Metrics for bug333 (missed optimization)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample1.9s (26.9%)

Memory

-1.2MiB live, 2 294.5MiB allocated

Samples

750.0ms	3 085×	2	valid
745.0ms	4 894×	1	valid
20.0ms	277×	0	valid

Precisions

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

ival-sqrt: 405.0ms (33.6% of total)

ival-sub: 314.0ms (26.1% of total)

adjust: 263.0ms (21.8% of total)

ival-add: 135.0ms (11.2% of total)

ival-<=: 64.0ms (5.3% of total)

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

exact: 9.0ms (0.7% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain142.0ms (2%)

Memory

23.4MiB live, 262.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
254	-	-	`(-.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	254	1

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	1	1

Precision?

0.996078431372549

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms	194×	2	valid
36.0ms	298×	1	valid
1.0ms	20×	0	valid

Compiler

Compiled 64 to 25 computations (60.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

adjust: 18.0ms (30.3% of total)

ival-sqrt: 18.0ms (30.3% of total)

ival-sub: 15.0ms (25.3% of total)

ival-add: 6.0ms (10.1% of total)

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

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

exact: 0.0ms (0% of total)

preprocess37.0ms (0.5%)

Memory

-37.0MiB live, 18.2MiB 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)))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Symmetry

(negabs x)

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.1%	(-.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)

simplify8.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB 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)))
(-.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize52.0ms (0.8%)

Memory

4.5MiB live, 115.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.01171875	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.01171875	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	58.181844265156094	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

21.0ms	97×	2	valid
20.0ms	149×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

adjust: 10.0ms (35.1% of total)

ival-sqrt: 8.0ms (28% of total)

ival-add: 5.0ms (17.5% of total)

ival-sub: 5.0ms (17.5% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB 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
1.0ms	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))

simplify203.0ms (2.9%)

Memory

0.6MiB live, 237.0MiB 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))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x 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)))) x)
(* 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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))))))) (+ (* -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 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (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 (neg.f64 x) (-.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (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 (neg.f64 x) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* 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 (fma.f64 (/.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))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) x)
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (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 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 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 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

rewrite150.0ms (2.2%)

Memory

11.4MiB live, 206.3MiB 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 (/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #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 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)) (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #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) (-.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 (-.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (+.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 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (+.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 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.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))) (/.f64 (-.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)))))
(.f64 (+.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)) (sqrt.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))))))
(*.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (-.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)))))
(*.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #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))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #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))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.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))))
(pow.f64 (/.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)) #s(literal -1 binary64))
(pow.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 (.f64 (.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) (+.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) #s(literal 1 binary64)) x))
(/.f64 (.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #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))))) (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) 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) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (.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 (-.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 (-.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 (.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))) (.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.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)))) #s(literal 3 binary64)) (pow.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)))) #s(literal 3 binary64))) (fma.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)))) (fma.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 (-.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 (pow.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (fma.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (-.f64 (+.f64 (-.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)))))
(/.f64 (.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x) (.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 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) 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) x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (-.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 #s(literal 1 binary64) x)))) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (+.f64 (-.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) x)))
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(+.f64 (.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (fma.f64 (.f64 x x) x #s(literal -1 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (fma.f64 (.f64 x x) x #s(literal -1 binary64))) (fma.f64 x x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (neg.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 #s(literal 1 binary64) x)
(.f64 (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.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 (sqrt.f64 (fma.f64 (neg.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 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 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 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 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 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(/.f64 (/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #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)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 x))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(/.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))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))

eval123.0ms (1.8%)

Memory: -28.1MiB live, 102.7MiB allocated
Compiler: Compiled 9 873 to 1 159 computations (88.3% saved)

prune105.0ms (1.5%)

Memory

-7.1MiB live, 69.6MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	373	3	376
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	373	4	377

Accuracy

100.0%

Counts

377 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.1%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.8%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
▶	99.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
▶	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))

Compiler

Compiled 55 to 31 computations (43.6% saved)

simplify428.0ms (6.2%)

