Metrics for Given's Rotation SVD example, simplified

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 19 to 11 computations (42.1% saved)

sample1.5s (17.7%)

Memory

37.3MiB live, 2 341.2MiB allocated

Samples

717.0ms	3 597×	1	valid
390.0ms	4 599×	0	valid
21.0ms	60×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 861.0ms

ival-hypot: 360.0ms (41.8% of total)

ival-sqrt: 112.0ms (13% of total)

ival-div: 101.0ms (11.7% of total)

ival-mult: 83.0ms (9.6% of total)

adjust: 74.0ms (8.6% of total)

ival-sub: 57.0ms (6.6% of total)

ival-add: 56.0ms (6.5% of total)

exact: 8.0ms (0.9% of total)

ival-true: 6.0ms (0.7% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain201.0ms (2.3%)

Memory

-15.0MiB live, 251.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
63	-	-	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
0	-	-	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(hypot.f64 #s(literal 1 binary64) x)`
0	-	-	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
0	-	-	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
0	-	-	`#s(literal 1/2 binary64)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`	cancellation	63	0

Confusion

	Predicted +	Predicted -
+	63	0
-	0	193

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	0	0	193

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	193
1	63

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms	314×	0	valid
34.0ms	196×	1	valid
1.0ms	2×	2	valid

Compiler

Compiled 223 to 40 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-hypot: 19.0ms (42.1% of total)

ival-div: 5.0ms (11.1% of total)

ival-sqrt: 5.0ms (11.1% of total)

ival-mult: 4.0ms (8.9% of total)

ival-sub: 3.0ms (6.6% of total)

adjust: 3.0ms (6.6% of total)

ival-add: 3.0ms (6.6% of total)

exact: 1.0ms (2.2% of total)

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

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

preprocess20.0ms (0.2%)

Memory

6.5MiB live, 40.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	120	26
4	172	26
5	202	26
6	214	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs x)

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	49
0	18	49
1	31	43
2	38	43
3	43	43
4	49	43
5	57	43
6	67	43
7	78	43
8	81	43
0	81	43

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize69.0ms (0.8%)

Memory

24.9MiB live, 100.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy	0.00390625	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Samples

17.0ms	98×	1	valid
13.0ms	157×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 130 to 20 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-hypot: 8.0ms (37.6% of total)

ival-div: 3.0ms (14.1% of total)

ival-sqrt: 3.0ms (14.1% of total)

ival-sub: 2.0ms (9.4% of total)

adjust: 2.0ms (9.4% of total)

ival-mult: 2.0ms (9.4% of total)

ival-add: 2.0ms (9.4% of total)

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

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

exact: 0.0ms (0% of total)

series21.0ms (0.2%)

Memory

-38.1MiB live, 15.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (patch (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())

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

Calls

3 calls:

Time	Variable		Point	Expression
16.0ms	x	@	0	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	inf	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	-inf	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))

Time

Variable

Point

Expression

16.0ms

((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))

1.0ms

inf

((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))

1.0ms

-inf

((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))

simplify194.0ms (2.3%)

Memory

-19.9MiB live, 172.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	206	855
1	592	781
2	1621	742
3	4409	701
0	8156	662

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 11/32 binary64) #s(literal 1/4 binary64))) (.f64 x x) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 69/256 binary64) #s(literal -11/64 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(fma.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 11/32 binary64) #s(literal -1/4 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 69/256 binary64) #s(literal 11/64 binary64)))))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 3/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (.f64 x x) #s(literal 3/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 3/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (.f64 x x) #s(literal 3/8 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal -3/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1 (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))) x) #s(literal 1/2 binary64))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) x)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x))
1
#s(literal 1 binary64)
(- 1 (/ 1 x))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
(+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x) #s(literal 1 binary64))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x)) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x)
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x)

rewrite193.0ms (2.2%)

Memory

18.5MiB live, 175.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	18	43
1	78	37
2	562	37
3	5209	37
0	8824	37

Stop Event

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

Counts

5 → 417

Calls

Call 1

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

Outputs
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eval84.0ms (1%)

Memory: 0.1MiB live, 159.2MiB allocated
Compiler: Compiled 10 877 to 1 898 computations (82.6% saved)

prune32.0ms (0.4%)

Memory

-31.3MiB live, 45.3MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	466	11	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	467	11	478

Accuracy

78.1%

Counts

478 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.8%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
	76.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
	55.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
	21.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
▶	21.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
▶	20.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
	56.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
	22.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
▶	56.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶	56.9%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
	56.9%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 296 to 216 computations (27% saved)

simplify208.0ms (2.4%)

Memory

19.9MiB live, 173.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	512	(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
cost-diff	128	(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
cost-diff	192	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	349
0	72	349
1	127	327
2	222	321
3	338	321
4	512	321
5	906	321
6	1674	321
7	2563	321
8	2785	321
9	3030	321
10	4397	321
11	5958	321
12	6237	321
13	6486	321
14	6753	321
15	6813	321
0	8084	321

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
#s(literal 3/16 binary64)
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)

Outputs
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
#s(literal 3/16 binary64)
(*.f64 x x)
x
#s(literal -1/4 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)

localize197.0ms (2.3%)

Memory

-7.3MiB live, 277.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.09603500976844202	(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	0.48828125	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	27.545472267642797	#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.05078125	(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.06640625	(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
accuracy	35.0199268517515	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
accuracy	36.10321283679128	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy	23.034409835078428	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.00390625	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	0.01171875	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
accuracy	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	14.244889191866234	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))

Samples

100.0ms	98×	1	valid
39.0ms	157×	0	valid
28.0ms	1×	2	valid

Compiler

Compiled 615 to 70 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-sub: 33.0ms (34% of total)

ival-div: 12.0ms (12.4% of total)

ival-neg: 11.0ms (11.3% of total)

ival-mult: 10.0ms (10.3% of total)

ival-hypot: 9.0ms (9.3% of total)

ival-add: 8.0ms (8.2% of total)

ival-sqrt: 7.0ms (7.2% of total)

adjust: 6.0ms (6.2% of total)

exact: 1.0ms (1% of total)

