Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze18.0ms (0.1%)

Memory

-16.4MiB live, 29.4MiB 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)

sample1.4s (11%)

Memory

24.8MiB live, 1 781.5MiB allocated

Samples

461.0ms	4 942×	0	valid
374.0ms	2 730×	1	valid
97.0ms	584×	2	valid
54.0ms	175×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 585.0ms

ival-sub: 146.0ms (25% of total)

ival-<=: 134.0ms (22.9% of total)

ival-sqrt: 95.0ms (16.2% of total)

ival-mult: 94.0ms (16.1% of total)

adjust: 78.0ms (13.3% of total)

ival-and: 21.0ms (3.6% of total)

exact: 15.0ms (2.6% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain108.0ms (0.8%)

Memory

-11.5MiB live, 147.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
112	-	1	(5.985320594452893e-76 1.4001022789219088e-152)	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	0	-	`eps`
0	-	0	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	0	-	`(-.f64 (*.f64 x x) eps)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	111	1

Confusion

	Predicted +	Predicted -
+	111	1
-	0	144

Precision

1.0

Recall

0.9910714285714286

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	1	0
-	0	0	144

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	145
1	111

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms	164×	1	valid
15.0ms	302×	0	valid
6.0ms	46×	2	valid

Compiler

Compiled 62 to 22 computations (64.5% saved)

Precisions

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

ival-sub: 10.0ms (40.6% of total)

ival-sqrt: 5.0ms (20.3% of total)

ival-mult: 5.0ms (20.3% of total)

adjust: 4.0ms (16.2% of total)

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

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

preprocess33.0ms (0.3%)

Memory

18.0MiB live, 55.5MiB 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 10 to 6 computations (40% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify16.0ms (0.1%)

Memory

-23.6MiB live, 12.5MiB 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

localize311.0ms (2.4%)

Memory

16.1MiB live, 53.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.529735361125557	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

293.0ms	151×	0	valid
8.0ms	82×	1	valid
3.0ms	23×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 296.0ms

ival-mult: 288.0ms (97.2% of total)

ival-sqrt: 3.0ms (1% of total)

ival-sub: 3.0ms (1% of total)

adjust: 2.0ms (0.7% of total)

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

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

series9.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB 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 (* (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 (* 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 (* 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 (* 1/2 (/ 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 (* -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 (-.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 (* (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 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 (* -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 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 (* (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 (* (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 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 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 (.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 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 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 (* -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 (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 (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 (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

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	0	(- x (sqrt (- (* x x) eps)))
1.0ms	x	@	0	(- x (sqrt (- (* x x) eps)))
0.0ms	eps	@	-inf	(- x (sqrt (- (* x x) eps)))

simplify316.0ms (2.5%)

Memory

1.1MiB live, 442.7MiB 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	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

Inputs
(* -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))
(/ (- (* 1/8 (/ (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)
(* 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))
(* 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 (* (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))
(* -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)))))
(* (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)))))))))
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 (* -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))))))))
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)))))
(* (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 (* (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)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) 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) (+ 1 (* -1 (/ eps (pow x 2)))))
(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)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -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 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite286.0ms (2.2%)

Memory

-37.4MiB live, 333.9MiB 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 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) #s(literal -1 binary64)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 x (/.f64 (.f64 x x) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))))
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))))
(fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64) x)
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
(fma.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (fma.f64 (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)) (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 (.f64 x x) eps) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))) (-.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))))))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))))) (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x eps)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x eps))) (.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps)) (/.f64 (.f64 eps eps) (fma.f64 x x eps)))) (fma.f64 x (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps)))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (*.f64 eps eps))))
(/.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 eps eps) (fma.f64 eps eps (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (.f64 (fma.f64 eps eps (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 eps eps (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (exp.f64 (log.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (exp.f64 (log.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (exp.f64 (log.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (log.f64 (fma.f64 x x eps))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x x eps)))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 4 binary64))
(pow.f64 (.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log.f64 (-.f64 (.f64 x x) eps))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 x x) eps))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (-.f64 (.f64 x x) eps) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)))
(.f64 (fma.f64 x x eps) (.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))))
(.f64 (fma.f64 x x eps) (/.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps)))
(.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) eps))
(.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (neg.f64 (.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) (.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))
(.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (.f64 x x) eps)))
(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (fma.f64 eps (-.f64 eps (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps)) (.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x eps))) (-.f64 (.f64 x x) eps))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (fma.f64 x x eps)) (.f64 eps (.f64 (fma.f64 x x eps) (.f64 eps (fma.f64 x x eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))) (fma.f64 (.f64 eps (fma.f64 x x eps)) (-.f64 (.f64 eps (fma.f64 x x eps)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (fma.f64 x x eps))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 eps (fma.f64 x x eps))))
(.f64 (exp.f64 (log.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 eps (fma.f64 x x eps) (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (exp.f64 (log.f64 (.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x eps)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)

eval43.0ms (0.3%)