Memory

28.1MiB live, 104.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

9 608×	`lower-fma.f32`
9 596×	`lower-fma.f64`
2 536×	`lower-*.f32`
2 528×	`lower-*.f64`
1 198×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	185
0	39	185
1	73	185
2	136	185
3	300	179
4	770	179
5	1259	179
6	1365	179
7	1609	179
8	2259	179
9	3208	179
10	3902	179
11	5231	179
12	6161	179
13	6697	179
14	6711	179
15	6725	179
16	6782	179
17	6785	179
18	6787	179
19	6787	179
20	6787	179
21	6869	179
22	6897	179
23	6897	179
24	6897	179
25	6897	179
26	6919	179
0	6919	173

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize1.3s (18.3%)

Memory

-15.4MiB live, 104.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
accuracy	0.09390712398787643	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
accuracy	0	(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
accuracy	0.17059529826548675	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
accuracy	0.32027519926170867	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))

Samples

689.0ms	149×	1	valid
37.0ms	97×	2	valid
2.0ms	10×	0	valid

Compiler

Compiled 161 to 28 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 705.0ms

ival-mult: 663.0ms (94.1% of total)

adjust: 17.0ms (2.4% of total)

ival-add: 10.0ms (1.4% of total)

ival-sqrt: 9.0ms (1.3% of total)

ival-sub: 5.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

13 → 156

Calls

Call 1

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

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

Calls

39 calls:

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

simplify322.0ms (4.7%)

Memory

4.3MiB live, 188.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 126×	`lower-fma.f64`
14 126×	`lower-fma.f32`
6 102×	`lower-*.f64`
6 102×	`lower-*.f32`
4 066×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	166	2464
1	520	2245
2	1670	2097
0	8341	1971

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 150

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))))
(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)
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)))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 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
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))
(+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
7/128
(+ 7/128 (* 33/1024 (pow x 2)))
(+ 7/128 (* 33/1024 (pow x 2)))
(+ 7/128 (* 33/1024 (pow x 2)))
(* 33/1024 (pow x 2))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 2))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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))))))) (+ (* -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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (-.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (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 (neg.f64 x) (-.f64 (fma.f64 (/.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))) #s(literal 1/16 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (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 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* 1/8 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* 1/8 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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))))))) (+ (* -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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (-.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (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))))))))
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x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* 7/128 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 7/128 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 7/128 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 7/128 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 7/128 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 7/128 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(.f64 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (-.f64 #s(literal -7/128 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #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 (neg.f64 (pow.f64 x #s(literal 5 binary64))) (-.f64 #s(literal -7/128 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 7/128 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 7/128 binary64))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(* 7/128 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 7/128 binary64))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* 7/128 (pow x 2))
(.f64 #s(literal 7/128 binary64) (.f64 x x))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* 7/128 (pow x 2))
(.f64 #s(literal 7/128 binary64) (.f64 x x))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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))))))) (+ (* -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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (-.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (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 (neg.f64 x) (-.f64 (fma.f64 (/.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))) #s(literal 1/16 binary64) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (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 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* 33/1024 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 33/1024 binary64))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (+.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 33/1024 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 33/1024 binary64))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(.f64 (neg.f64 (pow.f64 x #s(literal 7 binary64))) (-.f64 #s(literal -33/1024 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 7/128 binary64)) (*.f64 x x))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x)) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64))) (pow.f64 x #s(literal 7 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* 33/1024 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 33/1024 binary64))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 1 binary64))
(* 33/1024 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 33/1024 binary64))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 1 binary64))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 7/128 (pow x 2)))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(* 33/1024 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 33/1024 binary64))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) x) x)
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 7/128 binary64) (.f64 x x)))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 7/128 binary64) (.f64 x x)))
(* 33/1024 (pow x 4))
(.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 33/1024 binary64))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) x) x)
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 7/128 binary64) (.f64 x x)))
(* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 7/128 binary64) (.f64 x x)))
7/128
#s(literal 7/128 binary64)
(+ 7/128 (* 33/1024 (pow x 2)))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(+ 7/128 (* 33/1024 (pow x 2)))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(+ 7/128 (* 33/1024 (pow x 2)))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* 33/1024 (pow x 2))
(.f64 #s(literal 33/1024 binary64) (.f64 x x))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* 33/1024 (pow x 2))
(.f64 #s(literal 33/1024 binary64) (.f64 x x))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))

rewrite365.0ms (5.3%)

Memory

-38.2MiB live, 189.4MiB allocated

Rules

5 200×	`lower-*.f32`
5 192×	`lower-*.f64`
4 414×	`lower-fma.f32`
4 402×	`lower-fma.f64`
4 400×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	167
0	39	167
1	174	167
2	1325	167
0	8304	167

