Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze21.0ms (0.2%)

Memory

-14.1MiB live, 29.9MiB 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)

sample1.8s (17.2%)

Memory

-6.6MiB live, 1 651.6MiB allocated

Samples

728.0ms	2 263×	1	valid
599.0ms	5 982×	0	valid
10.0ms	158×	0	invalid
2.0ms	11×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 981.0ms

ival-<=: 460.0ms (46.9% of total)

ival-sub: 173.0ms (17.6% of total)

adjust: 142.0ms (14.5% of total)

ival-sqrt: 88.0ms (9% of total)

ival-mult: 78.0ms (7.9% of total)

ival-and: 22.0ms (2.2% of total)

exact: 16.0ms (1.6% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain142.0ms (1.4%)

Memory

17.3MiB live, 213.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	123	0

Confusion

	Predicted +	Predicted -
+	123	0
-	0	133

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	123	0	0
-	0	0	133

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	133
1	123

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms	344×	0	valid
26.0ms	168×	1	valid

Compiler

Compiled 84 to 28 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sub: 7.0ms (37.2% of total)

ival-sqrt: 5.0ms (26.6% of total)

ival-mult: 4.0ms (21.3% of total)

adjust: 2.0ms (10.6% of total)

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

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

preprocess30.0ms (0.3%)

Memory

8.4MiB live, 43.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify16.0ms (0.2%)

Memory

-36.3MiB live, 14.1MiB 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)))

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

localize35.0ms (0.3%)

Memory

-0.5MiB live, 36.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	28.168442123109813	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

9.0ms	172×	0	valid
8.0ms	84×	1	valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 3.0ms (33% of total)

ival-sqrt: 3.0ms (33% of total)

ival-mult: 2.0ms (22% of total)

adjust: 1.0ms (11% of total)

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

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

series9.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify212.0ms (2.1%)

Memory

13.0MiB live, 168.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

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

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

rewrite146.0ms (1.4%)

Memory

16.9MiB live, 291.7MiB allocated

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
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eval91.0ms (0.9%)

Memory: -3.3MiB live, 71.6MiB allocated
Compiler: Compiled 7 073 to 1 088 computations (84.6% saved)

prune14.0ms (0.1%)

Memory

7.3MiB live, 43.0MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	296	10	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	296	11	307

Accuracy

99.7%

Counts

307 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.2%	(fma.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
▶	55.6%	(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
▶	55.7%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
	44.0%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
	55.5%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	56.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	51.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	31.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps x)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
	45.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	50.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 384 to 206 computations (46.4% saved)

simplify279.0ms (2.7%)

Memory

-72.2MiB live, 254.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	128	(neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
cost-diff	9024	(fma.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	128	(neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
cost-diff	2944	(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
cost-diff	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	284
0	47	255
1	90	255
2	162	238
3	349	232
4	705	232
5	1584	232
6	3684	232
7	5158	232
8	6237	232
9	6586	232
10	6920	232
11	7215	232
12	7645	232
0	8129	232

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

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

localize135.0ms (1.3%)

Memory

37.2MiB live, 190.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.12109375	(pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))
accuracy	0.29296875	(/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	28.40650682826565	(fma.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.11328125	(/.f64 x (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	0.29296875	(/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	28.14105768456663	(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.1953125	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	31.845106063704527	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0	(neg.f64 x)
accuracy	28.168442123109813	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.461248949843586	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.25390625	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	27.763514045326275	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Samples

80.0ms	172×	0	valid
32.0ms	84×	1	valid

Compiler

Compiled 543 to 48 computations (91.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-mult: 34.0ms (37.8% of total)

ival-sub: 28.0ms (31.2% of total)

ival-div: 8.0ms (8.9% of total)

ival-add: 6.0ms (6.7% of total)

adjust: 4.0ms (4.5% of total)

ival-sqrt: 3.0ms (3.3% of total)

ival-pow: 3.0ms (3.3% of total)

ival-neg: 2.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series52.0ms (0.5%)

