Metrics for bug333 (missed optimization)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample2.2s (23.6%)

Memory

30.9MiB live, 2 522.4MiB allocated

Samples

1.0s	4 805×	1	valid
803.0ms	3 202×	2	valid
13.0ms	249×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-sqrt: 467.0ms (35.5% of total)

adjust: 312.0ms (23.7% of total)

ival-sub: 278.0ms (21.1% of total)

ival-add: 181.0ms (13.8% of total)

ival-<=: 51.0ms (3.9% of total)

ival-and: 12.0ms (0.9% of total)

exact: 11.0ms (0.8% of total)

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

Bogosity

explain141.0ms (1.5%)

Memory

-12.0MiB live, 322.8MiB 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	0

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	0	2

Precision?

1.0

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

42.0ms	314×	1	valid
34.0ms	176×	2	valid
1.0ms	22×	0	valid

Compiler

Compiled 63 to 25 computations (60.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 18.0ms (36.6% of total)

adjust: 13.0ms (26.4% of total)

ival-sub: 12.0ms (24.4% of total)

ival-add: 6.0ms (12.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess25.0ms (0.3%)

Memory

-13.5MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

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 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify7.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB 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)))

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)

localize59.0ms (0.6%)

Memory

-15.7MiB live, 63.4MiB 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	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.283514529070985	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Samples

18.0ms	157×	1	valid
17.0ms	88×	2	valid
11.0ms	11×	0	valid

Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-sqrt: 19.0ms (54.8% of total)

adjust: 6.0ms (17.3% of total)

ival-sub: 5.0ms (14.4% of total)

ival-add: 4.0ms (11.5% 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

9.9MiB live, 9.9MiB 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 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 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 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 (* 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 (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 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 (* (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 (* 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 (* (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 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 (* (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

3 calls:

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

Time

Variable

Point

Expression

2.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))

2.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) (sqrt (- 1 x)))

simplify204.0ms (2.2%)

Memory

9.3MiB live, 235.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	971
1	493	856
2	1730	798
3	7227	798
0	8089	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))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* 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)))))))
(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))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (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 (* 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 (* (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)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))

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

rewrite107.0ms (1.1%)

Memory

21.7MiB live, 147.3MiB allocated

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
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eval117.0ms (1.2%)

Memory: -34.3MiB live, 107.5MiB allocated
Compiler: Compiled 8 829 to 1 202 computations (86.4% saved)

prune16.0ms (0.2%)

Memory

-10.6MiB live, 28.6MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	370	6	376
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	370	7	377

Accuracy

100.0%

Counts

377 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.9%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
✓	9.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	8.3%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	8.1%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	6.4%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x))

Compiler

Compiled 139 to 103 computations (25.9% saved)

simplify163.0ms (1.7%)

Memory

1.3MiB live, 78.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
cost-diff	2432	(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (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	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #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	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	210
0	56	196
1	90	196
2	163	196
3	269	196
4	326	196
5	406	196
6	518	196
7	793	196
8	1107	196
9	1482	196
10	1858	196
11	2249	196
12	2509	196
13	2610	196
14	2626	196
15	2630	196
16	2630	196
17	2656	196
18	2664	196
19	2664	196
20	2668	196
0	2668	196

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)
(*.f64 x x)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)
(*.f64 x x)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (sqrt.f64 (-.f64 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
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

localize195.0ms (2.1%)

Memory

11.7MiB live, 134.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.015625	(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.02734375	(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy	58.283514529070985	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.4349943245073523	#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	0.5632429613905655	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	1.458269128713835	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0	(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	0	(pow.f64 x #s(literal 3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.24285649817809335	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))

Samples

109.0ms	157×	1	valid
60.0ms	88×	2	valid
2.0ms	11×	0	valid

Compiler

Compiled 177 to 29 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-sqrt: 43.0ms (45.1% of total)

adjust: 19.0ms (19.9% of total)

ival-mult: 12.0ms (12.6% of total)

ival-add: 10.0ms (10.5% of total)

ival-sub: 8.0ms (8.4% of total)

ival-pow: 3.0ms (3.1% of total)

exact: 1.0ms (1% of total)

