Metrics for bug333 (missed optimization)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.8s (17.7%)

Memory

35.8MiB live, 2 403.2MiB allocated

Samples

744.0ms	3 107×	2	valid
648.0ms	4 873×	1	valid
33.0ms	276×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 329.0ms (28% of total)

ival-sub: 302.0ms (25.7% of total)

adjust: 256.0ms (21.8% of total)

ival-add: 208.0ms (17.7% of total)

ival-<=: 44.0ms (3.7% of total)

ival-assert: 15.0ms (1.3% of total)

ival-and: 11.0ms (0.9% of total)

exact: 10.0ms (0.9% of total)

Bogosity

explain136.0ms (1.3%)

Memory

-19.0MiB live, 248.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
253	-	-	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
0	-	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`
0	-	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`	cancellation	253	0

Confusion

	Predicted +	Predicted -
+	253	0
-	0	3

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	0	0	3

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	3
1	253

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms	218×	2	valid
34.0ms	276×	1	valid
1.0ms	18×	0	valid

Compiler

Compiled 64 to 25 computations (60.9% saved)

Precisions

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

ival-sqrt: 18.0ms (34.8% of total)

adjust: 13.0ms (25.1% of total)

ival-sub: 13.0ms (25.1% of total)

ival-add: 6.0ms (11.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess25.0ms (0.2%)

Memory

6.6MiB live, 45.2MiB allocated

Algorithm

1×	egg-herbie

Rules

92×	`lower-fma.f64`
92×	`lower-fma.f32`
64×	`lower-+.f32`
62×	`lower-+.f64`
56×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	22	19
2	52	18
3	101	18
4	163	18
5	237	18
6	264	18
7	272	18
0	7	9
0	12	9
1	19	9
2	26	9
3	37	9
4	51	9
5	74	9
6	114	9
7	149	9
8	196	9
9	211	9
10	219	9
0	219	9

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Symmetry

(negabs x)

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify11.0ms (0.1%)

Memory

-25.7MiB live, 16.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Rules

92×	`lower-fma.f64`
92×	`lower-fma.f32`
64×	`lower-+.f32`
62×	`lower-+.f64`
56×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
0	12	25
1	19	25
2	26	25
3	37	25
4	51	25
5	74	25
6	114	25
7	149	25
8	196	25
9	211	25
10	219	25
0	219	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

Outputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize46.0ms (0.4%)

Memory

26.9MiB live, 104.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.50269754198558	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

18.0ms	109×	2	valid
16.0ms	138×	1	valid
0.0ms	9×	0	valid

Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions

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

ival-sqrt: 9.0ms (36.7% of total)

adjust: 6.0ms (24.4% of total)

ival-sub: 6.0ms (24.4% of total)

ival-add: 3.0ms (12.2% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

-27.9MiB live, 11.3MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
1.0ms	x	@	-inf	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms	x	@	0	(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
0.0ms	x	@	-inf	(sqrt (+ 1 x))
0.0ms	x	@	inf	(sqrt (- 1 x))

simplify376.0ms (3.6%)

Memory

30.5MiB live, 334.5MiB allocated

Algorithm

1×	egg-herbie

Rules

21 484×	`lower-fma.f64`
21 484×	`lower-fma.f32`
4 942×	`lower-+.f64`
4 942×	`lower-+.f32`
4 596×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	971
1	493	856
2	1729	798
3	7219	798
0	8083	746

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 45

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (+.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (neg.f64 x) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(neg.f64 (.f64 x (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (-.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(neg.f64 (.f64 x (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))

rewrite241.0ms (2.3%)

Memory

-18.9MiB live, 140.4MiB allocated

Rules

3 412×	`lower-fma.f64`
3 412×	`lower-fma.f32`
2 124×	`lower-*.f64`
2 124×	`lower-*.f32`
1 648×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	12	20
1	51	20
2	368	20
3	5664	20
0	9321	20

Stop Event

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

Counts

4 → 331

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))

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

eval98.0ms (0.9%)

Memory: 17.3MiB live, 102.7MiB allocated
Compiler: Compiled 9 873 to 1 183 computations (88% saved)

prune93.0ms (0.9%)

Memory

10.1MiB live, 87.9MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	372	4	376
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	372	5	377

Accuracy

100.0%

Counts

377 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.6%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
✓	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
▶	99.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
▶	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))

Compiler

Compiled 74 to 41 computations (44.6% saved)

simplify430.0ms (4.1%)