Stop Event

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

Counts

13 → 286

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) x) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x)) x (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) (.f64 #s(literal 1/8 binary64) x)))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x)) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64))))
(fma.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) x #s(literal 1/8 binary64))
(fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) #s(literal 1/8 binary64))
(fma.f64 x (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) #s(literal 1/8 binary64))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) x))) (/.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) x) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x)) x) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) x) x))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x) x) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) x)) x) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal -1/8 binary64))))
(+.f64 (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) x) x) #s(literal 1/8 binary64))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) x) x))
(.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal -7/128 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (*.f64 x x) #s(literal 231/131072 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64)))) (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 49/16384 binary64) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (fma.f64 (/.f64 #s(literal 49/16384 binary64) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (/.f64 #s(literal 49/16384 binary64) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (.f64 (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (/.f64 #s(literal 49/16384 binary64) (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal -7/128 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 49/16384 binary64) (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 7/128 binary64) (.f64 #s(literal 33/1024 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 2401/268435456 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 49/16384 binary64)) (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal -7/128 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 117649/4398046511104 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 2401/268435456 binary64) (.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 49/16384 binary64)))) (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal -7/128 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) #s(literal 117649/4398046511104 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) #s(literal 343/2097152 binary64)) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x))) (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) #s(literal 40353607/9223372036854775808 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) (.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x)) (-.f64 #s(literal 117649/4398046511104 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal 12326391/2251799813685248 binary64)))) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)) #s(literal 49/16384 binary64))) (.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)) (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal -7/128 binary64))))
(/.f64 (-.f64 #s(literal 49/16384 binary64) (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 7/128 binary64) (.f64 #s(literal 33/1024 binary64) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64)))) (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64))) (neg.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64))) (neg.f64 (+.f64 #s(literal 49/16384 binary64) (-.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64))) (neg.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64))))))
(/.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64)) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (+.f64 #s(literal 49/16384 binary64) (-.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal 231/131072 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64)) (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -49/16384 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x)) (-.f64 #s(literal 49/16384 binary64) (.f64 (.f64 x x) #s(literal 231/131072 binary64)))) (fma.f64 (.f64 #s(literal 35937/1073741824 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64))))
(fma.f64 (*.f64 #s(literal 33/1024 binary64) x) x #s(literal 7/128 binary64))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
(fma.f64 (*.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64))
(fma.f64 x (*.f64 #s(literal 33/1024 binary64) x) #s(literal 7/128 binary64))
(-.f64 (/.f64 #s(literal 49/16384 binary64) (-.f64 #s(literal 7/128 binary64) (.f64 #s(literal 33/1024 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 7/128 binary64) (.f64 #s(literal 33/1024 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(literal 1089/1048576 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))) (/.f64 #s(literal 49/16384 binary64) (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal -7/128 binary64))))
(+.f64 (.f64 #s(literal 33/1024 binary64) (.f64 x x)) #s(literal 7/128 binary64))
(+.f64 #s(literal 7/128 binary64) (.f64 #s(literal 33/1024 binary64) (.f64 x x)))

eval76.0ms (1.1%)

Memory: 30.9MiB live, 68.2MiB allocated
Compiler: Compiled 17 812 to 1 403 computations (92.1% saved)

prune115.0ms (1.7%)

Memory

-11.4MiB live, 71.0MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	543	3	546
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	544	6	550

Accuracy

100.0%

Counts

550 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.1%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x x))
▶	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))
✓	99.8%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
▶	98.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 71 to 39 computations (45.1% saved)

simplify300.0ms (4.3%)

Memory

4.1MiB live, 81.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

6 520×	`lower-fma.f32`
6 514×	`lower-fma.f64`
2 040×	`lower-*.f32`
2 030×	`lower-*.f64`
1 574×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	181
0	41	181
1	82	181
2	138	177
3	265	177
4	509	174
5	770	174
6	850	174
7	1038	174
8	1428	174
9	1778	174
10	2148	174
11	2475	174
12	2899	174
13	4782	174
14	5413	174
15	5453	174
16	5477	174
17	5486	174
18	5488	174
19	5488	174
20	5488	174
21	5830	174
22	5978	174
23	5978	174
24	5978	174
25	5978	174
26	5984	174
0	5984	164