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

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

series27.0ms (0.3%)

Memory

8.3MiB live, 45.0MiB allocated

Counts

23 → 276

Calls

Call 1

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

Outputs
#s(alt (* -1/4 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4)) (taylor 0 x) (#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -2 (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (pow x 2)) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2) (taylor 0 x) (#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.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 (* 3/16 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (patch (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))
3.0ms	x	@	-inf	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))
3.0ms	x	@	0	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))

Time

Variable

Point

Expression

5.0ms

inf

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))

3.0ms

-inf

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))

3.0ms

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (+ (* 3/16 (* x x)) -1/4) (* x x)) 1) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (/ (sqrt 1/2) x) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* 3/16 (* x x)) -1/4))

simplify175.0ms (2%)

Memory

20.4MiB live, 210.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	4273
1	1259	3873
2	3930	3682
0	8371	3498

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* -1/4 (pow x 2)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(* -1/8 (/ (sqrt 1/2) (pow x 2)))
(/ (+ (* -1/8 (sqrt 1/2)) (* 1/2 (* x (sqrt 1/2)))) (pow x 2))
(/ (+ (* -1/8 (sqrt 1/2)) (* x (+ (* 1/2 (sqrt 1/2)) (* x (sqrt 1/2))))) (pow x 2))
(/ (+ (* -1/8 (sqrt 1/2)) (* x (+ (* 1/2 (sqrt 1/2)) (* x (sqrt 1/2))))) (pow x 2))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/4
(- (* 3/16 (pow x 2)) 1/4)
(- (* 3/16 (pow x 2)) 1/4)
(- (* 3/16 (pow x 2)) 1/4)
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))
(* -1 (+ 1 (sqrt 1/2)))
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))
(- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))
(* 3/16 (pow x 4))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))
(+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ -1/2 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (/ 1/4 (* x (sqrt 1/2))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 3/16 (pow x 2))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/4))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(* 3/16 (pow x 4))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 3/16 (pow x 2))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))

Outputs
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 35/256 binary64) (.f64 x x) #s(literal -5/32 binary64)) (.f64 x x) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
-2
#s(literal -2 binary64)
(- (* 1/8 (pow x 2)) 2)
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(fma.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (fma.f64 (/.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* (sqrt 1/2) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
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(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 3/16 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 x))) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(* 3/16 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/16 binary64))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(* (pow x 4) (- (+ 3/16 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(- 1 (sqrt 1/2))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 3/16 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (neg.f64 x))) x))
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(-.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 3/16 (pow x 2))
(.f64 #s(literal 3/16 binary64) (.f64 x x))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)

rewrite215.0ms (2.5%)

Memory

-25.0MiB live, 257.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	307
0	72	307
1	319	285
2	2632	275
0	8729	275

Stop Event

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

Counts

23 → 505

Calls

Call 1

Inputs
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 x x)
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))

Outputs
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eval168.0ms (2%)

Memory: 26.7MiB live, 212.1MiB allocated
Compiler: Compiled 22 609 to 2 897 computations (87.2% saved)

prune37.0ms (0.4%)

Memory

9.5MiB live, 91.6MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	900	12	912
Fresh	3	3	6
Picked	3	2	5
Done	0	0	0
Total	906	17	923

Accuracy

99.9%

Counts

923 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	77.8%	(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	56.4%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64))))
	57.2%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
✓	77.8%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
▶	22.8%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
▶	77.8%	(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
	45.2%	(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
	55.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
▶	56.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
✓	56.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶	28.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
	57.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
	43.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
	45.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
	43.5%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	45.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
	56.9%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 736 to 418 computations (43.2% saved)

simplify142.0ms (1.7%)

Memory

2.9MiB live, 159.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
cost-diff	192	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64)))
cost-diff	0	#s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))
cost-diff	0	#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
cost-diff	0	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
cost-diff	128	(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
cost-diff	192	(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
cost-diff	8576	(-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
cost-diff	14976	(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	548
0	102	548
1	204	494
2	448	483
3	1315	478
4	5073	478
0	8213	477

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
#s(literal -1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))))
#s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))
(+.f64 #s(literal 1/2 binary64) x)
x
#s(literal -1/8 binary64)
(*.f64 x x)
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64))
#s(literal 69/1024 binary64)
(*.f64 x x)
#s(literal -11/128 binary64)
#s(literal 1/8 binary64)
#s(literal -2 binary64)

Outputs
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(*.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal -1 binary64)
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(*.f64 x x)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64))))))
#s(literal 1 binary64)
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)))))
#s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))
#s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))
(*.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64)))
(*.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))
(fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64))
(+.f64 #s(literal 1/2 binary64) x)
(+.f64 x #s(literal 1/2 binary64))
x
#s(literal -1/8 binary64)
(*.f64 x x)
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64))
#s(literal 69/1024 binary64)
(*.f64 x x)
#s(literal -11/128 binary64)
#s(literal 1/8 binary64)
#s(literal -2 binary64)

localize245.0ms (2.9%)

Memory

16.4MiB live, 386.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.04296875	(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
accuracy	0.07421875	(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64))
accuracy	14.244889191866234	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
accuracy	36.01792294811124	#s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)))
accuracy	0.10546875	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64)))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
accuracy	18.17460196736336	(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))
accuracy	27.545472267642797	#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))))
accuracy	0	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
accuracy	0.00390625	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))
accuracy	14.784303323226393	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
accuracy	26.26781882084844	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	35.040951500502416	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy	0.00390625	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	14.253213504419477	(-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))

Samples

131.0ms	98×	1	valid
71.0ms	157×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 1 014 to 99 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

adjust: 36.0ms (21.3% of total)

ival-mult: 34.0ms (20.1% of total)

ival-sub: 32.0ms (18.9% of total)

ival-div: 27.0ms (16% of total)

ival-add: 15.0ms (8.9% of total)

ival-hypot: 11.0ms (6.5% of total)

ival-sqrt: 8.0ms (4.7% of total)

ival-pow2: 3.0ms (1.8% of total)

exact: 1.0ms (0.6% of total)

ival-neg: 1.0ms (0.6% of total)

