Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze105.0ms (0.9%)

Memory

-23.3MiB live, 15.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.5s (13.9%)

Memory

-0.4MiB live, 1 609.0MiB allocated

Samples

497.0ms	2 729×	1	valid
377.0ms	4 908×	0	valid
137.0ms	619×	2	valid
88.0ms	160×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 649.0ms

ival-<=: 175.0ms (27% of total)

ival-sqrt: 127.0ms (19.6% of total)

ival-sub: 113.0ms (17.4% of total)

ival-mult: 112.0ms (17.3% of total)

adjust: 76.0ms (11.7% of total)

ival-and: 25.0ms (3.9% of total)

exact: 17.0ms (2.6% of total)

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

Bogosity

explain110.0ms (1%)

Memory

3.9MiB live, 164.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
108	-	-	`(-.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	108	0

Confusion

	Predicted +	Predicted -
+	108	0
-	0	148

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	108	0	0
-	0	0	148

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	148
1	108

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms	162×	1	valid
15.0ms	306×	0	valid
6.0ms	44×	2	valid

Compiler

Compiled 62 to 22 computations (64.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 16.0ms (48.7% of total)

ival-sub: 7.0ms (21.3% of total)

ival-sqrt: 6.0ms (18.3% of total)

adjust: 4.0ms (12.2% of total)

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

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

preprocess59.0ms (0.5%)

Memory

17.9MiB live, 53.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify19.0ms (0.2%)

Memory

-17.8MiB live, 26.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize34.0ms (0.3%)

Memory

-10.6MiB live, 63.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.321251506026215	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

12.0ms	153×	0	valid
8.0ms	81×	1	valid
3.0ms	22×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sub: 7.0ms (48.9% of total)

ival-sqrt: 3.0ms (21% of total)

ival-mult: 3.0ms (21% of total)

adjust: 2.0ms (14% of total)

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

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

series9.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

simplify260.0ms (2.3%)

Memory

-9.4MiB live, 386.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 82

Calls

Call 1

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

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

rewrite550.0ms (4.9%)

Memory

26.9MiB live, 293.7MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 224

Calls

Call 1

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

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

eval44.0ms (0.4%)

Memory: -16.5MiB live, 103.0MiB allocated
Compiler: Compiled 9 677 to 1 047 computations (89.2% saved)

prune126.0ms (1.1%)

Memory

-59.2MiB live, 152.1MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	293	13	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	13	307

Accuracy

99.8%

Counts

307 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.7%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	61.6%	(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	45.6%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
	36.2%	(/.f64 (.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (-.f64 (.f64 x x) eps))))
	61.5%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
▶	62.0%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	7.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
▶	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	3.3%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) #s(literal -1 binary64)))
	42.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x))
	44.4%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
▶	27.9%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))

Compiler

Compiled 608 to 232 computations (61.8% saved)

simplify188.0ms (1.7%)

Memory

32.5MiB live, 222.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

9 076×	`lower-fma.f32`
9 066×	`lower-fma.f64`
5 632×	`lower-*.f32`
5 626×	`lower-*.f64`
2 096×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	255
0	66	236
1	121	236
2	213	231
3	371	229
4	560	229
5	1728	229
6	6888	229
0	8045	229

Stop Event

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

Calls

Call 1

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

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

localize142.0ms (1.3%)

Memory

4.2MiB live, 286.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	5.981114161847521	(fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))
accuracy	6.193757096033219	(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	35.94594764414926	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))
accuracy	41.69373005710086	(fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.02734375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.2890625	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	23.99314660900119	(-.f64 (fma.f64 x x eps) (*.f64 x x))
accuracy	0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	0.13671875	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
accuracy	24.321251506026215	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
accuracy	35.17692422530545	#s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
accuracy	0	(neg.f64 x)
accuracy	24.321251506026215	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.41001929635387	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0	(fma.f64 x x (neg.f64 eps))
accuracy	0	(neg.f64 eps)
accuracy	0.0078125	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
accuracy	24.321251506026215	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

Samples

49.0ms	153×	0	valid
35.0ms	81×	1	valid
15.0ms	22×	2	valid

Compiler

Compiled 227 to 35 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 13.0ms (20.8% of total)

ival-add: 12.0ms (19.2% of total)

ival-div: 11.0ms (17.6% of total)

adjust: 8.0ms (12.8% of total)

ival-sub: 7.0ms (11.2% of total)

ival-sqrt: 6.0ms (9.6% of total)

ival-pow: 3.0ms (4.8% of total)

ival-neg: 2.0ms (3.2% of total)

exact: 1.0ms (1.6% of total)

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

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

series95.0ms (0.9%)