Memory

-17.2MiB live, 185.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
cost-diff	0	(*.f64 x #s(literal 1/8 binary64))
cost-diff	0	(.f64 x (.f64 x #s(literal 1/8 binary64)))
cost-diff	0	(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))

Rules

17 068×	`lower-fma.f32`
17 056×	`lower-fma.f64`
4 496×	`lower-*.f32`
4 480×	`lower-*.f64`
2 418×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	251
0	61	251
1	124	251
2	259	245
3	496	245
4	831	245
5	1202	245
6	1558	245
7	2051	245
8	2858	245
9	3990	245
10	5002	245
11	5415	245
12	5436	245
13	5450	245
14	6086	245
15	6356	245
16	7098	245
17	7949	245
0	8013	239

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
x
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(*.f64 x x)
x
(.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(*.f64 x #s(literal 7/128 binary64))
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
(*.f64 x x)
x
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
x
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x (*.f64 x x)) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(fma.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x (*.f64 x x)) x)
(*.f64 x x)
x
(.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(.f64 x (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)))
(fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(*.f64 x #s(literal 7/128 binary64))
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
(fma.f64 x (.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))) x)
(*.f64 x x)
x
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))

localize226.0ms (2.2%)

Memory

19.0MiB live, 96.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.03515625	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
accuracy	58.50269754198558	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)))
accuracy	0.09765625	(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
accuracy	0.31119811089277843	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 7/128 binary64))
accuracy	0.015625	(.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
accuracy	0.40095890609372625	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
accuracy	0	(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
accuracy	0	(.f64 x (.f64 x #s(literal 1/8 binary64)))
accuracy	0	(*.f64 x #s(literal 1/8 binary64))
accuracy	0.5637198809857296	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))

Samples

126.0ms	104×	2	valid
49.0ms	131×	1	valid
9.0ms	12×	3	valid
2.0ms	9×	0	valid

Compiler

Compiled 225 to 37 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-add: 62.0ms (39.4% of total)

ival-sub: 29.0ms (18.4% of total)

adjust: 23.0ms (14.6% of total)

ival-mult: 22.0ms (14% of total)

ival-sqrt: 16.0ms (10.2% of total)

ival-div: 5.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series649.0ms (6.2%)

Memory

-18.5MiB live, 19.6MiB allocated

Counts

19 → 228

Calls

Call 1

Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) (patch (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) (patch (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x) (patch (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) (patch (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 7/128 binary64)) (patch (.f64 x #s(literal 7/128 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) (patch (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 3)) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) (patch (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (.f64 x #s(literal 1/8 binary64))) (patch (.f64 x (.f64 x #s(literal 1/8 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/8 binary64)) (patch (.f64 x #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 3/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())

Calls

57 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* x (+ (* x (* x (+ (* (* x x) 33/1024) 7/128))) 1/8))
1.0ms	x	@	inf	(sqrt (/ 1 (+ 1 x)))
1.0ms	x	@	0	(+ (* x (* x (* x 1/8))) x)
0.0ms	x	@	-inf	(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)
0.0ms	x	@	inf	(+ (* (* x x) (* x (+ (* x (* x 7/128)) 1/8))) x)

simplify681.0ms (6.5%)

Memory

2.4MiB live, 366.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 696×	`lower-fma.f64`
14 696×	`lower-fma.f32`
6 058×	`lower-+.f64`
6 058×	`lower-+.f32`
3 876×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	283	3587
1	878	3221
2	2741	3010
0	8136	2855

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 219

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (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))
(* 1/8 (pow x 2))
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(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)
(* 1/8 x)
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 3))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 3))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(* 1/8 x)
(* x (+ 1/8 (* 7/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* x (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 5))
(* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 5))
(* (pow x 5) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* 7/128 x)
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- x 1)))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(/ 1 x)
(/ (- 1 (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (-.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x 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))
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (+.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (-.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 x (.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(* 7/128 (pow x 5))
(*.f64 #s(literal 7/128 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* 7/128 (pow x 5))
(*.f64 #s(literal 7/128 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 7/128 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 x x)) #s(literal -7/128 binary64)) (neg.f64 (pow.f64 x #s(literal 5 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(.f64 (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 x x)) #s(literal -7/128 binary64)) (neg.f64 (pow.f64 x #s(literal 5 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)
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(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* 33/1024 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* 33/1024 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 33/1024 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(fma.f64 x x (-.f64 #s(literal 1 binary64) x))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(fma.f64 x (fma.f64 x (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (.f64 x (*.f64 x x))))

rewrite290.0ms (2.8%)