Memory: 13.6MiB live, 97.1MiB allocated
Compiler: Compiled 9 677 to 1 047 computations (89.2% saved)

prune61.0ms (0.5%)

Memory

5.0MiB live, 160.7MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	291	15	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	291	16	307

Accuracy

99.3%

Counts

307 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.9%	(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
▶	60.7%	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
	61.2%	(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	61.4%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	61.3%	(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	47.0%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
	61.2%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	61.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	56.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	7.9%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
▶	3.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	43.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x))
	32.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x))
	45.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
	19.9%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))
	27.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))

Compiler

Compiled 776 to 306 computations (60.6% saved)

simplify357.0ms (2.8%)

Memory

-46.3MiB live, 271.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	0	(*.f64 x x)
cost-diff	128	(neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
cost-diff	3264	(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff	2752	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
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 x x)
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
cost-diff	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Rules

15 160×	`lower-fma.f32`
15 152×	`lower-fma.f64`
3 176×	`lower-*.f32`
3 174×	`lower-*.f64`
1 870×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	257
0	51	273
1	98	264
2	172	228
3	392	214
4	747	214
5	1627	214
6	3756	214
7	5243	214
8	6345	214
9	6751	214
10	7099	214
11	7380	214
12	7813	214
0	8084	214

Stop Event

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

Calls

Call 1

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

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

localize118.0ms (0.9%)

Memory

18.7MiB live, 210.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.35546875	(/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	24.74688144053668	(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.08203125	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	25.184928796127494	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
accuracy	0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	0.13671875	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
accuracy	24.529735361125557	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
accuracy	34.363914278557246	#s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
accuracy	0	(neg.f64 x)
accuracy	24.529735361125557	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.40530788160989	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.3203125	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	24.094536796493998	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Samples

39.0ms	151×	0	valid
29.0ms	82×	1	valid
12.0ms	23×	2	valid

Compiler

Compiled 245 to 27 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-div: 15.0ms (29% of total)

ival-add: 8.0ms (15.5% of total)

ival-mult: 8.0ms (15.5% of total)

adjust: 6.0ms (11.6% of total)

ival-sub: 5.0ms (9.7% of total)

ival-sqrt: 5.0ms (9.7% of total)

ival-neg: 4.0ms (7.7% of total)

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

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

exact: 0.0ms (0% of total)

series100.0ms (0.8%)

Memory

-28.9MiB live, 91.8MiB allocated

Counts

20 → 444

Calls

Call 1

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

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

Calls

111 calls:

Time	Variable		Point	Expression
18.0ms	x	@	-inf	(/ 1 (+ x (sqrt (- (* x x) eps))))
15.0ms	eps	@	-inf	(/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps))))
3.0ms	x	@	inf	(sqrt (sqrt (- (* x x) eps)))
2.0ms	x	@	0	(sqrt (sqrt (- (* x x) eps)))
2.0ms	eps	@	-inf	(+ x (sqrt (- (* x x) eps)))

simplify349.0ms (2.7%)

Memory

45.8MiB live, 552.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 530×	`lower-fma.f64`
11 530×	`lower-fma.f32`
6 734×	`lower-+.f64`
6 734×	`lower-+.f32`
5 770×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1073	8665
1	3472	7995
0	8531	7580

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 408

Calls

Call 1

Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* 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))))
(+ (* 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))))
(* 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)
(* -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))
(* 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))))
(* (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 eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -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)))
(+ (* -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
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
(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) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
eps
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
eps
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -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))
(/ (- (* 1/8 (/ (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)
(* 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))
(* 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 (* (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))
(* -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)))))
(* (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)))))))))
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 (* -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))))))))
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)))))
(* (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 (* (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 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 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)))
(* 1/2 (/ 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)
(* 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))
(* 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 (* (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))
(* -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)))))
(* (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)))))))))
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 (* -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))))))))
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)))))
(* (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 (* (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)))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* (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)))))))))
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 (* -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))))))))
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)))))
(* (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 (* (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)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) 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) (+ 1 (* -1 (/ eps (pow x 2)))))
(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)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -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 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* 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))))
(+ (* 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))))
(* 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)
(* -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))
(* 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))))
(* (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 eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt 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 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (/ 1 (* eps (pow (sqrt -1) 2)))) (* -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)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* -1/2 x)
(* x (- (+ (* -1/8 (/ eps (pow x 2))) (* 1/2 (/ eps (pow x 2)))) 1/2))
(* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (+ 1/2 (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (- (+ (* -1/8 (/ eps (pow x 2))) (+ (* -1/16 (/ (pow eps 2) (pow x 4))) (+ (* -1/32 (/ (pow eps 3) (pow x 6))) (+ (* -1/128 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ eps (pow x 2))))))) (+ 1/2 (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (+ (* -1/2 (/ eps (pow x 4))) (* 5/2 (/ 1 (pow x 2)))))))
(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))))))))
(* -1/2 x)
(- (* 3/8 (/ eps x)) (* 1/2 x))
(- (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))) (* 1/2 x))
(- (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))) (* 1/2 x))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ (+ (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))) eps)) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* 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 x 3) (* eps (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ x (pow (sqrt -1) 2))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (- (* -1 (* eps x)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* 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))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (- (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* eps (pow x 3))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt 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 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (pow eps 2) (pow x 3))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))) eps))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt eps) (sqrt -1)))
(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* 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))))
(+ (* 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))))
(/ 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 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 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)))
(* (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 (/ 1 eps)) (sqrt -1)))
(* -1 (/ (+ (* -1 x) (* (sqrt eps) (sqrt -1))) 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))
(* -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))
(* (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)))
(* 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 (/ (+ (* -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)
(+ (* -1/2 (/ 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)))))
(* (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)))))
(* -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) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(* 1/2 x)
(* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* -3/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -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 eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(* (sqrt eps) (sqrt -1))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (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 eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))

Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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))) (/.f64 x #s(literal 1 binary64)))
(+ (* 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 x (fma.f64 x (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.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 x (fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) 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)
(/.f64 (-.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #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 x) (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64))))
(* -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 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) eps) (fma.f64 #s(literal -1/4 binary64) (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/8 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (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)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.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))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -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)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps))) (/.f64 x #s(literal 1 binary64)))
(- (+ (* -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))) (/.f64 (fma.f64 (/.f64 (.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 eps)) (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (.f64 x x) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 x #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (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)))
(-.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x)) eps) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -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 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 eps (.f64 x (.f64 x x))) (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)))))) (neg.f64 eps)) (.f64 eps x)) eps)))
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) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(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)
eps
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 eps (/.f64 (*.f64 x x) eps) eps)
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 eps (/.f64 (*.f64 x x) eps) eps)
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 eps (/.f64 (*.f64 x x) eps) eps)
eps
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(.f64 (+.f64 (neg.f64 (/.f64 (.f64 x x) eps)) #s(literal -1 binary64)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(.f64 (+.f64 (neg.f64 (/.f64 (.f64 x x) eps)) #s(literal -1 binary64)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(.f64 (+.f64 (neg.f64 (/.f64 (.f64 x x) eps)) #s(literal -1 binary64)) (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)
(pow x 2)
(*.f64 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 x (fma.f64 x (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) 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)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (neg.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64)) (neg.f64 x))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64))))
(* -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 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (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)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 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 (* (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 eps (-.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) x) 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)))))
(neg.f64 (.f64 eps (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)))) eps)) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 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 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 (fma.f64 (/.f64 eps (.f64 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)))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (*.f64 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 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 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 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (neg.f64 eps))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -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 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) 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)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (neg.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
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(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64)) (neg.f64 x))
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(* -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))))))))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* 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))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* 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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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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(+ (* (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 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
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(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* -1 x)
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(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
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(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
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(* -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))))))))
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x
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 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)))) (+ (* 1/2 (* (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)))
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(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -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))))))
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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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(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
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(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
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(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x)))
(* -1/2 (/ eps x))
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(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
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(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
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(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
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(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
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(/ (+ (* -1/2 eps) (pow x 2)) x)
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(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
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(/ -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 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(fma.f64 x (fma.f64 x (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 eps (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64)) (neg.f64 x))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x)) #s(literal -2 binary64)))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x)) #s(literal -2 binary64))))))
(+ x (* -1 x))
#s(literal 0 binary64)
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 0 binary64))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(fma.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 0 binary64))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(.f64 eps (-.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) x) eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
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(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64))) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (.f64 #s(literal -3/32 binary64) (.f64 (.f64 x x) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64))))) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
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(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 x))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
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(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
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(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(fma.f64 #s(literal -1/4 binary64) (.f64 eps (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(fma.f64 #s(literal -1/4 binary64) (.f64 eps (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 eps eps) #s(literal -3/32 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(fma.f64 #s(literal -1/4 binary64) (.f64 eps (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 eps eps) #s(literal -3/32 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -7/128 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))))
(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 eps (fma.f64 #s(literal -3/32 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -7/128 binary64) (.f64 eps (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))))) (.f64 #s(literal -3/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (sqrt.f64 x))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 x x) (exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps))))) eps) (exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps)))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
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(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 x x) (exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps))))) eps) (fma.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps)))) (+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (.f64 eps eps)) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (.f64 eps (.f64 eps eps)))) (exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 eps))))))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64))) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))) (.f64 x x)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)))) eps))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))) (.f64 x x)) (/.f64 (-.f64 (.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64))) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64)))) eps)) eps))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 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 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 (fma.f64 (/.f64 eps (.f64 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)))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (*.f64 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 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 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 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(fma.f64 eps (/.f64 (*.f64 x x) eps) (neg.f64 eps))
(* eps (- (/ (pow x 2) eps) 1))
(fma.f64 eps (/.f64 (*.f64 x x) eps) (neg.f64 eps))
(* eps (- (/ (pow x 2) eps) 1))
(fma.f64 eps (/.f64 (*.f64 x x) eps) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (fma.f64 eps (neg.f64 (/.f64 (*.f64 x x) eps)) eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (fma.f64 eps (neg.f64 (/.f64 (*.f64 x x) eps)) eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (fma.f64 eps (neg.f64 (/.f64 (*.f64 x x) 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))) (/.f64 x #s(literal 1 binary64)))
(+ (* 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 x (fma.f64 x (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (/.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 x (fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64)))) 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)
(/.f64 (-.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #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 x) (-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64))))
(* -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 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) eps) (fma.f64 #s(literal -1/4 binary64) (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/8 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* 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))))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
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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)))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
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(* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))
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(/ (- (+ (* -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)
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(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
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(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(+.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (sqrt.f64 eps) (.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 eps x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 eps eps))) (-.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))))
(- (+ (* -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 eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(-.f64 (-.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (/.f64 (.f64 x (fma.f64 (sqrt.f64 eps) (.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 eps x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 eps)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (.f64 x x)) (fma.f64 (sqrt.f64 eps) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 eps x) #s(literal -1 binary64))))) #s(literal -1 binary64))) (.f64 eps (.f64 eps eps)))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 eps x) #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 x #s(literal 1 binary64)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (*.f64 eps x)) (neg.f64 eps)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 #s(literal 3/2 binary64) (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x)))) (*.f64 eps x))) (neg.f64 eps)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 eps (.f64 eps eps)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 (sqrt.f64 eps) x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x)))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 eps (.f64 eps eps)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 (sqrt.f64 eps) x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x))))))) (neg.f64 eps)) (fma.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) (.f64 eps x))) eps))

