Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze14.0ms (0.1%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.7s (17.1%)

Memory

-30.4MiB live, 1 420.8MiB allocated

Samples

607.0ms	4 907×	0	valid
431.0ms	2 720×	1	valid
102.0ms	629×	2	valid
44.0ms	174×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 831.0ms

ival-<=: 207.0ms (24.9% of total)

ival-sqrt: 192.0ms (23.1% of total)

ival-sub: 183.0ms (22% of total)

ival-mult: 120.0ms (14.4% of total)

adjust: 87.0ms (10.5% of total)

ival-and: 22.0ms (2.6% of total)

exact: 17.0ms (2% of total)

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

Bogosity

explain170.0ms (1.8%)

Memory

6.9MiB live, 241.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
110	-	-	`(-.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	110	0

Confusion

	Predicted +	Predicted -
+	110	0
-	0	146

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	110	0	0
-	0	0	146

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	146
1	110

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms	174×	1	valid
15.0ms	296×	0	valid
6.0ms	42×	2	valid

Compiler

Compiled 132 to 40 computations (69.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 23.0ms (56.1% of total)

ival-sub: 7.0ms (17.1% of total)

ival-sqrt: 6.0ms (14.6% of total)

adjust: 4.0ms (9.7% of total)

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

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

preprocess30.0ms (0.3%)

Memory

0.9MiB live, 37.6MiB 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

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB 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

localize33.0ms (0.3%)

Memory

-25.8MiB live, 24.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	25.563187629553955	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

17.0ms	87×	1	valid
7.0ms	148×	0	valid
3.0ms	21×	2	valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

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

ival-sqrt: 9.0ms (47.8% of total)

adjust: 4.0ms (21.3% of total)

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

ival-mult: 2.0ms (10.6% of total)

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

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

series9.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB 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))

simplify210.0ms (2.2%)

Memory

1.5MiB live, 190.2MiB 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)

rewrite152.0ms (1.6%)

Memory

17.1MiB live, 208.7MiB 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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eval57.0ms (0.6%)

Memory: -17.6MiB live, 102.3MiB allocated
Compiler: Compiled 7 073 to 1 088 computations (84.6% saved)

prune12.0ms (0.1%)

Memory

0.3MiB live, 38.9MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	298	8	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	298	9	307

Accuracy

99.8%

Counts

307 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.6%	(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))))
▶	59.6%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
	46.8%	(/.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)))
✓	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	56.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	25.4%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps x)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
▶	40.1%	#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))
▶	45.9%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 298 to 170 computations (43% saved)

simplify139.0ms (1.4%)

Memory

21.7MiB live, 192.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.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)
cost-diff	0	#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))
cost-diff	320	(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))))))
cost-diff	6464	(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)))))
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	0	(/.f64 #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: 0 (0.0ms)

Iter	Nodes	Cost
0	45	339
0	78	332
1	136	332
2	248	327
3	423	325
4	607	321
5	1585	321
6	5625	321
0	8247	311

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

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

localize194.0ms (2%)

Memory

15.1MiB live, 317.8MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	12.160156250000002	(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))))))
accuracy	35.367683231436594	(*.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))))
accuracy	35.776354537911764	(fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps)
accuracy	35.982355682159906	#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))
accuracy	0.109375	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	8.374202669884214	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	10.160870400955435	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	35.931270054928774	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.26171875	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	34.480715461928575	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0	(neg.f64 x)
accuracy	25.563187629553955	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.427300014756845	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.00390625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.2890625	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	25.181560527266136	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Samples

72.0ms	148×	0	valid
65.0ms	87×	1	valid
22.0ms	21×	2	valid

Compiler

Compiled 599 to 84 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-mult: 31.0ms (30.3% of total)

ival-pow: 17.0ms (16.6% of total)

ival-div: 14.0ms (13.7% of total)

ival-sqrt: 12.0ms (11.7% of total)

adjust: 11.0ms (10.7% of total)

ival-add: 10.0ms (9.8% of total)

ival-sub: 5.0ms (4.9% of total)

exact: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

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

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

series95.0ms (1%)

Memory

3.0MiB live, 83.2MiB allocated

Counts

22 → 480

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

Calls

6 calls:

Time	Variable		Point	Expression
45.0ms	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 (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4)))) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps) (* (pow eps 3) (/ 1/16 (pow x 4))))
8.0ms	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 (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4)))) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps) (* (pow eps 3) (/ 1/16 (pow x 4))))
7.0ms	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 (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4)))) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps) (* (pow eps 3) (/ 1/16 (pow x 4))))
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 (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4)))) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps) (* (pow eps 3) (/ 1/16 (pow x 4))))
5.0ms	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 (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4)))) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps) (* (pow eps 3) (/ 1/16 (pow x 4))))

simplify201.0ms (2.1%)