Memory

13.1MiB live, 408.7MiB allocated

Rules

5 540×	`lower-fma.f32`
5 528×	`lower-fma.f64`
4 888×	`lower-*.f32`
4 872×	`lower-*.f64`
4 174×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	200
0	61	198
1	258	175
2	1919	175
0	9136	168

Stop Event

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

Counts

19 → 503

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(*.f64 x #s(literal 1/8 binary64))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x)
(*.f64 x x)
(.f64 x (fma.f64 x (.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x)
(.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 x #s(literal 7/128 binary64))
(.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
(+.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(+.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64)))) x)
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))) (neg.f64 x))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64)))))) (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (-.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 x x) x)
(fma.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) x x)
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/8 binary64)) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) (neg.f64 x)) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) (neg.f64 x)) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (*.f64 x x)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))) (fma.f64 x (-.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal 1/64 binary64))))
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(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 35937/1073741824 binary64) #s(literal 343/2097152 binary64)) x) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) (-.f64 #s(literal 49/16384 binary64) (.f64 (*.f64 x x) #s(literal 231/131072 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) #s(literal -49/16384 binary64)) x) (fma.f64 x (*.f64 x #s(literal 33/1024 binary64)) #s(literal -7/128 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 35937/1073741824 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (-.f64 (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (*.f64 x #s(literal 7/128 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (.f64 x #s(literal 7/128 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 35937/1073741824 binary64) #s(literal 343/2097152 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) (-.f64 #s(literal 49/16384 binary64) (.f64 (*.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) #s(literal -49/16384 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal 33/1024 binary64)) #s(literal -7/128 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 35937/1073741824 binary64) #s(literal 343/2097152 binary64)) x)) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) (-.f64 #s(literal 49/16384 binary64) (.f64 (*.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1089/1048576 binary64) #s(literal -49/16384 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal 33/1024 binary64)) #s(literal -7/128 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/2097152 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 35937/1073741824 binary64)))) (fma.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x #s(literal 7/128 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 33/1024 binary64))))) (.f64 (.f64 x #s(literal 7/128 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 33/1024 binary64))))))))
(.f64 x (fma.f64 x (.f64 x #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)) x)
(exp.f64 (neg.f64 (log1p.f64 x)))
(exp.f64 (fma.f64 (neg.f64 (log1p.f64 x)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log1p.f64 x)) #s(literal 1/2 binary64))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x))) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(fabs.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))

eval115.0ms (1.1%)

Memory: -1.8MiB live, 239.1MiB allocated
Compiler: Compiled 25 733 to 2 440 computations (90.5% saved)

prune157.0ms (1.5%)

Memory

-10.2MiB live, 270.0MiB allocated

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	879	8	887
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	880	12	892

Accuracy

100.0%

Counts

892 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.7%	(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
	8.6%	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	8.7%	(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
	8.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
	8.8%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
▶	8.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
✓	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
✓	99.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
▶	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
▶	6.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))

Compiler

Compiled 381 to 184 computations (51.7% saved)

simplify187.0ms (1.8%)

Memory

8.0MiB live, 217.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
cost-diff	128	(fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	576	(+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 x (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
cost-diff	512	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
cost-diff	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
cost-diff	0	(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
cost-diff	0	#s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
cost-diff	0	(*.f64 x #s(literal 1/8 binary64))
cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))

Rules

8 180×	`lower-fma.f32`
8 170×	`lower-fma.f64`
2 146×	`lower-*.f32`
2 132×	`lower-*.f64`
1 880×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	367
0	77	361
1	135	349
2	256	345
3	612	337
4	1440	337
5	2982	337
6	4894	321
7	7522	321
0	8051	312

Stop Event

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

Calls

Call 1

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

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

localize282.0ms (2.7%)

Memory

-8.2MiB live, 342.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.171875	(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
accuracy	58.338122462149386	(fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
accuracy	0.01953125	(-.f64 (fma.f64 x x #s(literal 1 binary64)) x)
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.49822652926811	(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy	0.00390625	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
accuracy	58.50269754198558	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
accuracy	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	0.06640625	(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
accuracy	0.5637198809857296	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
accuracy	59.85298946452544	#s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x))))
accuracy	0	(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
accuracy	0	(*.f64 x #s(literal 1/8 binary64))
accuracy	0.01171875	(.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)
accuracy	0.5637198809857296	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))