rewrite449.0ms (3.5%)

Memory

-1.5MiB live, 735.5MiB allocated

Rules

5 766×	`lower-/.f32`
5 758×	`lower-/.f64`
4 678×	`lower-*.f32`
4 676×	`lower-*.f64`
4 422×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	202
0	51	190
1	216	172
2	1834	172
0	9049	172

Stop Event

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

Counts

20 → 1 443

Calls

Call 1

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

Outputs
(+.f64 eps (fma.f64 x x (neg.f64 (*.f64 x x))))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
(+.f64 (fma.f64 x x eps) (neg.f64 (*.f64 x x)))
(+.f64 (.f64 x x) (-.f64 eps (.f64 x x)))
(+.f64 (neg.f64 (*.f64 x x)) (fma.f64 x x eps))
(+.f64 (-.f64 eps (.f64 x x)) (.f64 x x))
(-.f64 (fma.f64 x x eps) (*.f64 x x))
(-.f64 (/.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps))))))
(-.f64 (/.f64 (.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (fma.f64 x x (fma.f64 x x eps))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x (fma.f64 x x eps))))
(-.f64 (/.f64 (.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (neg.f64 (.f64 x x)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (fma.f64 x x eps) (neg.f64 (.f64 x x)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (-.f64 eps (.f64 x x)))) (/.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (-.f64 (.f64 x x) (-.f64 eps (.f64 x x)))))
(fma.f64 x x (-.f64 eps (*.f64 x x)))
(fma.f64 x (neg.f64 x) (fma.f64 x x eps))
(fma.f64 x (.f64 x #s(literal 1 binary64)) (-.f64 eps (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (-.f64 eps (.f64 x x)))
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (-.f64 eps (.f64 x x)))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (fma.f64 x x eps))
(fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (.f64 x x))))) (neg.f64 (*.f64 x x)))
(fma.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) eps)) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (fma.f64 x x eps))) (neg.f64 (*.f64 x x)))
(fma.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) (fma.f64 x x eps) (neg.f64 (*.f64 x x)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (-.f64 eps (*.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (/.f64 (-.f64 (.f64 x x) eps) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (/.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (fma.f64 x x eps))))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (/.f64 (-.f64 (.f64 x x) eps) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (neg.f64 (*.f64 x x)))
(fma.f64 (/.f64 (fma.f64 x x eps) (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (-.f64 (.f64 x x) eps) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (.f64 x x))))) (neg.f64 (.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)))) (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)))) (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x))))))
(/.f64 (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)))))
(/.f64 (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (fma.f64 x x eps) (neg.f64 (.f64 x x))))))
(/.f64 (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (fma.f64 x x (fma.f64 x x eps)))
(/.f64 (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (-.f64 (fma.f64 x x eps) (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (neg.f64 (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps))))))
(/.f64 (neg.f64 (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (neg.f64 (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (fma.f64 x x eps) (neg.f64 (.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x)))) (neg.f64 (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (fma.f64 x x eps) (.f64 x x)))) (neg.f64 (-.f64 (fma.f64 x x eps) (neg.f64 (*.f64 x x)))))
(/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 eps (.f64 x x)) (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))))) (fma.f64 x (.f64 x (.f64 x x)) (-.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (.f64 (.f64 x x) (-.f64 eps (*.f64 x x))))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x)))) (-.f64 (.f64 x x) (-.f64 eps (.f64 x x))))
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eval705.0ms (5.5%)