Memory

-24.8MiB live, 100.9MiB allocated

Counts

21 → 456

Calls

Call 1

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

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

Calls

114 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	-inf	(+ (* eps (/ -1/2 x)) x)
3.0ms	x	@	-inf	(* eps (+ (* eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)))
1.0ms	x	@	inf	(/ -1/2 x)
1.0ms	eps	@	inf	(/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps))))
1.0ms	eps	@	0	(* eps (+ (* eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)))

simplify269.0ms (2.4%)

Memory

42.8MiB live, 417.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 708×	`lower-fma.f64`
9 708×	`lower-fma.f32`
6 220×	`lower-*.f64`
6 220×	`lower-*.f32`
2 380×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	527	7046
1	1649	6885
2	5536	6770
0	8580	6374

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 418

Calls

Call 1

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

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

rewrite407.0ms (3.7%)

Memory

0.4MiB live, 633.0MiB allocated

Rules

5 676×	`lower-*.f32`
5 670×	`lower-*.f64`
4 926×	`lower-/.f32`
4 916×	`lower-/.f64`
3 702×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	210
0	66	202
1	284	202
2	2215	202
0	9871	202

Stop Event

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

Counts

21 → 702

Calls

Call 1

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

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

eval269.0ms (2.4%)

Memory: 2.3MiB live, 367.7MiB allocated
Compiler: Compiled 45 665 to 3 248 computations (92.9% saved)

prune201.0ms (1.8%)

Memory

-2.1MiB live, 348.6MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	1 148	8	1 156
Fresh	6	2	8
Picked	2	3	5
Done	0	0	0
Total	1 156	13	1 169

Accuracy

100.0%

Counts

1 169 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.3%	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	61.4%	(/.f64 (fma.f64 x x (-.f64 eps (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
	25.2%	(/.f64 (/.f64 (-.f64 (.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (fma.f64 x x eps))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (fma.f64 x x eps) (fma.f64 x x eps) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (fma.f64 x x eps) (.f64 x (neg.f64 x)))))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	99.6%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	61.5%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	62.0%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
▶	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	42.1%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x))
	44.4%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
	39.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps (fma.f64 eps #s(approx (+ ( eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x)))) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))))
▶	42.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps #s(approx (+ ( eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))

Compiler

Compiled 452 to 210 computations (53.5% saved)

simplify275.0ms (2.5%)

Memory

-23.2MiB live, 283.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 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 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	896	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
cost-diff	0	(/.f64 (.f64 eps eps) (.f64 x x))
cost-diff	0	(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x))
cost-diff	320	(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (+ (* eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
cost-diff	0	(.f64 eps #s(approx (+ ( eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps #s(approx (+ ( eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) 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 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
cost-diff	192	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	832	(-.f64 (.f64 x x) (.f64 x x))

Rules

13 736×	`lower-fma.f32`
13 728×	`lower-fma.f64`
2 920×	`lower-*.f32`
2 912×	`lower-*.f64`
2 550×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	362
0	81	333
1	149	313
2	242	307
3	827	307
4	4749	307
0	8510	301

Stop Event

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

Calls

Call 1

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

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

localize171.0ms (1.5%)

Memory

15.5MiB live, 244.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.02734375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.28515625	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.35973430226206016	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
accuracy	0.00390625	(fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))
accuracy	0.1015625	(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
accuracy	23.653139386257212	(/.f64 (.f64 eps eps) (.f64 x x))
accuracy	36.88208531736485	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x))
accuracy	6.0843820960332184	(.f64 eps #s(approx (+ ( eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
accuracy	14.812593897362527	(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy	35.94594764414926	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 eps #s(approx (+ ( eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
accuracy	37.29333560609159	#s(approx (+ (* eps (+ (* eps (/ 1/16 (pow x 5))) (/ 1/8 (* x (* x x))))) (/ 1/2 x)) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0.38228482406588793	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	1.7086581791578765	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.02734375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.28515625	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Samples

45.0ms	154×	0	valid
42.0ms	102×	1	exit

Compiler

Compiled 293 to 44 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 18.0ms (27.4% of total)

ival-div: 16.0ms (24.4% of total)

ival-add: 10.0ms (15.2% of total)

adjust: 8.0ms (12.2% of total)

ival-sub: 5.0ms (7.6% of total)

ival-pow: 3.0ms (4.6% of total)

ival-sqrt: 2.0ms (3% of total)

ival-neg: 2.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series54.0ms (0.5%)

Memory

-24.0MiB live, 60.8MiB allocated

Counts

24 → 528

Calls

Call 1

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

Outputs
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 0 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) (.f64 x x)) (patch (-.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
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#s(alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) (taylor -inf eps) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (/ eps (pow x 2))) (taylor 0 x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor inf x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor -inf x) (#s(alt (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x 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 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