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

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

series17.0ms (0.2%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 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 (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#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 (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#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 (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#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 (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#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 x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (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 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (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 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (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 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<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 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -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 (* -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 (* -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 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (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 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (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 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (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 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (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 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<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 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<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 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/8 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (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 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (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 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (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 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (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)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<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)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<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)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<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)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) (patch (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))) #<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 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 (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 (* -1 x) 1/4) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/4 (pow (/ -1 (pow x 3)) 1/4)) (pow (* -1 x) 1/4)) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* 3/32 (pow (/ -1 (pow x 3)) 1/4)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4)) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4)) (taylor -inf x) (#s(alt (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))
3.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))
2.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))

Time

Variable

Point

Expression

3.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))

3.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))

2.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (pow x 3) (+ (* 7/128 (* x x)) 1/8)) x) (pow x 3) (+ (* 7/128 (* x x)) 1/8) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- 1 x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* (+ (* -1/8 x) 1/2) x) 1) (+ (* -1/8 x) 1/2) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x)))) (- (sqrt (+ 1 x)) (* (sqrt (sqrt (- 1 x))) (sqrt (sqrt (- 1 x))))) (sqrt (+ 1 x)) (+ 1 x) (* x x) (sqrt (sqrt (- 1 x))))

simplify256.0ms (2.7%)

Memory

-29.3MiB live, 164.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	253	4515
1	728	4000
2	2268	3706
3	7900	3679
0	8393	3427

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 244

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
(* 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))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (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))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -1/4 x))
(+ 1 (* x (- (* -3/32 x) 1/4)))
(+ 1 (* x (- (* x (- (* -7/128 x) 3/32)) 1/4)))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (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)))))))
(* 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)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 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 (- (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)))))))
(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))))))))
(* (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 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* 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)))))))
(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))))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 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)))))))
(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))))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* (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))))))
(* 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)))))))
(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))))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (+ (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)) (* -3/32 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 2)))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (+ (* -1/4 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) x)) (+ (* -3/32 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 2))) (* -7/128 (/ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 x)))))) (pow x 3))))))
(* -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))))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 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)))))
(* -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 (* (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 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -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 (* (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)))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* -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 (* (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)))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* 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 (* (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)))))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow (* -1 x) 1/4)
(+ (* -1/4 (pow (/ -1 (pow x 3)) 1/4)) (pow (* -1 x) 1/4))
(+ (* -1 (/ (+ (* 3/32 (pow (/ -1 (pow x 3)) 1/4)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 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))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
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(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
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(.f64 (.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))))
(* -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 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (.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) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))))) (neg.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))) (fma.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))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))))) (neg.f64 x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(.f64 (-.f64 (fma.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))) (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) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 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) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))))) (neg.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64)))))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.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) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))))) (neg.f64 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)
(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 (* -1 x) 1/4)
(pow.f64 (neg.f64 x) #s(literal 1/4 binary64))
(+ (* -1/4 (pow (/ -1 (pow x 3)) 1/4)) (pow (* -1 x) 1/4))
(fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* 3/32 (pow (/ -1 (pow x 3)) 1/4)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(-.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 3/32 binary64) (*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) x))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (pow (* -1 x) 1/4)) (* -7/128 (pow (/ -1 (pow x 3)) 1/4))) x)) (* 1/4 (pow (* -1 x) 1/4))) x)) (pow (* -1 x) 1/4))
(-.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal 3/32 binary64) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (*.f64 #s(literal 7/128 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/4 binary64)))) x)) x))

rewrite1.4s (14.5%)

Memory

23.6MiB live, 135.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	174
0	56	160
1	217	160
2	1578	160
0	8875	160

Stop Event

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

Counts

21 → 599

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(*.f64 x x)
(sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
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eval373.0ms (3.9%)

Memory: 21.1MiB live, 297.7MiB allocated
Compiler: Compiled 32 964 to 3 461 computations (89.5% saved)

prune186.0ms (2%)

Memory

-20.2MiB live, 107.1MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	1 375	9	1 384
Fresh	1	0	1
Picked	3	2	5
Done	0	1	1
Total	1 379	12	1 391

Accuracy

100.0%

Counts

1 391 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.0%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
	9.1%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	9.0%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 (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))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
✓	9.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	8.1%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	8.0%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
	8.1%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
▶	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓	6.4%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
▶	5.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
▶	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Compiler

Compiled 296 to 187 computations (36.8% saved)

simplify196.0ms (2.1%)