Memory: 10.4MiB live, 1 052.2MiB allocated
Compiler: Compiled 126 005 to 6 540 computations (94.8% saved)

prune475.0ms (3.7%)

Memory

14.6MiB live, 856.9MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	2 931	9	2 940
Fresh	9	1	10
Picked	2	3	5
Done	0	1	1
Total	2 942	14	2 956

Accuracy

100.0%

Counts

2 956 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.9%	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	60.9%	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	61.4%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	56.4%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
	8.4%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x #s(approx (sqrt (- ( x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))))
	20.0%	(/.f64 (-.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 x x))) (.f64 (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64))) (.f64 (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (*.f64 x x))))
▶	99.5%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	56.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.9%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	45.1%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
▶	37.8%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))))
▶	4.5%	#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Compiler

Compiled 451 to 197 computations (56.3% saved)

simplify955.0ms (7.5%)

Memory

-4.2MiB live, 304.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 eps (*.f64 x x))
cost-diff	0	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
cost-diff	896	(fma.f64 x x (-.f64 eps (*.f64 x x)))
cost-diff	0	(/.f64 eps (.f64 x (.f64 x x)))
cost-diff	0	(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))))
cost-diff	320	(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
cost-diff	0	#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	192	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	832	(-.f64 (.f64 x x) (.f64 x x))

Rules

13 320×	`lower-fma.f32`
13 316×	`lower-fma.f64`
3 348×	`lower-*.f32`
3 340×	`lower-*.f64`
1 932×	`lower--.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	249
0	57	207
1	107	177
2	173	177
3	620	177
4	2813	177
5	7187	177
0	8032	177

Stop Event

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

Calls

Call 1

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

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

localize1.3s (10.4%)

Memory

-27.1MiB live, 111.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.3125	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	0.3671079461053137	(fma.f64 x x (-.f64 eps (*.f64 x x)))
accuracy	0.046875	(.f64 x (.f64 x x))
accuracy	7.192166260688929	(/.f64 eps (.f64 x (.f64 x x)))
accuracy	8.43165176709114	(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	36.101900677455646	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 1/2 binary64))
accuracy	34.81137546022293	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
accuracy	36.33022446902808	#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.3125	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Samples

447.0ms	151×	0	valid
416.0ms	105×	1	exit

Compiler

Compiled 232 to 32 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 827.0ms

ival-add: 405.0ms (49% of total)

ival-mult: 397.0ms (48% of total)

ival-div: 9.0ms (1.1% of total)

adjust: 6.0ms (0.7% of total)

ival-sub: 4.0ms (0.5% of total)

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

ival-neg: 1.0ms (0.1% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.3%)

Memory

0.2MiB live, 37.0MiB allocated

Counts

19 → 408

Calls

Call 1

Inputs
#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 (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64)) (patch #s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ ( x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 eps #s(literal 1/2 binary64)) x) (patch (/.f64 (.f64 eps #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 1/2 binary64)) (patch (.f64 eps #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))) (patch (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (/ (- (+ ( x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 eps (.f64 x (.f64 x x))) (patch (/.f64 eps (.f64 x (.f64 x x))) #<representation binary64>) () ())
#s(alt (fma.f64 x x (-.f64 eps (.f64 x x))) (patch (fma.f64 x x (-.f64 eps (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())
#s(alt (-.f64 eps (.f64 x x)) (patch (-.f64 eps (.f64 x x)) #<representation binary64>) () ())
#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 (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor -inf x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.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 eps (taylor inf 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 inf 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 inf 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 inf 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 -inf 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 -inf 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 -inf 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 -inf 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 x) (#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 x) (#s(alt (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (patch (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
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#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())) ())

Calls

102 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(/ eps (* x (* x x)))
1.0ms	eps	@	0	(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
1.0ms	eps	@	inf	(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
1.0ms	x	@	0	(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
0.0ms	eps	@	-inf	(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))

simplify385.0ms (3%)

Memory

11.5MiB live, 484.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 520×	`lower-fma.f64`
13 520×	`lower-fma.f32`
6 856×	`lower-*.f64`
6 856×	`lower-*.f32`
2 304×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	473	5253
1	1468	4877
2	5109	4745
0	8498	4491

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 355

Calls

Call 1

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

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

rewrite501.0ms (3.9%)

Memory

4.4MiB live, 370.2MiB allocated

Rules

4 736×	`lower-/.f32`
4 728×	`lower-/.f64`
4 088×	`lower-*.f32`
4 080×	`lower-*.f64`
2 990×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	209
0	57	159
1	243	137
2	1909	137
0	8395	137

Stop Event

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

Counts

19 → 956

Calls

Call 1

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

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

eval632.0ms (4.9%)