Memory

-15.5MiB live, 234.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	598	6536
1	1885	6366
2	6167	6271
0	8275	5955

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 448

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

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

rewrite270.0ms (2.8%)

Memory

-2.9MiB live, 302.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	277
0	78	277
1	313	273
2	2433	273
0	9600	269

Stop Event

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

Counts

22 → 842

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

Outputs
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eval598.0ms (6.2%)

Memory: -14.8MiB live, 410.2MiB allocated
Compiler: Compiled 39 035 to 4 202 computations (89.2% saved)

prune59.0ms (0.6%)

Memory

-3.2MiB live, 110.1MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1 333	4	1 337
Fresh	2	1	3
Picked	4	1	5
Done	0	1	1
Total	1 339	7	1 346

Accuracy

100.0%

Counts

1 346 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.3%	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	99.5%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	56.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	46.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	43.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)) x))

Compiler

Compiled 135 to 95 computations (29.6% saved)

simplify186.0ms (1.9%)

Memory

22.2MiB live, 255.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(neg.f64 x)
cost-diff	0	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	896	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)
cost-diff	0	#s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps))
cost-diff	0	(/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
cost-diff	0	(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: 0 (0.0ms)

Iter	Nodes	Cost
0	53	343
0	77	311
1	142	307
2	252	298
3	825	298
4	5412	295
0	8420	286

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

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

localize305.0ms (3.1%)

Memory

-24.1MiB live, 354.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.28515625	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	11.193148489626264	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
accuracy	0.15234375	(fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64))
accuracy	4.798204182374846	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)
accuracy	30.11391763568326	#s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps))
accuracy	35.982355682159906	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x) #s(literal 1/2 binary64)) eps)) x))
accuracy	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	34.434164684393096	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
accuracy	0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0	(neg.f64 eps)
accuracy	11.268742096926257	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	12.290642093275665	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.00390625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.28515625	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

122.0ms	70×	1	valid
59.0ms	125×	0	valid
30.0ms	48×	1	exit
8.0ms	13×	2	exit

Compiler

Compiled 481 to 76 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 195.0ms

ival-mult: 119.0ms (61.1% of total)

ival-add: 20.0ms (10.3% of total)

ival-div: 15.0ms (7.7% of total)

ival-pow: 15.0ms (7.7% of total)

adjust: 13.0ms (6.7% of total)

ival-sub: 4.0ms (2.1% of total)

ival-neg: 4.0ms (2.1% of total)

ival-sqrt: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series92.0ms (0.9%)

Memory

-18.5MiB live, 59.9MiB allocated

Counts

23 → 492

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

Calls

6 calls:

Time	Variable		Point	Expression
34.0ms	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 (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (+ (* (/ 1/8 x) (/ eps x)) 1/2))
3.0ms	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 (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (+ (* (/ 1/8 x) (/ eps x)) 1/2))
3.0ms	eps	@	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 (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (+ (* (/ 1/8 x) (/ eps x)) 1/2))
2.0ms	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 (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (+ (* (/ 1/8 x) (/ eps x)) 1/2))
2.0ms	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 (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* (/ 1/8 x) (/ eps x)) 1/2) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (- (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (+ (* (/ 1/8 x) (/ eps x)) 1/2))

simplify189.0ms (1.9%)

Memory

21.8MiB live, 251.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	675	6994
1	2161	6536
2	7431	6522
0	8059	6198

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 447

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

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

rewrite206.0ms (2.1%)

Memory

-26.4MiB live, 228.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	302
0	77	274
1	343	260
2	2568	260
0	8268	251

Stop Event

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

Counts

23 → 789

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

Outputs
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eval284.0ms (2.9%)

Memory: 60.1MiB live, 436.2MiB allocated
Compiler: Compiled 33 884 to 3 230 computations (90.5% saved)

prune138.0ms (1.4%)

Memory

-48.9MiB live, 85.6MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 473	3	1 476
Fresh	0	0	0
Picked	3	2	5
Done	0	2	2
Total	1 476	7	1 483

Accuracy

100.0%

Counts

1 483 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	56.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	4.3%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) x))
✓	46.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	43.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)) x))

Compiler

Compiled 54 to 47 computations (13% saved)

simplify211.0ms (2.2%)

Memory

40.3MiB live, 189.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
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	#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
cost-diff	0	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	0	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) x))
cost-diff	704	(/.f64 #s(literal 0 binary64) x)
cost-diff	0	(.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)
cost-diff	0	#s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps))
cost-diff	0	(/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	260
0	62	256
1	111	250
2	210	238
3	343	220
4	484	217
5	1303	217
6	5258	217
0	8279	208