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

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

series53.0ms (0.6%)

Memory

33.6MiB live, 102.4MiB allocated

Counts

25 → 300

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) (patch (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (patch (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
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#s(alt #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))) (patch #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))) (patch #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))) #<representation binary64>) () ())
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#s(alt (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())
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Outputs
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) (patch (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) (patch (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) (patch (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) (patch (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* -13/32 (pow x 2)))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 183/512 (pow x 2)) 13/32)))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 183/512 (* -1335/4096 (pow x 2)))) 13/32)))) (taylor 0 x) (#s(alt (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor 0 x) (#s(alt (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (patch (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/4 (- (* -1 (sqrt 1/2)) 1))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 1/2) (taylor -inf x) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) (patch (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))) (patch #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))) (patch #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))) (patch #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))) (patch #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 69/1024 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (patch (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 69/1024 (pow x 4)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

21.0ms

inf

((/ (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (pow (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) 2)) (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (/ (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (* x x)) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (+ (* 69/1024 (* x x)) -11/128) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8))

4.0ms

-inf

((/ (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (pow (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) 2)) (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (/ (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (* x x)) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (+ (* 69/1024 (* x x)) -11/128) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8))

3.0ms

((/ (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (pow (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) 2)) (- (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (* 1/2 (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* 1/8 (* x x)) (* x x) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (/ 1/2 x) 1/2) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (/ (* (sqrt 1/2) (+ (* (+ 1/2 x) x) -1/8)) (* x x)) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (+ (* 69/1024 (* x x)) -11/128) (+ (* (+ (* 69/1024 (* x x)) -11/128) (* x x)) 1/8))

simplify231.0ms (2.7%)

Memory

-12.2MiB live, 362.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	754	7352
1	2450	6449
0	8312	6147

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -13/32 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 183/512 (pow x 2)) 13/32))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 183/512 (* -1335/4096 (pow x 2)))) 13/32))))
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
-1
(- (* 1/16 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/16 (* -11/256 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/16 (* (pow x 2) (- (* 69/2048 (pow x 2)) 11/256)))) 1)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(* (sqrt 1/2) (sqrt 2))
(+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))
(+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(- 1 (* (sqrt 1/2) (sqrt 2)))
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(* 69/1024 (pow x 2))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (pow (- (* -1 (sqrt 1/2)) 1) 2))
(- (+ (* -1 (/ (- (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) x)) (+ (/ 1/2 (- (* -1 (sqrt 1/2)) 1)) (/ 1 (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* -1 (/ (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* -1/2 (/ (- (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) (* (sqrt 1/2) (- (* -1 (sqrt 1/2)) 1)))) (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (/ (* (+ (* 1/16 (/ (- (* -1 (sqrt 1/2)) 1) (pow (sqrt 1/2) 3))) (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2)))) (pow (- (* -1 (sqrt 1/2)) 1) 4)))))) x)) (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1))))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) x)) (+ (/ 1/2 (- (* -1 (sqrt 1/2)) 1)) (/ 1 (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* -1 (/ (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2))))
(- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2))))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* -1/2 (/ (- (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) (* (sqrt 1/2) (- (* -1 (sqrt 1/2)) 1)))) (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (/ (* (+ (* 1/16 (/ (- (* -1 (sqrt 1/2)) 1) (pow (sqrt 1/2) 3))) (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2)))) (pow (- (* -1 (sqrt 1/2)) 1) 4)))))) (* (sqrt 1/2) (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* 1/4 (/ 1 (- (* -1 (sqrt 1/2)) 1))) (+ (/ (* (+ (* 1/16 (/ (- (* -1 (sqrt 1/2)) 1) (pow (sqrt 1/2) 3))) (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (- (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2))))))) (pow (- (* -1 (sqrt 1/2)) 1) 2)) (/ (* (- (* -1 (/ (* (- (* -1 (sqrt 1/2)) 1) (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4)) (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 4)))) (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2)))) (pow (- (* -1 (sqrt 1/2)) 1) 4))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2))))) (+ (* -1/2 (/ (- (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1)))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) (* (sqrt 1/2) (- (* -1 (sqrt 1/2)) 1)))) (+ (* 1/32 (/ 1 (* (pow (sqrt 1/2) 3) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (/ (* (+ (* 1/16 (/ (- (* -1 (sqrt 1/2)) 1) (pow (sqrt 1/2) 3))) (* 1/16 (/ 1 (pow (sqrt 1/2) 2)))) (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2)))) (pow (- (* -1 (sqrt 1/2)) 1) 4)))))) x)) (+ (* 1/4 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* 1/2 (/ 1 (- (* -1 (sqrt 1/2)) 1))))) (+ (* -1/2 (/ (- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2))) (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 3)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2)))))) x)) (+ (/ 1/2 (- (* -1 (sqrt 1/2)) 1)) (/ 1 (pow (- (* -1 (sqrt 1/2)) 1) 2)))) (* -1 (/ (sqrt 1/2) (pow (- (* -1 (sqrt 1/2)) 1) 2))))
(- (+ 1 (* 1/2 (- (* -1 (sqrt 1/2)) 1))) (* -1 (sqrt 1/2)))
(- (+ 1 (+ (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (+ (* -1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* 1/2 (- (* -1 (sqrt 1/2)) 1)))) (* -1 (sqrt 1/2)))
(- (+ 1 (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 3))) (+ (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* -1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* 1/2 (- (* -1 (sqrt 1/2)) 1)))) (* -1 (sqrt 1/2)))
(- (+ 1 (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/4 (- (* -1 (sqrt 1/2)) 1)))) x)) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) (+ (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) (+ (* -1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* 1/2 (- (* -1 (sqrt 1/2)) 1)))) (* -1 (sqrt 1/2)))
(- (* -1 (sqrt 1/2)) 1)
(- (+ (* -1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2))))) 1)
(- (+ (* -1 (sqrt 1/2)) (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) 1)
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(* 1/2 (- (* -1 (sqrt 1/2)) 1))
(+ (* 1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/8 (/ 1 (* x (sqrt 1/2)))))
(+ (* 1/2 (- (* -1 (sqrt 1/2)) 1)) (+ (/ 1/64 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/8 (* x (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (- (* -1 (sqrt 1/2)) 1)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(* (pow x 2) (sqrt 1/2))
(* (pow x 2) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))
(* (pow x 2) (+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x))))
(* (pow x 2) (+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x))))
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(sqrt 1/2)
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(- (* -1 (sqrt 1/2)) 1)
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (* -1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/4 (- (* -1 (sqrt 1/2)) 1))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(* 69/1024 (pow x 2))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))