Memory

-29.5MiB live, 90.1MiB allocated

Counts

18 → 396

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (+ (* x (/ x (+ (sqrt (- (* x x) eps)) x))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ x (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (+ (* (* x x) (pow (+ (sqrt (- (* x x) eps)) x) -1)) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (* x x) eps) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))
7.0ms	eps	@	inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (+ (* x (/ x (+ (sqrt (- (* x x) eps)) x))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ x (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (+ (* (* x x) (pow (+ (sqrt (- (* x x) eps)) x) -1)) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (* x x) eps) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))
6.0ms	eps	@	-inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (+ (* x (/ x (+ (sqrt (- (* x x) eps)) x))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ x (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (+ (* (* x x) (pow (+ (sqrt (- (* x x) eps)) x) -1)) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (* x x) eps) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))
5.0ms	eps	@	0	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (+ (* x (/ x (+ (sqrt (- (* x x) eps)) x))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ x (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (+ (* (* x x) (pow (+ (sqrt (- (* x x) eps)) x) -1)) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (* x x) eps) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))
4.0ms	x	@	-inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (+ (* x (/ x (+ (sqrt (- (* x x) eps)) x))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x))) (/ x (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (+ (* (* x x) (pow (+ (sqrt (- (* x x) eps)) x) -1)) (neg (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))) (pow (+ (sqrt (- (* x x) eps)) x) -1) (- (* x x) eps) (/ (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x)))

simplify255.0ms (2.5%)

Memory

12.4MiB live, 234.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	983	7616
1	3237	6885
0	8395	6567

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 367

Calls

Call 1

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

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

rewrite617.0ms (6%)

Memory

13.5MiB live, 388.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	194
0	47	192
1	197	154
2	1467	154
0	8615	154

Stop Event

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

Counts

18 → 1 564

Calls

Call 1

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

Outputs
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eval2.6s (25.1%)

Memory: 8.3MiB live, 1 177.3MiB allocated
Compiler: Compiled 129 042 to 6 055 computations (95.3% saved)

prune90.0ms (0.9%)

Memory

1.6MiB live, 203.3MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	3 014	4	3 018
Fresh	4	1	5
Picked	4	1	5
Done	0	1	1
Total	3 022	7	3 029

Accuracy

100.0%

Counts

3 029 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.3%	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
▶	51.5%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))
▶	99.6%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	56.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	51.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	50.2%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))

Compiler

Compiled 137 to 91 computations (33.6% saved)

simplify216.0ms (2.1%)

Memory

-6.0MiB live, 225.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 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 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
cost-diff	896	(fma.f64 x x (-.f64 eps (*.f64 x 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 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))
cost-diff	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))
cost-diff	0	(/.f64 eps x)
cost-diff	0	(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
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 x x)
cost-diff	0	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.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))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	245
0	53	196
1	90	188
2	129	188
3	325	188
4	943	188
5	3081	188
6	6848	188
0	8361	188

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

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

localize95.0ms (0.9%)

Memory

-15.7MiB live, 97.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 eps (*.f64 x x))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.25390625	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	8.565818877218591	(fma.f64 x x (-.f64 eps (*.f64 x x)))
accuracy	0.01953125	(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
accuracy	0.25390625	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))
accuracy	8.651500898700888	(-.f64 (fma.f64 x x eps) (*.f64 x x))
accuracy	10.58142633479184	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0	(/.f64 eps x)
accuracy	0	(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
accuracy	31.845106063704527	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	8.816888983542514	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	10.58142633479184	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.25390625	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

37.0ms	174×	0	valid
37.0ms	82×	1	exit

Compiler

Compiled 419 to 46 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-sub: 26.0ms (55.2% of total)

ival-div: 6.0ms (12.7% of total)

adjust: 4.0ms (8.5% of total)

ival-add: 4.0ms (8.5% of total)

ival-mult: 3.0ms (6.4% of total)

ival-sqrt: 2.0ms (4.2% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series36.0ms (0.4%)

Memory

-5.3MiB live, 35.0MiB allocated

Counts

21 → 468

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	-inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (* (/ eps x) 1/2) (/ eps x) (- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (+ (* x x) (- eps (* x x))) (/ (+ (* x x) (- eps (* x x))) (+ (sqrt (- (* x x) eps)) x)) (- eps (* x x)) (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps) (sqrt (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x))
1.0ms	eps	@	inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (* (/ eps x) 1/2) (/ eps x) (- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (+ (* x x) (- eps (* x x))) (/ (+ (* x x) (- eps (* x x))) (+ (sqrt (- (* x x) eps)) x)) (- eps (* x x)) (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps) (sqrt (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x))
1.0ms	x	@	-inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (* (/ eps x) 1/2) (/ eps x) (- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (+ (* x x) (- eps (* x x))) (/ (+ (* x x) (- eps (* x x))) (+ (sqrt (- (* x x) eps)) x)) (- eps (* x x)) (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps) (sqrt (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x))
1.0ms	x	@	inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (* (/ eps x) 1/2) (/ eps x) (- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (+ (* x x) (- eps (* x x))) (/ (+ (* x x) (- eps (* x x))) (+ (sqrt (- (* x x) eps)) x)) (- eps (* x x)) (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps) (sqrt (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x))
1.0ms	x	@	0	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (* (/ eps x) 1/2) (/ eps x) (- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (+ (* x x) (- eps (* x x))) (/ (+ (* x x) (- eps (* x x))) (+ (sqrt (- (* x x) eps)) x)) (- eps (* x x)) (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps) (sqrt (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x))

simplify247.0ms (2.4%)