132 calls:

Time	Variable		Point	Expression
17.0ms	eps	@	0	(/ (* eps eps) (* x x))
1.0ms	eps	@	inf	(/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
1.0ms	eps	@	-inf	(/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
1.0ms	eps	@	0	(/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps))))
1.0ms	eps	@	inf	(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)

simplify314.0ms (2.8%)

Memory

48.0MiB live, 469.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 020×	`lower-fma.f64`
9 020×	`lower-fma.f32`
5 738×	`lower-*.f64`
5 738×	`lower-*.f32`
3 148×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	629	7436
1	2013	6972
2	7019	6711
0	8475	6365

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 483

Calls

Call 1

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

rewrite315.0ms (2.8%)

Memory

-14.2MiB live, 606.7MiB allocated

Rules

5 872×	`lower-*.f32`
5 864×	`lower-*.f64`
4 622×	`lower-fma.f32`
4 614×	`lower-fma.f64`
3 672×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	309
0	81	270
1	352	252
2	2716	252
0	8974	246

Stop Event

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

Counts

24 → 588

Calls

Call 1

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

Outputs
#s(literal 0 binary64)
eps
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(.f64 (pow.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (-.f64 (.f64 x x) eps))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x)))) #s(literal 1 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (fma.f64 x x eps))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x eps) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (fma.f64 x x eps)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) (neg.f64 eps))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) (neg.f64 eps))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)))) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))))) (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (fma.f64 x x eps))))))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal 8 binary64))))
(+.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal 8 binary64))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) eps) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) eps #s(literal 1/2 binary64))
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (.f64 eps #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal 8 binary64))) (.f64 eps #s(literal 1/8 binary64))) (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))))
(/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (.f64 x x))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal 8 binary64)))))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))))))
(.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps #s(literal 1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))

eval209.0ms (1.9%)

Memory: 15.2MiB live, 387.3MiB allocated
Compiler: Compiled 33 293 to 2 233 computations (93.3% saved)

prune261.0ms (2.3%)

Memory

-13.9MiB live, 383.0MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	1 317	6	1 323
Fresh	5	0	5
Picked	4	1	5
Done	0	3	3
Total	1 326	10	1 336

Accuracy

100.0%

Counts

1 336 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	45.8%	(/.f64 (.f64 eps eps) (.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))
▶	99.6%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	62.0%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
▶	42.3%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))
▶	44.4%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
▶	4.5%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(literal 0 binary64))

Compiler

Compiled 176 to 105 computations (40.3% saved)

simplify460.0ms (4.1%)

Memory

-13.4MiB live, 290.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

15 990×	`lower-fma.f32`
15 988×	`lower-fma.f64`
3 076×	`lower-*.f32`
3 068×	`lower-*.f64`
2 162×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	234
0	51	269
1	91	259
2	141	209
3	283	189
4	456	189
5	1344	189
6	4203	189
0	8592	189

Stop Event

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

Calls

Call 1

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

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

localize847.0ms (7.6%)

Memory

-0.2MiB live, 160.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.1328125	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy	5.729080943229637	(.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
accuracy	14.812593897362527	(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
accuracy	36.88208531736485	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.02734375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.16015625	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.27734375	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
accuracy	0	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 1/2 binary64))
accuracy	35.6045118366583	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
accuracy	61.121655759184485	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(literal 0 binary64))
accuracy	0.0078125	(-.f64 (*.f64 x x) eps)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.02734375	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.2890625	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Samples

38.0ms	154×	0	valid
25.0ms	83×	1	valid
8.0ms	19×	2	valid

Compiler

Compiled 214 to 28 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 21.0ms (42.2% of total)

ival-div: 11.0ms (22.1% of total)

ival-add: 6.0ms (12.1% of total)

adjust: 5.0ms (10% of total)

ival-sub: 3.0ms (6% of total)

ival-sqrt: 2.0ms (4% of total)

ival-neg: 1.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series426.0ms (3.8%)

Memory

0.3MiB live, 37.8MiB allocated

Counts

16 → 360

Calls

Call 1

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

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

Calls

90 calls:

Time	Variable		Point	Expression
403.0ms	x	@	inf	(* eps (+ (* eps (/ 1/8 (* x x))) 1/2))
1.0ms	eps	@	-inf	(/ 1 (+ x (sqrt (- (* x x) eps))))
1.0ms	x	@	0	(/ 1 (+ x (sqrt (- (* x x) eps))))
1.0ms	x	@	-inf	(/ 1 (+ x (sqrt (- (* x x) eps))))
0.0ms	eps	@	inf	(/ (* eps 1/2) x)

simplify1.6s (14.3%)