Outputs
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -13/32 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -13/32 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 183/512 (pow x 2)) 13/32))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 183/512 binary64) (.f64 x x) #s(literal -13/32 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 183/512 (* -1335/4096 (pow x 2)))) 13/32))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1335/4096 binary64) (.f64 x x) #s(literal 183/512 binary64)) (.f64 x x) #s(literal -13/32 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
-2
#s(literal -2 binary64)
(- (* 1/8 (pow x 2)) 2)
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(fma.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))
-1
#s(literal -1 binary64)
(- (* 1/16 (pow x 2)) 1)
(fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/16 (* -11/256 (pow x 2)))) 1)
(fma.f64 (fma.f64 #s(literal -11/256 binary64) (.f64 x x) #s(literal 1/16 binary64)) (.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/16 (* (pow x 2) (- (* 69/2048 (pow x 2)) 11/256)))) 1)
(fma.f64 (fma.f64 (fma.f64 #s(literal 69/2048 binary64) (.f64 x x) #s(literal -11/256 binary64)) (.f64 x x) #s(literal 1/16 binary64)) (*.f64 x x) #s(literal -1 binary64))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
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(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (neg.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) x) (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (-.f64 (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64))) #s(literal 1/32 binary64) (fma.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -3/64 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))) x))) (neg.f64 x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64))) (neg.f64 x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(- (* -1 (sqrt 1/2)) 1)
(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (* -1/2 (- (* -1 (sqrt 1/2)) 1)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(fma.f64 (/.f64 (fma.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(fma.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x) #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ (* -1 (sqrt 1/2)) (* -1 (/ (- (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/4 (- (* -1 (sqrt 1/2)) 1))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))) x)) (* -1/2 (- (* -1 (sqrt 1/2)) 1))) (* 1/4 (/ 1 (sqrt 1/2)))) x))) 1)
(fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (fma.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 #s(literal 3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) x) #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* 1/8 (/ (sqrt 1/2) x))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(* -1 (+ 1 (sqrt 1/2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(-.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (/.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(fma.f64 (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal -1 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 69/1024 (pow x 2))
(.f64 #s(literal 69/1024 binary64) (.f64 x x))
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (*.f64 x x))) x) x)
(* 69/1024 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 69/1024 binary64))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 69/1024 binary64) (/.f64 #s(literal 11/128 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 69/1024 binary64)) (/.f64 #s(literal 11/128 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 69/1024 binary64)) (/.f64 #s(literal 11/128 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))

rewrite234.0ms (2.7%)

Memory

20.6MiB live, 316.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	451
0	102	451
1	478	398
2	3988	390
0	9605	386

Stop Event

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

Counts

25 → 684

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(*.f64 x x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
#s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))))
#s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x))
#s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64)))
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64))
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))

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eval302.0ms (3.5%)

Memory: -19.1MiB live, 542.9MiB allocated
Compiler: Compiled 72 217 to 5 605 computations (92.2% saved)

prune52.0ms (0.6%)

Memory

14.3MiB live, 130.6MiB allocated

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	1 622	5	1 627
Fresh	1	9	10
Picked	2	3	5
Done	0	2	2
Total	1 625	19	1 644

Accuracy

99.9%

Counts

1 644 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.8%	(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
	56.4%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64))))
▶	57.2%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
✓	77.8%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
	21.1%	(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
	23.0%	(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 #s(approx (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #s(literal 2 binary64)))
	22.8%	(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
	45.2%	(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
	55.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
✓	56.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
✓	56.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓	28.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
	28.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
	57.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	43.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
	45.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	43.5%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	45.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
▶	56.9%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 910 to 492 computations (45.9% saved)

simplify119.0ms (1.4%)

Memory

-4.5MiB live, 147.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
cost-diff	128	(-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
cost-diff	192	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
cost-diff	640	(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
cost-diff	0	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
cost-diff	0	(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64)))
cost-diff	192	(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
cost-diff	8512	(.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
cost-diff	43840	(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	722
0	131	722
1	234	680
2	563	678
3	2624	643
0	8771	641

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64)))
(pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))
(*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal -1 binary64)
(.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal -11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
#s(literal -1843/32768 binary64)
(*.f64 x x)
x
#s(literal 69/1024 binary64)
#s(literal -11/128 binary64)
#s(literal 1/8 binary64)
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 3/16 binary64) x) x)
(/.f64 #s(literal 3/16 binary64) x)
#s(literal 3/16 binary64)
(+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
#s(literal 1/4 binary64)
(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))

Outputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64)))
(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))
(pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64))
(*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal -1 binary64)
(.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -3/2 binary64)))
(pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64))
(*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(*.f64 (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (-.f64 #s(literal -3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -3/2 binary64))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))
#s(literal -11/128 binary64)
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
#s(literal -1843/32768 binary64)
(*.f64 x x)
x
#s(literal 69/1024 binary64)
#s(literal -11/128 binary64)
#s(literal 1/8 binary64)
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 3/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x)) x)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 3/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x)) x)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))
(-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 3/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x))
(/.f64 (/.f64 #s(literal 3/16 binary64) x) x)
(/.f64 #s(literal 3/16 binary64) x)
#s(literal 3/16 binary64)
(+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1 binary64)
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(neg.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))

localize304.0ms (3.5%)