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize200.0ms (2.9%)

Memory

-5.1MiB live, 190.7MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.015625	(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.17059529826548675	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x x))
accuracy	0	(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	0.32027519926170867	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))
accuracy	0.015625	(.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)
accuracy	0.09390712398787643	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x))
accuracy	0.8566604524699767	#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64))

Samples

97.0ms	97×	2	valid
62.0ms	149×	1	valid
2.0ms	10×	0	valid

Compiler

Compiled 138 to 29 computations (79% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-sqrt: 36.0ms (35.7% of total)

adjust: 35.0ms (34.7% of total)

ival-mult: 14.0ms (13.9% of total)

ival-add: 10.0ms (9.9% of total)

ival-sub: 5.0ms (5% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-19.4MiB live, 18.1MiB allocated

Counts

11 → 132

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 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 (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 33/1024 (pow x 7)) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))) (taylor inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 33/1024 (pow x 7)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2))))))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/8 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 33/1024 (pow x 6)) (taylor inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#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 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x 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 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 5)) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4))))) (taylor inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 5)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (patch (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 4)) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 3)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 7/128 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())

Calls

33 calls:

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

simplify176.0ms (2.5%)

Memory

12.4MiB live, 255.9MiB allocated

Algorithm

1×	egg-herbie

Rules

13 558×	`lower-fma.f64`
13 558×	`lower-fma.f32`
4 606×	`lower-+.f64`
4 606×	`lower-+.f32`
3 602×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	2258
1	494	2039
2	1614	1891
3	6757	1867
0	8270	1776

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 126

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 (* (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
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
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))
(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)
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)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (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)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (*.f64 x x) x) x) x))))) 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))))))) (+ (* -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 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (neg.f64 x) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) 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 (neg.f64 x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (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 (neg.f64 x) (-.f64 (fma.f64 (/.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))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x x) x) x) x))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* 33/1024 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 33/1024 binary64))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 33/1024 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
(* 33/1024 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 33/1024 binary64))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 7/128 binary64)) (*.f64 x x)) #s(literal -33/1024 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal -33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (.f64 x x)))) (pow.f64 x #s(literal 7 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/8 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* 33/1024 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 33/1024 binary64))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 1 binary64))
(* 33/1024 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 33/1024 binary64))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 7/128 binary64) (.f64 x x)) #s(literal 33/1024 binary64)))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 33/1024 binary64)) (/.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (+.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
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(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* 7/128 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 7/128 binary64))
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* (pow x 3) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)

rewrite188.0ms (2.7%)

Memory

-12.7MiB live, 266.8MiB allocated

Rules

4 856×	`lower-*.f32`
4 846×	`lower-*.f64`
4 550×	`lower-/.f64`
4 550×	`lower-/.f32`
4 322×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	165
0	41	165
1	183	161
2	1318	161
0	8616	148