Samples

108.0ms	99×	2	valid
63.0ms	110×	1	valid
43.0ms	39×	3	valid
2.0ms	8×	0	valid

Compiler

Compiled 347 to 41 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 174.0ms

ival-sqrt: 46.0ms (26.4% of total)

adjust: 34.0ms (19.5% of total)

ival-mult: 31.0ms (17.8% of total)

ival-div: 24.0ms (13.8% of total)

ival-add: 19.0ms (10.9% of total)

ival-sub: 16.0ms (9.2% of total)

ival-neg: 3.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.3%)

Memory

24.5MiB live, 62.4MiB allocated

Counts

26 → 312

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())

Calls

78 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(+ (* (- 1 x) (neg (sqrt (- 1 x)))) (* (+ 1 x) (sqrt (+ 1 x))))
2.0ms	x	@	0	(+ (* (- 1 x) (neg (sqrt (- 1 x)))) (* (+ 1 x) (sqrt (+ 1 x))))
2.0ms	x	@	inf	(/ (+ (* (- 1 x) (neg (sqrt (- 1 x)))) (* (+ 1 x) (sqrt (+ 1 x)))) (+ (- 1 x) (- (+ 1 x) (* (neg (sqrt (- 1 x))) (sqrt (+ 1 x))))))
1.0ms	x	@	-inf	(/ (+ (* (- 1 x) (neg (sqrt (- 1 x)))) (* (+ 1 x) (sqrt (+ 1 x)))) (+ (- 1 x) (- (+ 1 x) (* (neg (sqrt (- 1 x))) (sqrt (+ 1 x))))))
1.0ms	x	@	-inf	(+ (* (- 1 x) (neg (sqrt (- 1 x)))) (* (+ 1 x) (sqrt (+ 1 x))))

simplify257.0ms (2.5%)

Memory

-35.6MiB live, 215.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 878×	`lower-fma.f64`
9 878×	`lower-fma.f32`
4 866×	`lower-+.f64`
4 866×	`lower-+.f32`
4 806×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	634	5716
1	2041	4988
2	7107	4967
0	8004	4675