Memory

-9.2MiB live, 428.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	11.629038300439616	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	14.2279656899499	(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
accuracy	14.235607311470917	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy	14.244889191866234	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
accuracy	0.12109375	(/.f64 (/.f64 #s(literal 3/16 binary64) x) x)
accuracy	0.48828125	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy	1.0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	27.043236555208704	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	0.03125	(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.03515625	(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.0546875	(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
accuracy	36.03888134678093	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0.015625	(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.046875	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.08203125	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	36.147710092893035	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0.015625	(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
accuracy	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	0.55859375	(*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
accuracy	14.809794866929739	(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64)))

Samples

107.0ms	75×	1	valid
79.0ms	157×	0	valid
34.0ms	24×	2	valid

Compiler

Compiled 1 592 to 135 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 170.0ms

ival-sub: 42.0ms (24.7% of total)

ival-mult: 31.0ms (18.3% of total)

ival-div: 28.0ms (16.5% of total)

adjust: 17.0ms (10% of total)

ival-add: 16.0ms (9.4% of total)

ival-pow2: 11.0ms (6.5% of total)

ival-sqrt: 11.0ms (6.5% of total)

ival-hypot: 10.0ms (5.9% of total)

ival-neg: 3.0ms (1.8% of total)

exact: 1.0ms (0.6% of total)

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

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

series53.0ms (0.6%)

Memory

12.3MiB live, 92.2MiB allocated

Counts

28 → 312

Calls

Call 1

Inputs
#s(alt (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) (patch (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (patch (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (patch #s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (patch (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (patch (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (patch (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (patch (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (patch (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt -8 (taylor 0 x) (#s(alt (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) (patch (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* -1/2 (pow x 2)) 8) (taylor 0 x) (#s(alt (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) (patch (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* 3/4 (pow x 2)) 1/2)) 8) (taylor 0 x) (#s(alt (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) (patch (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (+ 3/4 (* -447/512 (pow x 2)))) 1/2)) 8) (taylor 0 x) (#s(alt (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) (patch (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/4 (pow x 2))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

16.0ms

inf

((/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) (+ (* (/ (sqrt 1/2) x) (- (/ (/ 3/16 x) x) (+ (/ -1/8 x) 1/2))) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -1843/32768 (* x x)) 69/1024) (- 1 (sqrt 1/2)) (/ (/ 3/16 x) x) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1/4 (/ 1/4 (+ (* x x) 1))) (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))

6.0ms

-inf

((/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) (+ (* (/ (sqrt 1/2) x) (- (/ (/ 3/16 x) x) (+ (/ -1/8 x) 1/2))) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -1843/32768 (* x x)) 69/1024) (- 1 (sqrt 1/2)) (/ (/ 3/16 x) x) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1/4 (/ 1/4 (+ (* x x) 1))) (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))

4.0ms

((/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)) (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* -11/128 (* x x)) 1/8) x) x) (* (+ (* -11/128 (* x x)) 1/8) x) (+ (* -11/128 (* x x)) 1/8) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (* (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) x) (* (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) x) (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) (+ (* (/ (sqrt 1/2) x) (- (/ (/ 3/16 x) x) (+ (/ -1/8 x) 1/2))) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))) (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (+ (* -1843/32768 (* x x)) 69/1024) (- 1 (sqrt 1/2)) (/ (/ 3/16 x) x) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1/4 (/ 1/4 (+ (* x x) 1))) (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))

simplify238.0ms (2.8%)

Memory

10.5MiB live, 273.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	846	9991
1	2654	8973
0	8749	8469

