
0	8305	163
0	257	1253
1	784	1238
2	2588	1200
3	6920	1197
0	8069	1129

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 332 to 151 computations (54.5% saved)

preprocess69.0ms (0.7%)

Memory: 22.8MiB live, 101.5MiB allocated
Compiler: Compiled 280 to 94 computations (66.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24

start0.0ms (0%)

analyze14.0ms (0.1%)

sample1.5s (16.1%)

explain119.0ms (1.3%)

preprocess45.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify10.0ms (0.1%)

localize41.0ms (0.4%)

series12.0ms (0.1%)

simplify153.0ms (1.6%)

rewrite168.0ms (1.8%)

eval45.0ms (0.5%)

prune16.0ms (0.2%)

simplify123.0ms (1.3%)

localize96.0ms (1%)

series46.0ms (0.5%)

simplify294.0ms (3.1%)

rewrite519.0ms (5.5%)

eval301.0ms (3.2%)

prune62.0ms (0.7%)

simplify208.0ms (2.2%)

localize206.0ms (2.2%)

series75.0ms (0.8%)

simplify216.0ms (2.3%)

rewrite272.0ms (2.9%)

eval366.0ms (3.9%)

prune75.0ms (0.8%)

simplify95.0ms (1%)

localize107.0ms (1.1%)

series50.0ms (0.5%)

simplify245.0ms (2.6%)

rewrite354.0ms (3.7%)

eval1.5s (15.6%)

prune906.0ms (9.6%)

regimes210.0ms (2.2%)

regimes104.0ms (1.1%)

regimes15.0ms (0.2%)

regimes42.0ms (0.4%)

regimes7.0ms (0.1%)

regimes35.0ms (0.4%)

regimes19.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify34.0ms (0.4%)

soundness677.0ms (7.2%)

preprocess69.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24