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 303

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 1/8 (pow x 3))
(* 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))
1
(+ 1 x)
(+ 1 (* x (+ 1 x)))
(+ 1 (* x (+ 1 (* x (+ 1 x)))))
(/ -1 x)
(* -1 (/ (+ 1 (/ 1 x)) x))
(/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x)
(/ (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) x)
(/ -1 x)
(* -1 (/ (+ 1 (/ 1 x)) x))
(* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x))) x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 (pow x 3)))
(+ 1 (* (pow x 3) (+ 1/2 (* -1/8 (pow x 3)))))
(+ 1 (* (pow x 3) (+ 1/2 (* (pow x 3) (- (* 1/16 (pow x 3)) 1/8)))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 7))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 13)))) (* 1/2 (sqrt (/ 1 (pow x 7)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 13)))) (+ (* 1/16 (sqrt (/ 1 (pow x 19)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
1
(+ 1 (pow x 3))
(+ 1 (pow x 3))
(+ 1 (pow x 3))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(* (pow x 3) (+ 1 (/ 1 (pow x 3))))
(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)
3
(+ 3 (* -1/2 (pow x 2)))
(+ 3 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (- (* 2 (/ 1 x)) (* -1 (sqrt -1))))
(* x (- (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 2 (/ 1 x))) (* -1 (sqrt -1))))
(* x (- (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(* -1 (* x (sqrt -1)))
(* x (+ (* -1 (sqrt -1)) (* 2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 2 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (* -1 (sqrt -1)))))
(* -1 (* x (- (* -1 (/ (+ 2 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)) (* -1 (sqrt -1)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* -1/2 x))))
(+ 2 (* x (+ 1 (* x (- (* -1/8 (pow x 2)) 1/2)))))
(* x (- 1 (* -1 (sqrt -1))))
(* x (- (+ 1 (/ 1 x)) (* -1 (sqrt -1))))
(* x (- (+ 1 (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))) (* -1 (sqrt -1))))
(* x (- (+ 1 (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(* x (+ 1 (* -1 (sqrt -1))))
(* x (+ 1 (+ (* -1 (sqrt -1)) (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)) (+ 1 (* -1 (sqrt -1))))))
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)) (+ 1 (* -1 (sqrt -1))))))
(* 3 x)
(* x (+ 3 (* -1/8 (pow x 2))))
(* x (+ 3 (* (pow x 2) (- (* -3/128 (pow x 2)) 1/8))))
(* x (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -9/1024 (pow x 2)) 3/128)) 1/8))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* 3/2 (sqrt (/ 1 (pow x 3))))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1))))))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 1 (* 9/4 (/ x (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1))))))))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (+ (* -3/2 (* (sqrt x) (sqrt -1))) (* -1 (/ (+ (* -1/2 (* (sqrt x) (* (sqrt -1) (- 1 (* -9/4 x))))) (* 1/2 (* (sqrt x) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) x)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ (* x (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1))))) (sqrt -1))
(* x (+ (* -2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* x (pow (sqrt -1) 2)))) (+ (* -1 (sqrt (/ 1 x))) (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))
(* x (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (+ (* -1 (sqrt (/ 1 x))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (+ (* -4 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* (pow x 2) (pow (sqrt -1) 3)))) (* 2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* x (pow (sqrt -1) 2))))))))
(* x (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (+ (* -1 (sqrt (/ 1 x))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))) (+ (* -4 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* (pow x 2) (pow (sqrt -1) 3)))) (+ (* -1 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* (pow x 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (* x (pow (sqrt -1) 2)))) (* 2 (/ (- (+ (* -3/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -4 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (pow (sqrt -1) 3))) (* 1/2 (/ (+ (sqrt (/ 1 x)) (* -1 (* (sqrt (/ 1 x)) (sqrt -1)))) (pow (sqrt -1) 3))))) (* (pow x 3) (sqrt -1))))))))))
(* -1 (/ (* x (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (sqrt -1)))
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (+ (* 2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -3/2 (sqrt x)) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -4 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))) (* 1/2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))))) x)) (* 2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (/ (- (* -1 (/ (- (+ (* -3/2 (sqrt x)) (+ (* -1 (/ (- (+ (* -3/2 (sqrt x)) (* -3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 4))) (* 2 (/ (- (+ (* -3/2 (sqrt x)) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -4 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))) (* 1/2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))))) (sqrt -1))))) x)) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (* -4 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))) (* 1/2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 3))))) x)) (* 2 (/ (+ (* -1 (* (sqrt (/ 1 x)) (sqrt -1))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 3/8 x))))
(+ 1 (* x (+ 1/2 (* x (+ 3/8 (* 5/16 x))))))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 1 (* 1/4 (/ x (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 1 (* -1/4 x)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- x 1)))
(+ 1 (* x (- x 1)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* -1 (pow x 2)))))
(+ 1 (* x (+ 1 (* (pow x 2) (- (* -1 x) 1)))))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (- (+ 1 (/ 1 x)) (/ 1 (pow x 3))) (pow x 2))
(/ (+ 1 (+ (* -1 (/ (+ 1 (/ 1 x)) (pow x 3))) (/ 1 x))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (+ 1 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))) (pow x 2))
(/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))) 1) x))) (pow x 2))
1
(+ 1 (* 3/2 x))
(+ 1 (* x (+ 3/2 (* 3/8 x))))
(+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* 3/2 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5))))))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))) (*.f64 x x) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (-.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(neg.f64 (.f64 x (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) (neg.f64 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
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(* 1/8 x)
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(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 3/8 x))))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (+ 3/8 (* 5/16 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 5/16 binary64) #s(literal 3/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (sqrt (/ 1 x)) (sqrt -1))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 1 (* 1/4 (/ x (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (/.f64 (fma.f64 (/.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* (sqrt (/ 1 x)) (sqrt -1))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 1 (* -1/4 x)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))) (.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- x 1)))
(fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
(* (pow x 2) (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) x)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* -1 (pow x 2)))))
(fma.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* (pow x 2) (- (* -1 x) 1)))))
(fma.f64 x (fma.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x))
(/ (- (+ 1 (/ 1 x)) (/ 1 (pow x 3))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (*.f64 x x))
(/ (+ 1 (+ (* -1 (/ (+ 1 (/ 1 x)) (pow x 3))) (/ 1 x))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) (.f64 x (.f64 x x))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x))
(/ (+ 1 (* -1 (/ (- (/ 1 (pow x 2)) 1) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x)) (.f64 x x))
(/ (+ 1 (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))) 1) x))) (pow x 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) x)) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (* 3/8 x))))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal 3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 3/8 binary64)) #s(literal 3/2 binary64)) #s(literal 1 binary64))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* 3/2 (sqrt (/ 1 (pow x 3))))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5))))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(.f64 (.f64 x x) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 x x) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/2 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 x) #s(literal -3/2 binary64))) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

rewrite343.0ms (3.3%)