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

Inputs
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
-8
(- (* -1/2 (pow x 2)) 8)
(- (* (pow x 2) (- (* 3/4 (pow x 2)) 1/2)) 8)
(- (* (pow x 2) (- (* (pow x 2) (+ 3/4 (* -447/512 (pow x 2)))) 1/2)) 8)
1
(+ 1 (* 1/4 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 5/8 (pow x 2)) 1))
(* (pow x 2) (- (* (pow x 2) (+ 5/8 (* -103/256 (pow x 2)))) 1))
(* (pow x 2) (- (* (pow x 2) (+ 5/8 (* (pow x 2) (- (* 497/2048 (pow x 2)) 103/256)))) 1))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* 3/16 (/ (sqrt 1/2) (pow x 3)))
(/ (+ (* 1/8 (* x (sqrt 1/2))) (* 3/16 (sqrt 1/2))) (pow x 3))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))))) (pow x 3))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))))))) (pow x 3))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
-2
(- (* -3/8 (pow x 2)) 2)
(- (* (pow x 2) (- (* 41/128 (pow x 2)) 3/8)) 2)
(- (* (pow x 2) (- (* (pow x 2) (+ 41/128 (* -297/1024 (pow x 2)))) 3/8)) 2)
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
69/1024
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(* -2/3 (/ (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2)) (pow (+ 1 (sqrt 1/2)) 3)))
(+ (* -1 (/ (- (* 2/3 (/ (- (* -1/4 (/ (- (* -1/2 (sqrt 1/2)) 1/2) (sqrt 1/2))) (+ (* -1 (pow (+ 1 (sqrt 1/2)) 2)) (* 1/2 (/ (+ 1 (sqrt 1/2)) (sqrt 1/2))))) (pow (+ 1 (sqrt 1/2)) 3))) (* 4/9 (/ (* (+ (* -1/2 (pow (+ 1 (sqrt 1/2)) 3)) (* 3/2 (+ (* 1/4 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))) (* 1/2 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2)))))) (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2))) (pow (+ 1 (sqrt 1/2)) 6)))) x)) (* -2/3 (/ (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2)) (pow (+ 1 (sqrt 1/2)) 3))))
(+ (* -1 (/ (- (* 2/3 (/ (- (* -1/4 (/ (- (* -1/2 (sqrt 1/2)) 1/2) (sqrt 1/2))) (+ (* -1 (pow (+ 1 (sqrt 1/2)) 2)) (* 1/2 (/ (+ 1 (sqrt 1/2)) (sqrt 1/2))))) (pow (+ 1 (sqrt 1/2)) 3))) (* 4/9 (/ (* (+ (* -1/2 (pow (+ 1 (sqrt 1/2)) 3)) (* 3/2 (+ (* 1/4 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))) (* 1/2 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2)))))) (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2))) (pow (+ 1 (sqrt 1/2)) 6)))) x)) (+ (* -1 (/ (- (* 2/3 (/ (- (+ (* 1/64 (/ 1 (pow (sqrt 1/2) 2))) (* 1/32 (/ (- (* -1/2 (sqrt 1/2)) 1/2) (pow (sqrt 1/2) 3)))) (+ (* -1/2 (/ (+ 1 (sqrt 1/2)) (sqrt 1/2))) (+ (* -1/16 (/ (+ 1 (sqrt 1/2)) (pow (sqrt 1/2) 3))) (+ (* 1/16 (/ 1 (pow (sqrt 1/2) 2))) (* 1/4 (pow (+ 1 (sqrt 1/2)) 2)))))) (pow (+ 1 (sqrt 1/2)) 3))) (+ (* 4/9 (/ (* (+ (* -1/2 (+ (* 1/4 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))) (* 1/2 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))))) (* 3/2 (+ (* -1/32 (/ (pow (+ 1 (sqrt 1/2)) 2) (pow (sqrt 1/2) 3))) (+ (* 1/8 (/ (+ 1 (sqrt 1/2)) (pow (sqrt 1/2) 2))) (* (+ 1 (sqrt 1/2)) (+ (* -1/16 (/ (+ 1 (sqrt 1/2)) (pow (sqrt 1/2) 3))) (* 1/16 (/ 1 (pow (sqrt 1/2) 2))))))))) (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2))) (pow (+ 1 (sqrt 1/2)) 6))) (* 2/3 (/ (* (+ (* -1/2 (pow (+ 1 (sqrt 1/2)) 3)) (* 3/2 (+ (* 1/4 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))) (* 1/2 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2)))))) (- (* 2/3 (/ (- (* -1/4 (/ (- (* -1/2 (sqrt 1/2)) 1/2) (sqrt 1/2))) (+ (* -1 (pow (+ 1 (sqrt 1/2)) 2)) (* 1/2 (/ (+ 1 (sqrt 1/2)) (sqrt 1/2))))) (pow (+ 1 (sqrt 1/2)) 3))) (* 4/9 (/ (* (+ (* -1/2 (pow (+ 1 (sqrt 1/2)) 3)) (* 3/2 (+ (* 1/4 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2))) (* 1/2 (/ (pow (+ 1 (sqrt 1/2)) 2) (sqrt 1/2)))))) (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2))) (pow (+ 1 (sqrt 1/2)) 6))))) (pow (+ 1 (sqrt 1/2)) 3))))) (pow x 2))) (* -2/3 (/ (- (pow (- (* -1/2 (sqrt 1/2)) 1/2) 2) (pow (+ 1 (sqrt 1/2)) 2)) (pow (+ 1 (sqrt 1/2)) 3)))))
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3/2
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(* -1843/32768 (pow x 8))
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(* -1843/32768 (pow x 7))
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(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(- 1 (sqrt 1/2))
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(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
-1/2
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1/2
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(* -1843/32768 (pow x 2))
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3/2
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(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 7))
(* -1 (* (pow x 7) (- 1843/32768 (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(- 1 (sqrt 1/2))
(- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- 1 (sqrt 1/2))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
(/ (sqrt 1/2) x)
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(* -3/2 (+ 1 (sqrt 1/2)))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (+ (* -1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 3/8 (* x (sqrt 1/2)))))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (* -1 (/ (+ (* -1 (+ (* -1/2 (+ 1 (sqrt 1/2))) (* 3/8 (/ 1 (sqrt 1/2))))) (* -1 (/ (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 3/64 (/ 1 (pow (sqrt 1/2) 3)))) x))) x)))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (* -1 (/ (+ (* -1 (+ (* -1/2 (+ 1 (sqrt 1/2))) (* 3/8 (/ 1 (sqrt 1/2))))) (* -1 (/ (+ (* 3/64 (/ 1 (pow (sqrt 1/2) 3))) (+ (* 1/8 (/ 1 (sqrt 1/2))) (+ (* 1/4 (/ (+ 1 (sqrt 1/2)) x)) (+ (* 3/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (/ 1/64 (* x (pow (sqrt 1/2) 3))))))) x))) x)))
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
(/ 3/16 (pow x 2))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))
1/4
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))