Memory

-18.7MiB live, 140.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
cost-diff	0	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
cost-diff	0	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
cost-diff	576	(+.f64 (fma.f64 (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)))
cost-diff	0	#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
cost-diff	0	#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	279
0	65	279
1	112	279
2	198	267
3	488	267
4	1161	267
5	2600	267
6	4300	267
7	6222	267
8	7333	267
9	7759	267
10	7885	267
11	7898	267
12	7898	267
0	8088	263

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(*.f64 x x)
x
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64))
#s(literal -1/8 binary64)
#s(literal -1/2 binary64)
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal 3/2 binary64)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(-.f64 #s(literal 1 binary64) x)
(+.f64 (fma.f64 (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)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))

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

localize597.0ms (6.3%)

Memory

11.3MiB live, 806.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
accuracy	0.04296875	(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
accuracy	0.15234375	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
accuracy	58.09498859419947	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.4538266261834164	#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
accuracy	0.5632429613905655	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.5632429613905655	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	1.524538892823443	#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
accuracy	1.458269128713835	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	1.524538892823443	#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
accuracy	0	(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy	0.24285649817809335	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Samples

271.0ms	105×	2	valid
144.0ms	25×	3	valid
117.0ms	117×	1	valid
2.0ms	9×	0	valid

Compiler

Compiled 231 to 36 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 489.0ms

ival-pow: 389.0ms (79.5% of total)

adjust: 36.0ms (7.4% of total)

ival-mult: 18.0ms (3.7% of total)

ival-add: 17.0ms (3.5% of total)

ival-sqrt: 14.0ms (2.9% of total)

ival-sub: 9.0ms (1.8% of total)

ival-div: 5.0ms (1% of total)

exact: 1.0ms (0.2% of total)

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

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

series23.0ms (0.2%)

Memory

-3.2MiB live, 35.6MiB allocated

Counts

18 → 216

Calls

Call 1

Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x x)) x x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (fma.f64 (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))) (patch (+.f64 (fma.f64 (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))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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)))) (patch (/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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)))) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (patch (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (patch (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #<representation binary64>) () ())

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

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (/ (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (pow (+ x 1) 3/2) (+ (* (+ (* -1/8 x) -1/2) x) 1) (pow (- 1 x) 3/2))

5.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (/ (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (pow (+ x 1) 3/2) (+ (* (+ (* -1/8 x) -1/2) x) 1) (pow (- 1 x) 3/2))

2.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (/ (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (- (pow (+ x 1) 3/2) (pow (- 1 x) 3/2)) (pow (+ x 1) 3/2) (+ (* (+ (* -1/8 x) -1/2) x) 1) (pow (- 1 x) 3/2))

simplify177.0ms (1.9%)

Memory

33.6MiB live, 225.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	5132
1	1562	4437
2	5892	4353
0	8388	4065

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 211

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))))))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
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(* -1 (* x (- (+ (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (/ (- (* 3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) x)) (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 4))) (+ (* 3/2 (sqrt x)) (* 2 (/ (- (* 3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) (sqrt -1)))))) x)) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) x)) (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* (pow x 2) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (- (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -3/2 (sqrt x)) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (+ (* -1 (/ (- (+ (* -3/2 (sqrt x)) (* -1 (/ (- (* 1/2 (* (sqrt x) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))))) (* 1/2 (* (sqrt x) (* (sqrt -1) (- 1 (* -9/4 x)))))) x))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 x)))))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
(* (pow x 2) (- (* -1 (/ (- 1/2 (/ 1 x)) x)) 1/8))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (- 1 (* -9/4 x))))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))

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

rewrite213.0ms (2.3%)

Memory

-2.1MiB live, 278.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	202
0	65	202
1	300	182
2	2620	182
0	10302	181

Stop Event

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

Counts

18 → 522

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64))
(*.f64 x x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(+.f64 (fma.f64 (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)))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))

Outputs
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eval140.0ms (1.5%)

Memory: -26.0MiB live, 228.7MiB allocated
Compiler: Compiled 28 129 to 2 471 computations (91.2% saved)

prune37.0ms (0.4%)

Memory

7.6MiB live, 54.0MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	817	2	819
Fresh	0	4	4
Picked	2	3	5
Done	2	1	3
Total	821	10	831