Memory: 22.3MiB live, 417.2MiB allocated
Compiler: Compiled 48 356 to 3 254 computations (93.3% saved)

prune227.0ms (1.8%)

Memory

-12.0MiB live, 344.3MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 623	4	1 627
Fresh	4	1	5
Picked	3	2	5
Done	1	3	4
Total	1 631	10	1 641

Accuracy

100.0%

Counts

1 641 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	99.3%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
▶	99.5%	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	56.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.9%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
✓	45.1%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
✓	4.5%	#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Compiler

Compiled 196 to 106 computations (45.9% saved)

simplify259.0ms (2%)

Memory

-9.0MiB live, 274.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
cost-diff	192	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	832	(-.f64 (.f64 x x) (.f64 x x))
cost-diff	2624	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
cost-diff	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff	0	(/.f64 #s(literal 1 binary64) eps)
cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) 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	(-.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)))
cost-diff	0	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Rules

13 952×	`lower-fma.f32`
13 950×	`lower-fma.f64`
1 888×	`lower-*.f32`
1 884×	`lower-*.f64`
1 690×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	241
0	43	193
1	74	193
2	119	193
3	237	193
4	594	193
5	1403	193
6	3229	193
7	5738	193
8	6756	193
9	7561	193
10	7896	193
11	7978	193
0	8039	193

Stop Event

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

Calls

Call 1

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

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

localize90.0ms (0.7%)

Memory

-2.8MiB live, 196.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.08203125	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.31478500976844204	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
accuracy	0.3203125	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.109375	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
accuracy	0.3203125	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.1484375	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0	(neg.f64 eps)
accuracy	0.01171875	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	1.2322758803037512	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	3.391965224403319	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.3203125	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Samples

28.0ms	99×	1	exit
25.0ms	157×	0	valid

Compiler

Compiled 236 to 23 computations (90.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-div: 9.0ms (26.1% of total)

ival-add: 9.0ms (26.1% of total)

ival-mult: 5.0ms (14.5% of total)

adjust: 4.0ms (11.6% of total)

ival-sub: 3.0ms (8.7% of total)

ival-sqrt: 3.0ms (8.7% of total)

ival-neg: 1.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.2%)

Memory

-5.6MiB live, 36.4MiB allocated

Counts

18 → 384

Calls

Call 1

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

Outputs
#s(alt (* 1/2 (/ eps x)) (taylor 0 eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt eps) (/ 1 (sqrt -1))) (taylor inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (taylor inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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))) (taylor inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -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))))) (taylor inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt eps) (sqrt -1))) (taylor -inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 (* (sqrt eps) (sqrt -1)))) (taylor -inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf eps) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt eps) (/ 1 (sqrt -1))) (taylor 0 x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (taylor 0 x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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)))) (taylor 0 x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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)))) (taylor 0 x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ eps x)) (taylor inf x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -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) (taylor inf x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<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 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (patch (/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #<representation binary64>) () ())) ())
#s(alt (* (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 (* 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 (* x (+ 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 (* x (+ 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 (* x (+ 2 (+ (* -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 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<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 (/ (+ (* -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 (/ (+ (* -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 (* -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 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* 2 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 (+ (* -1/2 (/ eps x)) (* 2 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 (+ (* 2 x) (* 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 (+ (* 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 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 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
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#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 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -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) (taylor inf x) (#s(alt (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.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 (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.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 (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.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 (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (patch (/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) #<representation binary64>) () ())) ())
#s(alt (pow (* -1 eps) 1/4) (taylor 0 x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4)) (taylor 0 x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4)) (taylor 0 x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4)) (taylor 0 x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow 1 1/4) (sqrt x)) (taylor 0 eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x))) (taylor 0 eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x))) (taylor 0 eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x))) (taylor 0 eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (taylor inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))) (taylor inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))) (taylor inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))))) (taylor inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (pow (* -1 eps) 1/4) (taylor -inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4)) (taylor -inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4)) (taylor -inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4)) (taylor -inf eps) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (patch (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #<representation binary64>) () ())) ())

Calls

96 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	-inf	(/ 1 eps)
0.0ms	eps	@	-inf	(/ 1 (/ 1 eps))
0.0ms	eps	@	inf	(/ (+ eps (- (* x x) (* x x))) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x))
0.0ms	eps	@	-inf	(/ eps (+ x (sqrt (- (* x x) eps))))
0.0ms	eps	@	-inf	(/ (+ eps (- (* x x) (* x x))) (+ (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) x))

simplify305.0ms (2.4%)

Memory

32.0MiB live, 456.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 440×	`lower-fma.f64`
11 440×	`lower-fma.f32`
6 780×	`lower-*.f64`
6 780×	`lower-*.f32`
4 174×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	690	6720
1	2180	6167
2	7348	6143
0	8089	5843