Stop Event

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

Calls

Call 1

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

localize234.0ms (2.4%)

Memory

-7.5MiB live, 340.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
accuracy	0.00390625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.2890625	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	0	(/.f64 #s(literal 0 binary64) x)
accuracy	61.22189450817214	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) x))
accuracy	4.798204182374846	(.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)
accuracy	11.761735346740174	(/.f64 eps (*.f64 x x))
accuracy	30.11391763568326	#s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps))
accuracy	35.982355682159906	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)) x))

Samples

92.0ms	87×	1	valid
61.0ms	148×	0	valid
19.0ms	21×	2	valid

Compiler

Compiled 301 to 62 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-pow: 50.0ms (33.1% of total)

ival-mult: 38.0ms (25.1% of total)

adjust: 23.0ms (15.2% of total)

ival-div: 21.0ms (13.9% of total)

ival-add: 11.0ms (7.3% of total)

ival-sub: 4.0ms (2.6% of total)

ival-sqrt: 3.0ms (2% of total)

exact: 1.0ms (0.7% of total)

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

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

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

series22.0ms (0.2%)

Memory

13.5MiB live, 51.0MiB allocated

Counts

12 → 276

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* 1/8 (/ eps (* x x))) 1/2) eps) (/ 0 x) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (* x x)) (- (* x x) eps))
1.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* 1/8 (/ eps (* x x))) 1/2) eps) (/ 0 x) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (* x x)) (- (* x x) eps))
1.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* 1/8 (/ eps (* x x))) 1/2) eps) (/ 0 x) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (* x x)) (- (* x x) eps))
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* 1/8 (/ eps (* x x))) 1/2) eps) (/ 0 x) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (* x x)) (- (* x x) eps))
1.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (/ (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) x) (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (* (+ (* 1/8 (/ eps (* x x))) 1/2) eps) (/ 0 x) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ eps (* x x)) (- (* x x) eps))

simplify217.0ms (2.2%)

Memory

-20.6MiB live, 246.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	619	5235
1	1967	4651
2	6761	4205
0	8541	3980

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 260

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))))
(* 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)
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (+ 1/2 (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2)))))))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(+ eps (+ (* -1 (pow x 2)) (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)))))
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)))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(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)))))
(* 5/128 (/ (pow eps 4) (pow x 7)))
(* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 5)))) (* 5/128 (/ 1 (pow x 7)))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (/ 1/8 (* (pow eps 2) (pow x 3))) (* 5/128 (/ 1 (pow x 7))))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 3)))) (+ (* 1/2 (/ 1 (* (pow eps 3) x))) (* 5/128 (/ 1 (pow x 7)))))))
(* 5/128 (/ (pow eps 4) (pow x 6)))
(* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 4)))) (* 5/128 (/ 1 (pow x 6)))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (/ 1/8 (* (pow eps 2) (pow x 2))) (* 5/128 (/ 1 (pow x 6))))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (* 1/8 (/ 1 (* (pow eps 2) (pow x 2)))) (+ (* 1/2 (/ 1 (pow eps 3))) (* 5/128 (/ 1 (pow x 6)))))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
eps
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (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)))))
(* (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))))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(* -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)))))
(* 5/128 (/ (pow eps 4) (pow x 7)))
(* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 5)))) (* 5/128 (/ 1 (pow x 7)))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 5))) (+ (/ 1/8 (* (pow eps 2) (pow x 3))) (* 5/128 (/ 1 (pow x 7))))))
(* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5)))) eps)) (* 5/128 (/ 1 (pow x 7)))))
(* 5/128 (/ (pow eps 4) (pow x 6)))
(* (pow eps 4) (+ (* 1/16 (/ 1 (* eps (pow x 4)))) (* 5/128 (/ 1 (pow x 6)))))
(* (pow eps 4) (+ (/ 1/16 (* eps (pow x 4))) (+ (/ 1/8 (* (pow eps 2) (pow x 2))) (* 5/128 (/ 1 (pow x 6))))))
(* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4)))) eps)) (* 5/128 (/ 1 (pow x 6)))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* 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 eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* 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 eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
eps
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(* -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)))))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(* -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)))
(* 5/128 (/ (pow eps 4) (pow x 7)))
(/ (+ (* 5/128 (pow eps 4)) (* 1/16 (* (pow eps 3) (pow x 2)))) (pow x 7))
(/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))))) (pow x 7))
(/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))))) (pow x 7))
(* 5/128 (/ (pow eps 4) (pow x 6)))
(/ (+ (* 5/128 (pow eps 4)) (* 1/16 (* (pow eps 3) (pow x 2)))) (pow x 6))
(/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))))) (pow x 6))
(/ (+ (* 5/128 (pow eps 4)) (* (pow x 2) (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))))) (pow x 6))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
0
0
0
0
(* (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) (/ 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
eps
eps
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (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)))))))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 5/128 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))) x)
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(+ (* 5/128 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
0
0
0
0
(* 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 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
eps
eps
eps
eps
(* 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)))))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (* -5/128 (/ (pow eps 4) (pow x 6)))))) x))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(+ (* 5/128 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
0
0
0
0
(* 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)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
eps
eps
eps
eps
(* 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))))))))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))