Accuracy

100.0%

Counts

831 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.0%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
▶	9.1%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	9.0%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 (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))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
✓	9.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	8.1%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
✓	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
▶	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
✓	5.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
▶	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Compiler

Compiled 250 to 145 computations (42% saved)

simplify157.0ms (1.7%)

Memory

9.8MiB live, 166.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
cost-diff	0	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
cost-diff	128	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
cost-diff	576	(+.f64 (fma.f64 (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)))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	256	(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
cost-diff	0	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	308
0	65	308
1	122	304
2	229	288
3	537	288
4	1945	288
5	3911	288
6	5965	288
7	7883	288
0	8051	278

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
#s(literal 3/2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 (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)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x))
(fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x)
(.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
(.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) x) x)
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
x
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 #s(literal 2 binary64) x) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal -1 binary64))
x
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.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)))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
(/.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (-.f64 x #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
(pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 3/2 binary64))
(+.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal -1 binary64))
x
#s(literal 1 binary64)
#s(literal 3/2 binary64)
(*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(+.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))

localize389.0ms (4.1%)

Memory

-14.9MiB live, 465.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy	0.03515625	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
accuracy	0.15234375	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
accuracy	58.09498859419947	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
accuracy	0.0078125	(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.01171875	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.01953125	(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy	58.220013704892246	(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy	0.5632429613905655	#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	0.591529178567592	#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
accuracy	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy	0.591529178567592	#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
accuracy	1.458269128713835	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	58.283514529070985	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy	0.24285649817809335	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
accuracy	0.603950199284135	#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))

Samples

141.0ms	98×	2	valid
124.0ms	33×	3	valid
83.0ms	116×	1	valid
2.0ms	9×	0	valid

Compiler

Compiled 260 to 36 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 287.0ms

ival-pow: 172.0ms (59.9% of total)

adjust: 32.0ms (11.1% of total)

ival-mult: 23.0ms (8% of total)

ival-add: 20.0ms (7% of total)

ival-sub: 16.0ms (5.6% of total)

ival-sqrt: 15.0ms (5.2% of total)

ival-div: 8.0ms (2.8% of total)

exact: 1.0ms (0.3% of total)

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

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

series28.0ms (0.3%)

Memory

-14.3MiB live, 22.0MiB allocated

Counts

23 → 276

Calls

Call 1

Inputs
#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (+.f64 (fma.f64 (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))) (patch (+.f64 (fma.f64 (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))) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (patch (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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)))) (patch (/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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)))) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (patch (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) #<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 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 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 #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) x x)) (patch #s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* 7/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 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 x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<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 (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* -1/8 x) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2))) (taylor 0 x) (#s(alt #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<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 (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) (patch (-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (patch #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/8 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<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 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<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 (* -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 (* -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 (* -1 x)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<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)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (- 1 (* -9/4 x))))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))) (+ x 1) (- 1 x) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (/ (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (pow (+ x 1) 3/2) (sqrt (- 1 x)) (sqrt (+ x 1)) (+ (sqrt (- 1 x)) (sqrt (+ x 1))) (* (- 1 x) (sqrt (- 1 x))))

4.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))) (+ x 1) (- 1 x) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (/ (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (pow (+ x 1) 3/2) (sqrt (- 1 x)) (sqrt (+ x 1)) (+ (sqrt (- 1 x)) (sqrt (+ x 1))) (* (- 1 x) (sqrt (- 1 x))))

2.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 7/128) 1/8) (* x x)) (+ (* (* x x) 7/128) 1/8) (* x x) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (sqrt (- 1 x)) (+ (* -1/2 x) 1) (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ (* 1/2 x) 1) (- (+ x 1) (- 1 x)) (/ (- (+ x 1) (- 1 x)) (+ (sqrt (- 1 x)) (sqrt (+ x 1)))) (+ x 1) (- 1 x) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1)) (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (/ (- (pow (+ x 1) 3/2) (* (- 1 x) (sqrt (- 1 x)))) (+ (+ (* (sqrt (- 1 x)) (sqrt (+ x 1))) (- 1 x)) (+ x 1))) (pow (+ x 1) 3/2) (sqrt (- 1 x)) (sqrt (+ x 1)) (+ (sqrt (- 1 x)) (sqrt (+ x 1))) (* (- 1 x) (sqrt (- 1 x))))

simplify189.0ms (2%)