Outputs
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
-8
#s(literal -8 binary64)
(- (* -1/2 (pow x 2)) 8)
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -8 binary64))
(- (* (pow x 2) (- (* 3/4 (pow x 2)) 1/2)) 8)
(fma.f64 (fma.f64 #s(literal 3/4 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal -8 binary64))
(- (* (pow x 2) (- (* (pow x 2) (+ 3/4 (* -447/512 (pow x 2)))) 1/2)) 8)
(fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/4 (pow x 2)))
(fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal -3/16 binary64) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 5/32 binary64) (.f64 x x) #s(literal -3/16 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (* 5/8 (pow x 2)) 1))
(.f64 (.f64 (fma.f64 #s(literal 5/8 binary64) (*.f64 x x) #s(literal -1 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 5/8 (* -103/256 (pow x 2)))) 1))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal -103/256 binary64) (.f64 x x) #s(literal 5/8 binary64)) (.f64 x x) #s(literal -1 binary64)) x) x)
(* (pow x 2) (- (* (pow x 2) (+ 5/8 (* (pow x 2) (- (* 497/2048 (pow x 2)) 103/256)))) 1))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 497/2048 binary64) (.f64 x x) #s(literal -103/256 binary64)) (.f64 x x) #s(literal 5/8 binary64)) (*.f64 x x) #s(literal -1 binary64)) x) x)
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(* 3/16 (/ (sqrt 1/2) (pow x 3)))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 3/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 1/8 (* x (sqrt 1/2))) (* 3/16 (sqrt 1/2))) (pow x 3))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 3/16 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))))) (pow x 3))
(/.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/8 binary64))) x (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 3/16 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* 3/16 (sqrt 1/2)) (* x (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))))))) (pow x 3))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/8 binary64)) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 3/16 binary64))) (pow.f64 x #s(literal 3 binary64)))
(- 1 (* (sqrt 1/2) (sqrt 2)))
(-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (fma.f64 (.f64 x x) (/.f64 (neg.f64 (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal 69/256 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(/ (sqrt 1/2) x)
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(* -1/4 (pow x 2))
(.f64 #s(literal -1/4 binary64) (.f64 x x))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
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(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (-.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64))) #s(literal 1/32 binary64) (fma.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -3/64 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))) x)) (.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64))) (neg.f64 x)) (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))))
(* -3/2 (+ 1 (sqrt 1/2)))
(fma.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -3/2 binary64))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (+ (* -1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 3/8 (* x (sqrt 1/2)))))
(fma.f64 #s(literal -3/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (* -1 (/ (+ (* -1 (+ (* -1/2 (+ 1 (sqrt 1/2))) (* 3/8 (/ 1 (sqrt 1/2))))) (* -1 (/ (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 3/64 (/ 1 (pow (sqrt 1/2) 3)))) x))) x)))
(-.f64 (fma.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -3/2 binary64)) (/.f64 (-.f64 (fma.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(+ (* -3/2 (+ 1 (sqrt 1/2))) (* -1 (/ (+ (* -1 (+ (* -1/2 (+ 1 (sqrt 1/2))) (* 3/8 (/ 1 (sqrt 1/2))))) (* -1 (/ (+ (* 3/64 (/ 1 (pow (sqrt 1/2) 3))) (+ (* 1/8 (/ 1 (sqrt 1/2))) (+ (* 1/4 (/ (+ 1 (sqrt 1/2)) x)) (+ (* 3/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (/ 1/64 (* x (pow (sqrt 1/2) 3))))))) x))) x)))
(-.f64 (fma.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -3/2 binary64)) (/.f64 (-.f64 (fma.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) x) #s(literal 1/4 binary64) (+.f64 (/.f64 (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -9/64 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 3/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64))) (neg.f64 x))
(* -1843/32768 (pow x 2))
(.f64 #s(literal -1843/32768 binary64) (.f64 x x))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(/ 3/16 (pow x 2))
(/.f64 #s(literal 3/16 binary64) (*.f64 x x))
(/ 3/16 (pow x 2))
(/.f64 #s(literal 3/16 binary64) (*.f64 x x))
(/ 3/16 (pow x 2))
(/.f64 #s(literal 3/16 binary64) (*.f64 x x))
(/ 3/16 (pow x 2))
(/.f64 #s(literal 3/16 binary64) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))
(-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) x)))
1/4
#s(literal 1/4 binary64)
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 6 binary64))))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/2 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) x) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))))

rewrite211.0ms (2.5%)

Memory

8.5MiB live, 328.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	492
0	131	481
1	587	421
2	5307	393
0	8744	393

Stop Event

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

Counts

28 → 834

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
(.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64)))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 3/16 binary64) x) x)
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Outputs
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eval557.0ms (6.5%)

Memory: -37.7MiB live, 836.8MiB allocated
Compiler: Compiled 98 330 to 6 783 computations (93.1% saved)

prune109.0ms (1.3%)

Memory

18.8MiB live, 209.7MiB allocated

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	1 753	9	1 762
Fresh	6	3	9
Picked	4	1	5
Done	1	4	5
Total	1 764	17	1 781

Accuracy

100.0%

Counts

1 781 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.1%	(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #s(approx ( (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))))
	11.7%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
	77.8%	(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	77.8%	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
	22.8%	(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
	55.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
✓	56.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
✓	56.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓	28.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
	28.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
	45.2%	#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
	57.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
	43.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
	43.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
✓	43.5%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	45.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
	56.9%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 1 455 to 457 computations (68.6% saved)

regimes93.0ms (1.1%)

Memory

1.3MiB live, 183.0MiB allocated

Counts

38 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 #s(approx (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #s(approx ( (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (*.f64 (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (*.f64 (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Calls

7 calls:

19.0ms	(hypot.f64 #s(literal 1 binary64) x)
17.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
12.0ms	x
11.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
11.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
100.0%	2	`x`
100.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
100.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
100.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
100.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
100.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes170.0ms (2%)

Memory

14.8MiB live, 158.3MiB allocated

Counts

37 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 #s(approx (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #s(approx ( (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Calls

7 calls:

90.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
22.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
15.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
11.0ms	x
9.0ms	(hypot.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes90.0ms (1%)

Memory

-19.4MiB live, 120.0MiB allocated

Counts

34 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 #s(approx (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #s(approx ( (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64)))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

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

Calls

7 calls:

34.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
10.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
10.0ms	x
8.0ms	(hypot.f64 #s(literal 1 binary64) x)
8.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes65.0ms (0.8%)

Memory

4.2MiB live, 161.6MiB allocated

Counts

33 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 #s(approx (+ (* -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 2 binary64))) #s(approx ( (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1)))) (fma.f64 (fma.f64 (fma.f64 #s(literal -447/512 binary64) (.f64 x x) #s(literal 3/4 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal -8 binary64))))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Calls

7 calls:

10.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
9.0ms	x
9.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
9.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
8.0ms	(hypot.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes61.0ms (0.7%)

Memory

2.1MiB live, 160.3MiB allocated

Counts

29 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64)))

Calls

7 calls:

11.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
10.0ms	x
9.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
8.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
7.0ms	(hypot.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes57.0ms (0.7%)

Memory

2.8MiB live, 121.5MiB allocated

Counts

28 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))

Calls

7 calls:

10.0ms	x
8.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
8.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
8.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
7.0ms	(hypot.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes56.0ms (0.7%)