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

rewrite440.0ms (4.5%)

Memory

-25.1MiB live, 293.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	238
0	62	234
1	278	222
2	2102	222
0	9202	210

Stop Event

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

Counts

12 → 174

Calls

Call 1

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

Outputs
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eval378.0ms (3.9%)

Memory: 22.9MiB live, 99.9MiB allocated
Compiler: Compiled 8 457 to 1 418 computations (83.2% saved)

prune127.0ms (1.3%)

Memory

1.8MiB live, 51.0MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	433	8	441

Accuracy

100.0%

Counts

441 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	46.6%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x))
✓	60.1%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	56.6%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	4.3%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
✓	46.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
✓	43.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* 1/2 (+ (* (pow eps 4) (/ 5/64 (pow x 6))) eps)) (+ (* (* 1/8 (/ eps x)) (/ eps x)) (* (pow eps 3) (/ 1/16 (pow x 4))))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) eps)) x))

Compiler

Compiled 317 to 144 computations (54.6% saved)

regimes445.0ms (4.6%)

Memory

-17.3MiB live, 21.3MiB allocated

Counts

18 → 1

Calls

Call 1

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

Calls

3 calls:

432.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
6.0ms	x
6.0ms	eps

Results

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

Compiler

Compiled 10 to 10 computations (0% saved)

regimes10.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

8 → 2

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
89.1%	2	`x`
83.0%	2	`eps`
99.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
98.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
98.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) 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
97.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes444.0ms (4.6%)

Memory

-30.6MiB live, 9.2MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

439.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
56.6%	1	`eps`
56.6%	1	`x`
58.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes6.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0221228359761618e-154	-1.1586129981690966e-160

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0221228359761618e-154	-1.1586129981690966e-160

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0221228359761618e-154	-1.1586129981690966e-160

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0221228359761618e-154	-1.1586129981690966e-160

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0221228359761618e-154	-1.1586129981690966e-160

Compiler

Compiled 11 to 11 computations (0% saved)

simplify471.0ms (4.9%)

Memory

2.3MiB live, 40.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	245
1	59	245
2	68	245
3	73	245
4	75	245

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))

Outputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))

soundness1.3s (13.6%)

Memory

15.0MiB live, 733.0MiB 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	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	619	5235
1	1967	4651
2	6761	4205
0	8541	3980
0	45	277
0	78	277
1	313	273
2	2433	273
0	9600	269
0	675	6994
1	2161	6536
2	7431	6522
0	8059	6198

Stop Event

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

Compiler

Compiled 367 to 178 computations (51.5% saved)

preprocess53.0ms (0.5%)

Memory: 13.2MiB live, 130.5MiB allocated
Compiler: Compiled 308 to 98 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze14.0ms (0.1%)

sample1.7s (17.1%)

explain170.0ms (1.8%)

preprocess30.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.1%)

localize33.0ms (0.3%)

series9.0ms (0.1%)

simplify210.0ms (2.2%)

rewrite152.0ms (1.6%)

eval57.0ms (0.6%)

prune12.0ms (0.1%)

simplify139.0ms (1.4%)

localize194.0ms (2%)

series95.0ms (1%)

simplify201.0ms (2.1%)

rewrite270.0ms (2.8%)

eval598.0ms (6.2%)

prune59.0ms (0.6%)

simplify186.0ms (1.9%)

localize305.0ms (3.1%)

series92.0ms (0.9%)

simplify189.0ms (1.9%)

rewrite206.0ms (2.1%)

eval284.0ms (2.9%)

prune138.0ms (1.4%)

simplify211.0ms (2.2%)

localize234.0ms (2.4%)

series22.0ms (0.2%)

simplify217.0ms (2.2%)

rewrite440.0ms (4.5%)

eval378.0ms (3.9%)

prune127.0ms (1.3%)

regimes445.0ms (4.6%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes444.0ms (4.6%)

regimes6.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify471.0ms (4.9%)

soundness1.3s (13.6%)

preprocess53.0ms (0.5%)

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