Memory

23.1MiB live, 182.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	634	6445
1	2066	5454
0	8066	5142

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 269

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))))))))
(* 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))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (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))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
3
(+ 3 (* -1/2 (pow x 2)))
(+ 3 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* 3 x)
(* x (+ 3 (* -1/8 (pow x 2))))
(* x (+ 3 (* (pow x 2) (- (* -3/128 (pow x 2)) 1/8))))
(* x (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -9/1024 (pow x 2)) 3/128)) 1/8))))
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))))))))
1
(+ 1 (* 3/2 x))
(+ 1 (* x (+ 3/2 (* 3/8 x))))
(+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
1
(+ 1 (* -3/2 x))
(+ 1 (* x (- (* 3/8 x) 3/2)))
(+ 1 (* x (- (* x (+ 3/8 (* 1/16 x))) 3/2)))
(* 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))))))
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x
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x
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(* -1 (* x (sqrt -1)))
(* -1 (* x (- (sqrt -1) (* 2 (/ 1 x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 2 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 2 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
(* (pow x 2) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (- (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -3/2 (sqrt x)) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (- (+ (* -1 (/ (- (+ (* -3/2 (sqrt x)) (* -1 (/ (- (* 1/2 (* (sqrt x) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))))) (* 1/2 (* (sqrt x) (* (sqrt -1) (- 1 (* -9/4 x)))))) x))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (/ (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))) (sqrt -1)))
(* -1 (* x (- (+ (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (* x (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (/ (- (* 3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) x)) (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 4))) (+ (* 3/2 (sqrt x)) (* 2 (/ (- (* 3/2 (* (sqrt x) (/ 1 (sqrt -1)))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) (sqrt -1)))))) x)) (* 3/2 (* (sqrt x) (/ 1 (sqrt -1))))) (+ (* -4 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (+ (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 3))) (* 3/2 (sqrt x))))) x)) (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1))) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (sqrt -1))) (sqrt (/ 1 x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* (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 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
(* (sqrt (pow x 3)) (sqrt -1))
(* (pow x 2) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (- 1 (* -9/4 x))))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))

Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) x)
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
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))
(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))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) 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))
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))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) 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))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) 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)
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) x) x #s(literal -1/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 3 binary64))
(* 3 x)
(*.f64 #s(literal 3 binary64) x)
(* x (+ 3 (* -1/8 (pow x 2))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) x #s(literal 3 binary64)) x)
(* x (+ 3 (* (pow x 2) (- (* -3/128 (pow x 2)) 1/8))))
(.f64 (fma.f64 (fma.f64 #s(literal -3/128 binary64) (.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 3 binary64)) x)
(* x (+ 3 (* (pow x 2) (- (* (pow x 2) (- (* -9/1024 (pow x 2)) 3/128)) 1/8))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -9/1024 binary64) (.f64 x x) #s(literal -3/128 binary64)) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 3 binary64)) x)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(fma.f64 (pow.f64 x #s(literal 3 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)) x)
1
#s(literal 1 binary64)
(+ 1 (* 3/2 x))
(fma.f64 #s(literal 3/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (* 3/8 x))))
(fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 3/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 3/8 binary64)) x #s(literal 3/2 binary64)) x #s(literal 1 binary64))
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))
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))
2
#s(literal 2 binary64)
(+ 2 (* -1/4 (pow x 2)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal -5/64 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -21/512 binary64) (.f64 x x) #s(literal -5/64 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 x))
(fma.f64 #s(literal -3/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 3/2)))
(fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal -3/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* 1/16 x))) 3/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal 3/8 binary64)) x #s(literal -3/2 binary64)) x #s(literal 1 binary64))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (fma.f64 (neg.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)) (* 1/2 (sqrt (/ 1 (pow x 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) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (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 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (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)))) (+ (* 1/16 (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 (+.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) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (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 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) x)
(* 7/128 (pow x 4))
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(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
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(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
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(* -1 (* (sqrt x) (sqrt -1)))
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(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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(* -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))))))
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(* -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)))))))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(* -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)))))))
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(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
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(* (pow x 2) (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (sqrt -1) (- 1 (* -9/4 x))))) (* 3/2 (* (sqrt x) (sqrt -1)))) (pow x 3))) (+ (* 3/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
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rewrite192.0ms (2%)