Memory

20.4MiB live, 97.6MiB allocated

Counts

27 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) x) x #s(literal -1/8 binary64))) (.f64 x x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) x) x) x (.f64 #s(literal 1/8 binary64) x)) x))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) #s(approx (+ (* (/ (sqrt 1/2) x) (+ (/ -1/8 x) 1/2)) (sqrt 1/2)) (*.f64 (/.f64 (/.f64 (fma.f64 (+.f64 x #s(literal 1/2 binary64)) x #s(literal -1/8 binary64)) x) x) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 (/.f64 #s(literal 3/16 binary64) x) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(approx (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (fma.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(approx (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x))))) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) (.f64 x x) #s(literal -3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x))))) #s(literal 1 binary64)))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

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

Calls

7 calls:

12.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
9.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
8.0ms	x
7.0ms	(hypot.f64 #s(literal 1 binary64) x)
6.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
99.2%	2	`x`
99.2%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.2%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.2%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.2%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.2%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.2%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes43.0ms (0.5%)

Memory

0.2MiB live, 38.7MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

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

Calls

7 calls:

20.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
4.0ms	x
4.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms	(hypot.f64 #s(literal 1 binary64) x)
3.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

Accuracy	Segments	Branch
99.2%	2	`x`
99.2%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.2%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.2%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.2%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.2%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.2%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes48.0ms (0.6%)

Memory

-22.0MiB live, 35.5MiB allocated

Counts

11 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (pow (+ (* (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) -1/2) -1/2) 2) (pow (* (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1) (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))))) 2)) (* (pow (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 2) (* (- -1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (+ 1/2 (+ (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) 1))))) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

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

Calls

7 calls:

26.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
4.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms	x
3.0ms	(hypot.f64 #s(literal 1 binary64) x)
3.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
99.1%	2	`x`
99.1%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.1%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.1%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.1%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.1%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.1%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes32.0ms (0.4%)

Memory

3.5MiB live, 38.8MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ 1/2 (sqrt (+ (* 1 1) (* x x)))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

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

Calls

7 calls:

15.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
3.0ms	x
3.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
3.0ms	(hypot.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
99.0%	2	`x`
99.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes17.0ms (0.2%)

Memory

6.2MiB live, 40.9MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

Outputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (*.f64 (*.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))

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

Calls

7 calls:

5.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms	x
2.0ms	(hypot.f64 #s(literal 1 binary64) x)
2.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
98.1%	2	`x`
98.1%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.1%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
98.1%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.1%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.1%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.1%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes14.0ms (0.2%)

Memory

-4.3MiB live, 32.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

Calls

7 calls:

3.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms	x
2.0ms	(hypot.f64 #s(literal 1 binary64) x)
2.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
97.9%	2	`x`
97.9%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
97.9%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
97.9%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.9%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.9%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.9%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes9.0ms (0.1%)

Memory

21.9MiB live, 21.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

1.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms	(hypot.f64 #s(literal 1 binary64) x)
1.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
1.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
45.2%	1	`x`
45.2%	1	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
45.2%	1	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
45.2%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
45.2%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
45.2%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
45.2%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000005997345303	1.0004232026696918

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch4.0ms (0%)

Memory

-50.9MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0004232026696918	8000.251582681235

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify60.0ms (0.7%)

Memory

8.1MiB live, 47.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1100
1	177	1100
2	250	1098
3	337	1098
4	386	1098
5	414	1098
6	427	1098
7	449	1098
8	487	1098
9	511	1098
10	653	1098
11	812	1098

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))

Outputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (pow.f64 (.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 2 binary64)))) (.f64 (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64)) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64))))) (.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64))) (*.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 3 binary64))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 (.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal 2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) #s(literal 1 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2252250173647985/2251799813685248 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))))
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(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))

soundness1.3s (15.6%)

Memory

40.0MiB live, 1 068.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	492
0	131	481
1	587	421
2	5307	393
0	8744	393
0	408	4273
1	1259	3873
2	3930	3682
0	8371	3498
0	65	451
0	102	451
1	478	398
2	3988	390
0	9605	386
0	43	307
0	72	307
1	319	285
2	2632	275
0	8729	275
0	9	43
0	18	43
1	78	37
2	562	37
3	5209	37
0	8824	37
0	206	855
1	592	781
2	1621	742
3	4409	701
0	8156	662

Stop Event

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

Compiler

Compiled 1 012 to 344 computations (66% saved)

preprocess208.0ms (2.4%)

Memory: -45.7MiB live, 205.3MiB allocated
Remove: (abs x)
Compiler: Compiled 1 544 to 308 computations (80.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	120	26
4	172	26
5	202	26
6	214	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	120	26
4	172	26
5	202	26
6	214	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (17.7%)

explain201.0ms (2.3%)

preprocess20.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize69.0ms (0.8%)

series21.0ms (0.2%)

simplify194.0ms (2.3%)

rewrite193.0ms (2.2%)

eval84.0ms (1%)

prune32.0ms (0.4%)

simplify208.0ms (2.4%)

localize197.0ms (2.3%)

series27.0ms (0.3%)

simplify175.0ms (2%)

rewrite215.0ms (2.5%)

eval168.0ms (2%)

prune37.0ms (0.4%)

simplify142.0ms (1.7%)

localize245.0ms (2.9%)

series53.0ms (0.6%)

simplify231.0ms (2.7%)

rewrite234.0ms (2.7%)

eval302.0ms (3.5%)

prune52.0ms (0.6%)

simplify119.0ms (1.4%)

localize304.0ms (3.5%)

series53.0ms (0.6%)

simplify238.0ms (2.8%)

rewrite211.0ms (2.5%)

eval557.0ms (6.5%)

prune109.0ms (1.3%)

regimes93.0ms (1.1%)

regimes170.0ms (2%)

regimes90.0ms (1%)

regimes65.0ms (0.8%)

regimes61.0ms (0.7%)

regimes57.0ms (0.7%)

regimes56.0ms (0.7%)

regimes43.0ms (0.5%)

regimes48.0ms (0.6%)

regimes32.0ms (0.4%)

regimes17.0ms (0.2%)

regimes14.0ms (0.2%)

regimes9.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch4.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify60.0ms (0.7%)

soundness1.3s (15.6%)

preprocess208.0ms (2.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	120	26
4	172	26
5	202	26
6	214	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10