Memory

13.5MiB live, 326.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 116×	`lower-fma.f64`
10 116×	`lower-fma.f32`
5 954×	`lower-*.f64`
5 954×	`lower-*.f32`
3 468×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	621	6802
1	1987	5906
2	7171	5880
0	8071	5604

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 344

Calls

Call 1

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

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

rewrite312.0ms (2.8%)

Memory

-13.5MiB live, 615.6MiB allocated

Rules

5 276×	`lower-fma.f32`
5 274×	`lower-fma.f64`
4 946×	`lower-/.f32`
4 936×	`lower-/.f64`
3 840×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	193
0	51	196
1	196	190
2	1391	152
0	8482	152

Stop Event

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

Counts

16 → 635

Calls

Call 1

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

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

eval185.0ms (1.7%)

Memory: 32.3MiB live, 471.9MiB allocated
Compiler: Compiled 35 865 to 3 021 computations (91.6% saved)

prune191.0ms (1.7%)

Memory

-15.9MiB live, 438.9MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	1 239	2	1 241
Fresh	1	0	1
Picked	0	5	5
Done	0	4	4
Total	1 240	11	1 251

Accuracy

100.0%

Counts

1 251 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	61.0%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
	45.1%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))))
✓	62.0%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.0%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) eps)
✓	42.3%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x))
✓	44.4%	#s(approx (/ (- (+ (* x x) eps) (* x x)) (+ x (sqrt (- (* x x) eps)))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
✓	4.5%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(literal 0 binary64))

Compiler

Compiled 654 to 178 computations (72.8% saved)

regimes53.0ms (0.5%)

Memory

-8.0MiB live, 29.4MiB allocated

Counts

30 → 1

Calls

Call 1

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

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

Calls

3 calls:

34.0ms	eps
9.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
9.0ms	x

Results

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes13.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

11 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
93.2%	2	`x`
81.0%	2	`eps`
98.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes4.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

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

Results

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

Compiler

Compiled 10 to 6 computations (40% saved)

regimes95.0ms (0.9%)

Memory

-31.3MiB live, 5.0MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

94.0ms

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

Results

Accuracy	Segments	Branch
97.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes6.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
57.8%	1	`eps`
57.8%	1	`x`
59.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes5.0ms (0%)

Memory

7.6MiB live, 7.6MiB allocated

Accuracy

Total -0.9b remaining (-1.5%)

Threshold costs -0.9b (-1.5%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.512573772245234e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.512573772245234e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.512573772245234e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.512573772245234e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify8.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	201
1	52	201
2	61	201
3	66	201
4	68	201

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness861.0ms (7.7%)

Memory

13.5MiB live, 686.9MiB allocated

Rules

11 222×	`lower-fma.f64`
11 222×	`lower-fma.f32`
10 116×	`lower-fma.f64`
10 116×	`lower-fma.f32`
9 020×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	621	6802
1	1987	5906
2	7171	5880
0	8071	5604
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	629	7436
1	2013	6972
2	7019	6711
0	8475	6365
0	38	210
0	66	202
1	284	202
2	2215	202
0	9871	202
0	257	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129

Stop Event

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

Compiler

Compiled 368 to 145 computations (60.6% saved)

preprocess61.0ms (0.5%)

Memory: 3.0MiB live, 119.2MiB allocated
Compiler: Compiled 270 to 78 computations (71.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze105.0ms (0.9%)

sample1.5s (13.9%)

explain110.0ms (1%)

preprocess59.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize34.0ms (0.3%)

series9.0ms (0.1%)

simplify260.0ms (2.3%)

rewrite550.0ms (4.9%)

eval44.0ms (0.4%)

prune126.0ms (1.1%)

simplify188.0ms (1.7%)

localize142.0ms (1.3%)

series95.0ms (0.9%)

simplify269.0ms (2.4%)

rewrite407.0ms (3.7%)

eval269.0ms (2.4%)

prune201.0ms (1.8%)

simplify275.0ms (2.5%)

localize171.0ms (1.5%)

series54.0ms (0.5%)

simplify314.0ms (2.8%)

rewrite315.0ms (2.8%)

eval209.0ms (1.9%)

prune261.0ms (2.3%)

simplify460.0ms (4.1%)

localize847.0ms (7.6%)

series426.0ms (3.8%)

simplify1.6s (14.3%)

rewrite312.0ms (2.8%)

eval185.0ms (1.7%)

prune191.0ms (1.7%)

regimes53.0ms (0.5%)

regimes13.0ms (0.1%)

regimes4.0ms (0%)

regimes95.0ms (0.9%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness861.0ms (7.7%)

preprocess61.0ms (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