Memory

26.2MiB live, 288.9MiB allocated

Rules

7 700×	`lower-fma.f32`
7 690×	`lower-fma.f64`
5 152×	`lower-/.f32`
5 144×	`lower-/.f64`
3 818×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	295
0	77	247
1	318	219
2	2836	203
0	9569	199

Stop Event

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

Counts

26 → 1 606

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) x))
(+.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))))
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x)
(fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) x)
(fma.f64 (.f64 x #s(literal 1/8 binary64)) (.f64 x x) x)
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/8 binary64)) x)
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) x)
(fma.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) x x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/512 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))) (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/64 binary64)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))) (fma.f64 x x (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64))))) (neg.f64 (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/64 binary64))))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64))))) (neg.f64 (fma.f64 x x (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x))) (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) x) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)) x) (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/64 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))))) (neg.f64 (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -1 binary64))))
(pow.f64 (/.f64 (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x))) #s(literal -1 binary64))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))))))
(.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))) x)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))
(fma.f64 x (.f64 (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) x #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/8 binary64))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal 1 binary64)) (.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/64 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -1 binary64))))
(*.f64 x #s(literal 1/8 binary64))
(*.f64 #s(literal 1/8 binary64) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))))
#s(approx (+ (* x (* x (* x 1/8))) x) (.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x))))
(.f64 x (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x #s(literal 1/8 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64))
(.f64 (.f64 x (*.f64 x #s(literal 1/8 binary64))) x)
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/8 binary64))))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(.f64 x (.f64 (*.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/8 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(.f64 (.f64 x (*.f64 x #s(literal 1/8 binary64))) #s(literal 1 binary64))
(exp.f64 (*.f64 (log1p.f64 (neg.f64 x)) #s(literal -1 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (log1p.f64 (neg.f64 x))) (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (neg.f64 x))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 x x) (*.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
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(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 3 binary64)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 2 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (pow.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 (pow.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 3/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 3/2 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 3/2 binary64)) (pow.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 3 binary64)))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (-.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (.f64 x (.f64 x x)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (neg.f64 x) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (/.f64 (fma.f64 x (neg.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))))
(.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))

eval695.0ms (6.7%)

Memory: -121.7MiB live, 583.6MiB allocated
Compiler: Compiled 132 841 to 8 896 computations (93.3% saved)

prune358.0ms (3.4%)

Memory

13.3MiB live, 654.2MiB allocated

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	2 949	3	2 952
Fresh	0	3	3
Picked	3	2	5
Done	0	4	4
Total	2 952	12	2 964

Accuracy

100.0%

Counts

2 964 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.7%	(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
▶	8.6%	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	8.7%	(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 1 binary64) (-.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))
▶	8.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
▶	8.8%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
▶	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
✓	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
✓	99.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
✓	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
▶	98.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 328 to 163 computations (50.3% saved)

simplify317.0ms (3%)

Memory

6.0MiB live, 123.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	2944	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))

Rules

9 904×	`lower-fma.f32`
9 902×	`lower-fma.f64`
2 296×	`lower-*.f32`
2 292×	`lower-*.f64`
2 092×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	272
0	56	254
1	96	248
2	157	242
3	294	242
4	787	242
5	3358	242
6	5039	242
7	6493	242
8	7070	242
9	7345	242
10	7454	242
11	7454	242
12	7517	242
13	7563	242
14	7601	242
15	7603	242
16	7603	242
17	7868	242
0	8224	239

Stop Event

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

Calls

Call 1

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

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

localize241.0ms (2.3%)

Memory

0.5MiB live, 76.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy	0.01171875	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.37744467571626	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
accuracy	0.03515625	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
accuracy	58.48722252239432	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy	58.50269754198558	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.01171875	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.40352911484076	(-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
accuracy	0.01171875	(.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)
accuracy	0.5637198809857296	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))
accuracy	0.8254398617528156	#s(approx (+ (* x (* x 1/8)) 1) #s(literal 1 binary64))

Samples

82.0ms	138×	1	valid
66.0ms	109×	2	valid
2.0ms	9×	0	valid

Compiler

Compiled 259 to 31 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-div: 21.0ms (23.1% of total)

adjust: 18.0ms (19.8% of total)

ival-sqrt: 16.0ms (17.6% of total)

ival-sub: 14.0ms (15.4% of total)

ival-add: 9.0ms (9.9% of total)

ival-mult: 9.0ms (9.9% of total)