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 344

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))))
(* (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 eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -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)))
(+ (* -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)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* 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))))
(+ (* 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))))
(* 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)
(* -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)))))))))
(* (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)))
(* 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 (/ (+ (* -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)
(+ (* -1/2 (/ 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)))))
(* (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)))))
(* -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)))))
(* (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)))))))))
x
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x
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(- (pow x 2) eps)
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(pow x 2)
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x
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x
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(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
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(pow x 2)
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(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
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(* eps (- (/ (pow x 2) eps) 1))
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(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
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(/ (+ (* 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)
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(* -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)))))))))
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(/ (+ 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)
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(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
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(/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) eps)
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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))))) eps)
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eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
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(* 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))))
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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)))))
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(/ (+ (* 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)
(* -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 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(/ 1 eps)
(* (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)))
(* 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 (/ (+ (* -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)
(+ (* -1/2 (/ 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)))))
(* (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)))))
(* -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)))))
0
0
0
0
0
0
0
0
0
0
0
0
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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))))
(* (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 eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -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)))
(+ (* -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)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* 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))))
(+ (* 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))))
(* 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)
(* -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 (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))

Outputs
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (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)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.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 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -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)))
(-.f64 (+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps 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)))))
(-.f64 (+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x) (/.f64 (fma.f64 (.f64 eps eps) (.f64 (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 (sqrt.f64 eps) x) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps (.f64 eps eps))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (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)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 eps) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (.f64 eps x)) eps) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -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 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 eps (.f64 x (.f64 x x))) (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))))) (neg.f64 eps)) (*.f64 eps 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 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* 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 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.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 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))) 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)
(/.f64 (-.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64))))
(* -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 x) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))))))
(* -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 (fma.f64 eps (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) eps)) (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/4 binary64)))) #s(literal -1/8 binary64)))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (neg.f64 x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.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 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 x (fma.f64 x (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) 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))
(/.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 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (*.f64 x #s(literal 2 binary64)))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 (/.f64 eps (.f64 x (.f64 x x))) #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x #s(literal 2 binary64)))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x #s(literal 2 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 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)))))
(.f64 eps (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) x) (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)))))
(neg.f64 (.f64 eps (-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64)))) eps)) eps))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 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 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(neg.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 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))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 (/.f64 eps (.f64 x (.f64 x x))) #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 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 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 x (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) x) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))) 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)
(/.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (neg.f64 x) (-.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -2 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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))))
(.f64 eps (fma.f64 eps (fma.f64 eps (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)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64)) (/.f64 x eps)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (-.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) x) (neg.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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)))))
(neg.f64 (.f64 eps (-.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (.f64 (sqrt.f64 eps) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)))) eps)) (neg.f64 eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 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 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(neg.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(neg.f64 (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 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))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 (/.f64 eps (.f64 x (.f64 x x))) #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 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 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (pow.f64 x #s(literal 4 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(neg.f64 (-.f64 eps (.f64 eps (/.f64 (.f64 x x) eps))))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -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 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* 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 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.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))))
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(* 1/2 (/ eps x))
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(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (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)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 eps) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)) (.f64 eps x)) eps) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -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 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 eps (.f64 x (.f64 x x))) (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))))) (neg.f64 eps)) (*.f64 eps 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 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* 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 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.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 x (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps))) 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)
(/.f64 (-.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 eps #s(literal -1/2 binary64) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x)) #s(literal -2 binary64))))
(* -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 x) (-.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/8 binary64) (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64))))))))
(* -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 (fma.f64 eps (.f64 #s(literal 1/16 binary64) (.f64 eps eps)) (fma.f64 #s(literal -2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) eps)) (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/4 binary64)))) #s(literal -1/8 binary64)))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (neg.f64 x))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -3/32 binary64)))) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -3/32 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -7/128 binary64)))) (.f64 #s(literal -1/4 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)))) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 x))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 eps (.f64 eps #s(literal -3/32 binary64))) (fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 x)))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(+.f64 (fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 x)) (fma.f64 (.f64 eps eps) (.f64 #s(literal -3/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -7/128 binary64)))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 eps (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 eps (.f64 eps #s(literal -3/32 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(fma.f64 eps (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) #s(literal -1/4 binary64)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -7/128 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 eps (.f64 eps #s(literal -3/32 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))))
(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (.f64 eps #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal -3/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -3/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (.f64 #s(literal -7/128 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (sqrt.f64 x))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 x x) eps)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 x x) eps)) (fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (/.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (*.f64 eps eps)))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(fma.f64 #s(literal -1/4 binary64) (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 x x) eps)) (fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -3/32 binary64) (.f64 eps eps)) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (.f64 eps (*.f64 eps eps)))))))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)))) eps))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -3/32 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64)))) eps)) eps))

rewrite334.0ms (2.6%)

Memory

-0.5MiB live, 463.7MiB allocated

Rules

9 228×	`lower-fma.f32`
9 226×	`lower-fma.f64`
3 846×	`lower-*.f32`
3 842×	`lower-*.f64`
2 800×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	168
0	43	120
1	180	120
2	1210	112
0	9012	112