Memory

5.2MiB live, 236.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	445	5968
1	1405	5588
2	4865	5453
0	8587	5154

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 386

Calls

Call 1

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

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

rewrite223.0ms (2.2%)

Memory

36.1MiB live, 190.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	190
0	53	147
1	217	133
2	1664	133
0	8518	133

Stop Event

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

Counts

21 → 1 345

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

Outputs
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eval796.0ms (7.7%)

Memory: 14.7MiB live, 477.0MiB allocated
Compiler: Compiled 60 646 to 4 101 computations (93.2% saved)

prune185.0ms (1.8%)

Memory

-10.5MiB live, 151.8MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	2 138	4	2 142
Fresh	0	0	0
Picked	3	2	5
Done	0	2	2
Total	2 141	8	2 149

Accuracy

100.0%

Counts

2 149 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.6%	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
▶	99.6%	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	54.3%	(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
▶	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
✓	56.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	51.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	50.2%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))

Compiler

Compiled 69 to 55 computations (20.3% saved)

simplify125.0ms (1.2%)

Memory

-8.6MiB live, 168.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
cost-diff	0	(*.f64 eps eps)
cost-diff	640	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
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 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
cost-diff	0	(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	177
0	34	177
1	51	177
2	78	171
3	87	171
4	217	171
5	620	171
6	1975	171
7	3688	171
8	4828	171
9	6791	171
0	8004	171

Stop Event

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

Calls

Call 1

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

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

localize64.0ms (0.6%)

Memory

5.4MiB live, 165.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.1015625	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
accuracy	35.189185712810534	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.25390625	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	0.00390625	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0.01953125	(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
accuracy	0.25390625	(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
accuracy	30.279192585818908	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.13671875	(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)
accuracy	0.265625	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))

Samples

48.0ms

256×

valid

Compiler

Compiled 324 to 34 computations (89.5% saved)

Precisions

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

ival-mult: 12.0ms (48.6% of total)

ival-div: 7.0ms (28.4% of total)

ival-sqrt: 2.0ms (8.1% of total)

ival-add: 1.0ms (4.1% of total)

ival-sub: 1.0ms (4.1% of total)

ival-neg: 1.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series25.0ms (0.2%)

Memory

-23.1MiB live, 58.4MiB allocated

Counts

13 → 300

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((/ 1 (/ (+ (sqrt (- (* x x) eps)) x) eps)) (/ (+ (sqrt (- (* x x) eps)) x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (/ eps (+ (sqrt (- (* x x) eps)) x)) (- (* x x) eps) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps))
1.0ms	eps	@	inf	((/ 1 (/ (+ (sqrt (- (* x x) eps)) x) eps)) (/ (+ (sqrt (- (* x x) eps)) x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (/ eps (+ (sqrt (- (* x x) eps)) x)) (- (* x x) eps) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps))
1.0ms	x	@	-inf	((/ 1 (/ (+ (sqrt (- (* x x) eps)) x) eps)) (/ (+ (sqrt (- (* x x) eps)) x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (/ eps (+ (sqrt (- (* x x) eps)) x)) (- (* x x) eps) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps))
1.0ms	x	@	inf	((/ 1 (/ (+ (sqrt (- (* x x) eps)) x) eps)) (/ (+ (sqrt (- (* x x) eps)) x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (/ eps (+ (sqrt (- (* x x) eps)) x)) (- (* x x) eps) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps))
1.0ms	x	@	0	((/ 1 (/ (+ (sqrt (- (* x x) eps)) x) eps)) (/ (+ (sqrt (- (* x x) eps)) x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps) (/ eps (+ (sqrt (- (* x x) eps)) x)) (- (* x x) eps) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps))

simplify160.0ms (1.6%)

Memory

34.3MiB live, 266.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	500	5864
1	1597	5468
2	5396	5352
0	8387	5031

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 296

Calls

Call 1

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

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

rewrite197.0ms (1.9%)