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

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

18 → 216

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor -inf x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))) (taylor inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))) (taylor inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 x)) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* x (- (* x (+ 1/16 (* -1/16 x))) 1/2))) (taylor 0 x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())

Calls

54 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(- (/ (+ 1 x) (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) (/ (- 1 x) (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))))
2.0ms	x	@	inf	(/ (- (+ 1 x) (- 1 x)) (+ (sqrt (+ 1 x)) (sqrt (- 1 x))))
2.0ms	x	@	-inf	(- (/ (+ 1 x) (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))) (/ (- 1 x) (+ (sqrt (+ 1 x)) (sqrt (- 1 x)))))
2.0ms	x	@	-inf	(/ (- (+ 1 x) (- 1 x)) (+ (sqrt (+ 1 x)) (sqrt (- 1 x))))
1.0ms	x	@	-inf	(/ (+ 1 x) (+ (sqrt (+ 1 x)) (sqrt (- 1 x))))

simplify259.0ms (2.5%)

Memory

-29.1MiB live, 206.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 084×	`lower-fma.f64`
10 084×	`lower-fma.f32`
5 672×	`lower-*.f64`
5 672×	`lower-*.f32`
5 304×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	609	6766
1	1950	5574
2	7599	5556
0	8158	5330

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 208

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
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(- (* 2 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* 2 (/ (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- (* 2 (/ (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 1/16 (* (sqrt (pow x 5)) (/ 1 (* (pow (sqrt -1) 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* 1/16 (* (sqrt (pow x 5)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))))) (pow x 6))) (+ (* -2 (/ (+ (* -1 (/ (* (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1/8 (* (sqrt (pow x 3)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1/2
(+ 1/2 (* 1/2 x))
(+ 1/2 (* x (+ 1/2 (* 1/16 x))))
(+ 1/2 (* x (+ 1/2 (* x (+ 1/16 (* 1/16 x))))))
(/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 2))) (+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (+ (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))))
(/ -1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (+ (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* x (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(- (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
1/2
(+ 1/2 (* -1/2 x))
(+ 1/2 (* x (- (* 1/16 x) 1/2)))
(+ 1/2 (* x (- (* x (+ 1/16 (* -1/16 x))) 1/2)))
(/ -1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(- (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(- (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) #s(literal 1/8 binary64)) x) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 x (-.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* 1/8 (pow x 3))
(.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
1
#s(literal 1 binary64)
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(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 #s(literal 1/16 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(neg.f64 (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(neg.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
(neg.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/16 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* x (+ 1/16 (* -1/16 x))) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/16 binary64)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(/ -1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(/.f64 #s(literal -1 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(- (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal -1 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(- (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal -1 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (/ 1 (* (sqrt -1) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 3))) (/ 1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -1 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 (/.f64 #s(literal -1 binary64) (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x))) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x)))))) (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) (.f64 x (*.f64 x x))))
(/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(- (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (/ 1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/2 (* (sqrt x) (/ (sqrt -1) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))) (.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))))) x)) x))

rewrite325.0ms (3.1%)

Memory

-30.7MiB live, 485.8MiB allocated

Rules

5 284×	`lower-/.f32`
5 272×	`lower-/.f64`
4 802×	`lower-fma.f32`
4 800×	`lower-fma.f64`
3 836×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	191
0	56	180
1	236	145
2	2026	145
0	8373	141

Stop Event

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

Counts

18 → 1 703

Calls

Call 1

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

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

eval465.0ms (4.5%)

Memory: 61.1MiB live, 540.4MiB allocated
Compiler: Compiled 142 228 to 7 156 computations (95% saved)

prune350.0ms (3.4%)

Memory

-16.5MiB live, 361.8MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	3 744	2	3 746
Fresh	1	0	1
Picked	4	1	5
Done	1	5	6
Total	3 750	8	3 758

Accuracy

100.0%

Counts

3 758 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
✓	8.7%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 x (+.f64 x #s(literal 0 binary64))))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
✓	99.4%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
✓	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
✓	99.1%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
✓	98.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 412 to 138 computations (66.5% saved)

regimes10.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 x (+.f64 x #s(literal 0 binary64))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 1 binary64) (-.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))

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

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes5.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))

Outputs

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (*.f64 x x) (*.f64 x (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(approx (+ (* x (* x (* x 1/8))) x) (.f64 x (.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 x (.f64 x (.f64 x #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes4.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes3.0ms (0%)