Stop Event

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

Counts

11 → 133

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x)
(.f64 x #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)))) (neg.f64 (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64))) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) x (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 x x)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64)) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x) #s(literal 9 binary64)) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/512 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/512 binary64)) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/512 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x)) (.f64 x x))) (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64))) (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 (neg.f64 x) x))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x) x)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 (neg.f64 x) x)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x) x))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)) (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x) x))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)))
(fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) x)
(fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x)
(fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) x)
(fma.f64 (.f64 x x) (.f64 #s(literal 1/8 binary64) x) x)
(fma.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x x)) x)
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x))) (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (-.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) #s(literal 1/64 binary64)) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64) (neg.f64 x))))
(+.f64 (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) x)
(+.f64 x (.f64 (.f64 #s(literal 1/8 binary64) (*.f64 x x)) x))
(.f64 (.f64 #s(literal 1/8 binary64) x) x)
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x x))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x #s(literal 1 binary64)) x)
(.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x x) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x (neg.f64 x))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x) x) (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) x) x) (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (.f64 x (-.f64 x (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x))))))
(.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x x)) #s(literal -1 binary64))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 7/1024 binary64)))) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64)) (.f64 x x))))
(.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(.f64 x (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 #s(literal 1/8 binary64) x)) (.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) (.f64 #s(literal 1/8 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 #s(literal 1/8 binary64) x)) (.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 #s(literal 1/8 binary64) x) (-.f64 (.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x)) (.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 #s(literal 1/8 binary64) x) (-.f64 (.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x)))) (.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64)) x)) (neg.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64)) x)) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64)))) (neg.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal 7/1024 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64)) x) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64)) x) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal 7/1024 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64))) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (.f64 x x) x) #s(literal 1/512 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal 7/1024 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 (fma.f64 (.f64 (.f64 (*.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 7/1024 binary64)))) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (*.f64 x x) x) #s(literal 1/512 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x (fma.f64 (.f64 (.f64 (*.f64 x x) x) x) #s(literal 49/16384 binary64) #s(literal -1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 49/16384 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 7/1024 binary64)))) (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 343/2097152 binary64)) (.f64 (*.f64 x x) x) #s(literal 1/512 binary64)))))
(fma.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x (*.f64 #s(literal 1/8 binary64) x))
(fma.f64 #s(literal 1/8 binary64) x (.f64 (.f64 #s(literal 7/128 binary64) (*.f64 x x)) x))
(fma.f64 #s(literal 1/8 binary64) x (.f64 x (.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(fma.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x)) (*.f64 #s(literal 1/8 binary64) x))
(fma.f64 x #s(literal 1/8 binary64) (.f64 (.f64 #s(literal 7/128 binary64) (*.f64 x x)) x))
(fma.f64 x #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(+.f64 (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x) (.f64 #s(literal 1/8 binary64) x))
(+.f64 (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))) (.f64 #s(literal 1/8 binary64) x))
(+.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 (.f64 #s(literal 7/128 binary64) (.f64 x x)) x))
(+.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x (.f64 #s(literal 7/128 binary64) (.f64 x x))))

eval34.0ms (0.5%)

Memory: 5.6MiB live, 89.1MiB allocated
Compiler: Compiled 7 713 to 589 computations (92.4% saved)

prune37.0ms (0.5%)

Memory

27.3MiB live, 104.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	281	6	287

Accuracy

100.0%

Counts

287 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.1%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.7%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x x))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))
✓	99.8%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
✓	98.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 151 to 65 computations (57% saved)

regimes8.0ms (0.1%)

Memory

-24.7MiB live, 12.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

5.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
3.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	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 (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 #s(approx (+ ( (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x 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 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x 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
99.7%	1	`x`
99.7%	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)

regimes4.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 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
99.7%	1	`x`
99.7%	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)

regimes41.0ms (0.6%)

Memory

-33.6MiB live, 49.2MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

33.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.5%	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)

regimes3.0ms (0%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	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)

regimes2.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	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)

simplify8.0ms (0.1%)

Memory

-21.1MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	143
1	50	143

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness534.0ms (7.7%)

Memory

12.6MiB live, 453.4MiB allocated

Rules

21 484×	`lower-fma.f64`
21 484×	`lower-fma.f32`
14 126×	`lower-fma.f64`
14 126×	`lower-fma.f32`
6 102×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	167
0	39	167
1	174	167
2	1325	167
0	8304	167
0	161	971
1	493	856
2	1729	798
3	7219	798
0	8083	746
0	166	2464
1	520	2245
2	1670	2097
0	8341	1971

Stop Event

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

Compiler

Compiled 185 to 86 computations (53.5% saved)

preprocess96.0ms (1.4%)

Memory: 4.8MiB live, 169.8MiB allocated
Remove: (negabs x)
Compiler: Compiled 230 to 96 computations (58.3% 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%)

sample1.9s (26.9%)

explain142.0ms (2%)

preprocess37.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize52.0ms (0.8%)

series6.0ms (0.1%)

simplify203.0ms (2.9%)

rewrite150.0ms (2.2%)

eval123.0ms (1.8%)

prune105.0ms (1.5%)

simplify428.0ms (6.2%)

localize1.3s (18.3%)

series12.0ms (0.2%)

simplify322.0ms (4.7%)

rewrite365.0ms (5.3%)

eval76.0ms (1.1%)

prune115.0ms (1.7%)

simplify300.0ms (4.3%)

localize200.0ms (2.9%)

series14.0ms (0.2%)

simplify176.0ms (2.5%)

rewrite188.0ms (2.7%)

eval34.0ms (0.5%)

prune37.0ms (0.5%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes41.0ms (0.6%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify8.0ms (0.1%)

soundness534.0ms (7.7%)

preprocess96.0ms (1.4%)

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