Memory

5.2MiB live, 124.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	239
0	65	225
1	311	200
2	2873	200
0	8788	196

Stop Event

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

Counts

23 → 1 092

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x))
#s(approx (+ (* (* x x) 7/128) 1/8) #s(literal 1/8 binary64))
(*.f64 x x)
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) x)
(+.f64 (fma.f64 (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)))
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(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
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eval336.0ms (3.6%)

Memory: 14.9MiB live, 423.2MiB allocated
Compiler: Compiled 82 727 to 6 085 computations (92.6% saved)

prune51.0ms (0.5%)

Memory

-2.3MiB live, 119.5MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	2 245	2	2 247
Fresh	1	0	1
Picked	2	3	5
Done	0	4	4
Total	2 248	9	2 257

Accuracy

100.0%

Counts

2 257 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	100.0%	(/.f64 #s(approx (- (+ x 1) (- 1 x)) (*.f64 #s(literal 2 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	9.0%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	8.1%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
✓	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓	6.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
	5.5%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
✓	5.3%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
✓	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
✓	99.5%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))

Compiler

Compiled 359 to 145 computations (59.6% saved)

regimes12.0ms (0.1%)

Memory

16.3MiB live, 16.3MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) #s(approx (+ (* -1/2 x) 1) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 #s(approx (+ ( (* x x) 7/128) 1/8) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) #s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)) x x))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 #s(approx (- (+ x 1) (- 1 x)) (*.f64 #s(literal 2 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (+.f64 (fma.f64 (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))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (fma.f64 (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))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 (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))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))

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

Calls

2 calls:

6.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes8.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes10.0ms (0.1%)

Memory

-27.1MiB live, 10.0MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
3.0ms	x

Results

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

Compiler

Compiled 10 to 8 computations (20% saved)

regimes5.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

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
8.1%	1	`x`
8.1%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

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
6.3%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
6.3%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
5.5%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
5.5%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes3.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

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
5.3%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
5.3%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify29.0ms (0.3%)

Memory

-2.3MiB live, 36.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	139
1	67	139
2	81	139
3	89	139
4	93	139

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (11.9%)

Memory

-14.4MiB live, 618.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	971
1	493	856
2	1730	798
3	7227	798
0	8089	746
0	471	5132
1	1562	4437
2	5892	4353
0	8388	4065
0	33	174
0	56	160
1	217	160
2	1578	160
0	8875	160
0	7	20
0	12	20
1	51	20
2	368	20
3	5664	20
0	9321	20
0	253	4515
1	728	4000
2	2268	3706
3	7900	3679
0	8393	3427
0	634	6445
1	2066	5454
0	8066	5142

Stop Event

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

Compiler

Compiled 209 to 143 computations (31.6% saved)

preprocess55.0ms (0.6%)

Memory: 31.6MiB live, 70.5MiB allocated
Remove: (negabs x)
Compiler: Compiled 240 to 152 computations (36.7% 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%)

sample2.2s (23.6%)

explain141.0ms (1.5%)

preprocess25.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.1%)

localize59.0ms (0.6%)

series6.0ms (0.1%)

simplify204.0ms (2.2%)

rewrite107.0ms (1.1%)

eval117.0ms (1.2%)

prune16.0ms (0.2%)

simplify163.0ms (1.7%)

localize195.0ms (2.1%)

series17.0ms (0.2%)

simplify256.0ms (2.7%)

rewrite1.4s (14.5%)

eval373.0ms (3.9%)

prune186.0ms (2%)

simplify196.0ms (2.1%)

localize597.0ms (6.3%)

series23.0ms (0.2%)

simplify177.0ms (1.9%)

rewrite213.0ms (2.3%)

eval140.0ms (1.5%)

prune37.0ms (0.4%)

simplify157.0ms (1.7%)

localize389.0ms (4.1%)

series28.0ms (0.3%)

simplify189.0ms (2%)

rewrite192.0ms (2%)

eval336.0ms (3.6%)

prune51.0ms (0.5%)

regimes12.0ms (0.1%)

regimes8.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

simplify29.0ms (0.3%)

soundness1.1s (11.9%)

preprocess55.0ms (0.6%)

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