Memory

-37.7MiB live, 2.7MiB allocated

Accuracy

Total -59.0b remaining (-6987.9%)

Threshold costs -59b (-6987.9%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

2.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
1.0ms	x

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
8×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	111
1	57	111
2	61	111
3	63	111
4	64	111

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))

Outputs
(/.f64 #s(approx (- (+ 1 x) (- 1 x)) (*.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (*.f64 x #s(literal 7/128 binary64)) #s(literal 1/8 binary64))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 x #s(approx (+ ( x (* x 1/8)) 1) #s(literal 1 binary64))))

soundness745.0ms (7.1%)

Memory

12.7MiB live, 12.7MiB allocated

Rules

21 484×	`lower-fma.f64`
21 484×	`lower-fma.f32`
10 084×	`lower-fma.f64`
10 084×	`lower-fma.f32`
9 878×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	634	5716
1	2041	4988
2	7107	4967
0	8004	4675
0	161	971
1	493	856
2	1729	798
3	7219	798
0	8083	746
0	7	20
0	12	20
1	51	20
2	368	20
3	5664	20
0	9321	20
0	609	6766
1	1950	5574
2	7599	5556
0	8158	5330
0	34	200
0	61	198
1	258	175
2	1919	175
0	9136	168

Stop Event

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

Compiler

Compiled 163 to 87 computations (46.6% saved)

preprocess104.0ms (1%)

Memory: 11.7MiB live, 50.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 262 to 148 computations (43.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	9	21
1	22	19
2	52	18
3	101	18
4	163	18
5	237	18
6	264	18
7	272	18
0	7	9
0	12	9
1	19	9
2	26	9
3	37	9
4	51	9
5	74	9
6	114	9
7	149	9
8	196	9
9	211	9
10	219	9
0	219	9

Iter	Nodes	Cost
0	7	25
0	12	25
1	19	25
2	26	25
3	37	25
4	51	25
5	74	25
6	114	25
7	149	25
8	196	25
9	211	25
10	219	25
0	219	25

Iter	Nodes	Cost
0	9	21
1	22	19
2	52	18
3	101	18
4	163	18
5	237	18
6	264	18
7	272	18
0	7	9
0	12	9
1	19	9
2	26	9
3	37	9
4	51	9
5	74	9
6	114	9
7	149	9
8	196	9
9	211	9
10	219	9
0	219	9

Iter	Nodes	Cost
0	7	25
0	12	25
1	19	25
2	26	25
3	37	25
4	51	25
5	74	25
6	114	25
7	149	25
8	196	25
9	211	25
10	219	25
0	219	25

start0.0ms (0%)

analyze0.0ms (0%)

sample1.8s (17.7%)

explain136.0ms (1.3%)

preprocess25.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize46.0ms (0.4%)

series7.0ms (0.1%)

simplify376.0ms (3.6%)

rewrite241.0ms (2.3%)

eval98.0ms (0.9%)

prune93.0ms (0.9%)

simplify430.0ms (4.1%)

localize226.0ms (2.2%)

series649.0ms (6.2%)

simplify681.0ms (6.5%)

rewrite290.0ms (2.8%)

eval115.0ms (1.1%)

prune157.0ms (1.5%)

simplify187.0ms (1.8%)

localize282.0ms (2.7%)

series29.0ms (0.3%)

simplify257.0ms (2.5%)

rewrite343.0ms (3.3%)

eval695.0ms (6.7%)

prune358.0ms (3.4%)

simplify317.0ms (3%)

localize241.0ms (2.3%)

series24.0ms (0.2%)

simplify259.0ms (2.5%)

rewrite325.0ms (3.1%)

eval465.0ms (4.5%)

prune350.0ms (3.4%)

regimes10.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify6.0ms (0.1%)

soundness745.0ms (7.1%)

preprocess104.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	21
1	22	19
2	52	18
3	101	18
4	163	18
5	237	18
6	264	18
7	272	18
0	7	9
0	12	9
1	19	9
2	26	9
3	37	9
4	51	9
5	74	9
6	114	9
7	149	9
8	196	9
9	211	9
10	219	9
0	219	9

Iter	Nodes	Cost
0	7	25
0	12	25
1	19	25
2	26	25
3	37	25
4	51	25
5	74	25
6	114	25
7	149	25
8	196	25
9	211	25
10	219	25
0	219	25