Stop Event

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

Counts

18 → 2 610

Calls

Call 1

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

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

eval881.0ms (6.9%)

Memory: -90.0MiB live, 810.5MiB allocated
Compiler: Compiled 118 398 to 6 072 computations (94.9% saved)

prune643.0ms (5%)

Memory

1.7MiB live, 767.5MiB allocated

Pruning

14 alts after pruning (6 fresh and 8 done)

	Pruned	Kept	Total
New	4 041	6	4 047
Fresh	0	0	0
Picked	2	3	5
Done	0	5	5
Total	4 043	14	4 057

Accuracy

100.0%

Counts

4 057 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	99.3%	(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 #s(literal -1 binary64) eps))
	99.3%	(/.f64 eps (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
✓	99.5%	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	58.7%	(/.f64 eps (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
	46.3%	(/.f64 eps (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))))
✓	61.7%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	56.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.9%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	46.2%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (- ( x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))) eps)
	43.5%	#s(approx (/ (/ 1 (/ 1 eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x))
✓	45.1%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
✓	4.5%	#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Compiler

Compiled 847 to 219 computations (74.1% saved)

regimes31.0ms (0.2%)

Memory

19.8MiB live, 57.7MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))
(-.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 eps #s(literal 1/2 binary64)) x))
#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 eps (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (- ( x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))) eps)
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x))
#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (/ (/ 1 (/ 1 eps)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (.f64 x x))) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x #s(approx (sqrt (- ( x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 #s(literal -1 binary64) eps))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
(/.f64 eps (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 x x))) (.f64 (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64))) (.f64 (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))

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

Calls

3 calls:

10.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
10.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes14.0ms (0.1%)

Memory

-23.5MiB live, 16.8MiB allocated

Counts

9 → 2

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
88.1%	2	`x`
84.6%	2	`eps`
99.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes4.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

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

Compiler

Compiled 10 to 6 computations (40% saved)

regimes3.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
96.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes9.0ms (0.1%)

Memory

-21.0MiB live, 15.9MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

(-.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))))
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Calls

3 calls:

5.0ms	eps
2.0ms	x
2.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
57.9%	2	`eps`
56.2%	1	`x`
58.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes5.0ms (0%)

Memory

14.3MiB live, 14.3MiB allocated

Accuracy

Total -0.9b remaining (-1.4%)

Threshold costs -0.9b (-1.4%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.5%	1	`x`
4.5%	1	`eps`
4.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5125889992755118e-153	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5125889992755118e-153	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5125889992755118e-153	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5125889992755118e-153	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify8.0ms (0.1%)

Memory

20.2MiB live, 20.2MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
12×	`sub-neg_binary64`
8×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	177
1	49	177
2	58	177
3	63	177
4	65	177

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) #s(literal 0 binary64))

soundness916.0ms (7.2%)

Memory

-1.4MiB live, 593.8MiB allocated

Rules

11 530×	`lower-fma.f64`
11 530×	`lower-fma.f32`
11 440×	`lower-fma.f64`
11 440×	`lower-fma.f32`
11 222×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	209
0	57	159
1	243	137
2	1909	137
0	8395	137
0	28	202
0	51	190
1	216	172
2	1834	172
0	9049	172
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	1073	8665
1	3472	7995
0	8531	7580
0	257	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129
0	690	6720
1	2180	6167
2	7348	6143
0	8089	5843

Stop Event

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

Compiler

Compiled 331 to 127 computations (61.6% saved)

preprocess53.0ms (0.4%)

Memory: 10.3MiB live, 118.0MiB allocated
Compiler: Compiled 266 to 78 computations (70.7% 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%)

analyze18.0ms (0.1%)

sample1.4s (11%)

explain108.0ms (0.8%)

preprocess33.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify16.0ms (0.1%)

localize311.0ms (2.4%)

series9.0ms (0.1%)

simplify316.0ms (2.5%)

rewrite286.0ms (2.2%)

eval43.0ms (0.3%)

prune61.0ms (0.5%)

simplify357.0ms (2.8%)

localize118.0ms (0.9%)

series100.0ms (0.8%)

simplify349.0ms (2.7%)

rewrite449.0ms (3.5%)

eval705.0ms (5.5%)

prune475.0ms (3.7%)

simplify955.0ms (7.5%)

localize1.3s (10.4%)

series35.0ms (0.3%)

simplify385.0ms (3%)

rewrite501.0ms (3.9%)

eval632.0ms (4.9%)

prune227.0ms (1.8%)

simplify259.0ms (2%)

localize90.0ms (0.7%)

series20.0ms (0.2%)

simplify305.0ms (2.4%)

rewrite334.0ms (2.6%)

eval881.0ms (6.9%)

prune643.0ms (5%)

regimes31.0ms (0.2%)

regimes14.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes9.0ms (0.1%)

regimes5.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness916.0ms (7.2%)

preprocess53.0ms (0.4%)

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