Memory

-26.7MiB live, 298.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	119
0	34	113
1	117	113
2	767	113
0	8448	113

Stop Event

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

Counts

13 → 1 160

Calls

Call 1

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

Outputs
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eval369.0ms (3.6%)

Memory: 1.6MiB live, 476.0MiB allocated
Compiler: Compiled 51 409 to 4 397 computations (91.4% saved)

prune45.0ms (0.4%)

Memory

11.2MiB live, 136.5MiB allocated

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	2 089	3	2 092
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	2 090	10	2 100

Accuracy

100.0%

Counts

2 100 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	44.6%	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
✓	99.6%	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	54.3%	(/.f64 eps (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	50.8%	(/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x))
	50.8%	(/.f64 eps #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) (*.f64 #s(literal 2 binary64) x))))
✓	56.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	51.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	99.4%	(.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 eps))
✓	50.2%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))

Compiler

Compiled 423 to 163 computations (61.5% saved)

regimes23.0ms (0.2%)

Memory

11.0MiB live, 49.1MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
7.0ms	eps
6.0ms	x

Results

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

Compiler

Compiled 10 to 10 computations (0% saved)

regimes45.0ms (0.4%)

Memory

-21.9MiB live, 16.3MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

3 calls:

39.0ms	eps
3.0ms	x
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
90.2%	2	`x`
81.0%	2	`eps`
99.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

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

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
97.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
96.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
52.7%	2	`eps`
51.1%	1	`x`
52.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes19.0ms (0.2%)

Memory

-31.1MiB live, 12.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	eps
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	x

Results

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

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.331602541539517e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.331602541539517e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.331602541539517e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.331602541539517e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch20.0ms (0.2%)

Memory

12.9MiB live, 50.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	-1.5710185301325866e-306	1.1266299649314096e-307

Samples

9.0ms	80×	1	valid
2.0ms	39×	0	valid
1.0ms	9×	2	valid
1.0ms	17×	0	invalid

Compiler

Compiled 99 to 115 computations (-16.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 3.0ms (33.6% of total)

ival-sub: 2.0ms (22.4% of total)

ival-sqrt: 2.0ms (22.4% of total)

adjust: 1.0ms (11.2% of total)

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

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

simplify27.0ms (0.3%)

Memory

-8.6MiB live, 68.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	208
1	61	208
2	75	208
3	83	208
4	86	208

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 eps #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 eps #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness785.0ms (7.6%)

Memory

31.6MiB live, 584.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1253
1	784	1238
2	2588	1200
3	6920	1197
0	8069	1129
0	27	194
0	47	192
1	197	154
2	1467	154
0	8615	154
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	983	7616
1	3237	6885
0	8395	6567
0	500	5864
1	1597	5468
2	5396	5352
0	8387	5031
0	31	190
0	53	147
1	217	133
2	1664	133
0	8518	133

Stop Event

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

Compiler

Compiled 337 to 149 computations (55.8% saved)

preprocess67.0ms (0.6%)

Memory: -18.5MiB live, 129.7MiB allocated
Compiler: Compiled 298 to 98 computations (67.1% 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%)

analyze21.0ms (0.2%)

sample1.8s (17.2%)

explain142.0ms (1.4%)

preprocess30.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify16.0ms (0.2%)

localize35.0ms (0.3%)

series9.0ms (0.1%)

simplify212.0ms (2.1%)

rewrite146.0ms (1.4%)

eval91.0ms (0.9%)

prune14.0ms (0.1%)

simplify279.0ms (2.7%)

localize135.0ms (1.3%)

series52.0ms (0.5%)

simplify255.0ms (2.5%)

rewrite617.0ms (6%)

eval2.6s (25.1%)

prune90.0ms (0.9%)

simplify216.0ms (2.1%)

localize95.0ms (0.9%)

series36.0ms (0.4%)

simplify247.0ms (2.4%)

rewrite223.0ms (2.2%)

eval796.0ms (7.7%)

prune185.0ms (1.8%)

simplify125.0ms (1.2%)

localize64.0ms (0.6%)

series25.0ms (0.2%)

simplify160.0ms (1.6%)

rewrite197.0ms (1.9%)

eval369.0ms (3.6%)

prune45.0ms (0.4%)

regimes23.0ms (0.2%)

regimes45.0ms (0.4%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes5.0ms (0.1%)

regimes19.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch20.0ms (0.2%)

simplify27.0ms (0.3%)

soundness785.0ms (7.6%)

preprocess67.0ms (0.6%)

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