Metrics for Given's Rotation SVD example, simplified

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample1.8s (27.3%)

Memory

36.8MiB live, 2 920.7MiB allocated

Samples

806.0ms	2 813×	2	valid
394.0ms	4 241×	0	valid
204.0ms	1 202×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-hypot: 399.0ms (35.5% of total)

ival-sqrt: 164.0ms (14.6% of total)

adjust: 122.0ms (10.8% of total)

ival-sub: 120.0ms (10.7% of total)

ival-div: 112.0ms (10% of total)

ival-mult: 104.0ms (9.2% of total)

ival-add: 87.0ms (7.7% of total)

exact: 7.0ms (0.6% of total)

ival-true: 6.0ms (0.5% of total)

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

Bogosity

explain200.0ms (3.1%)

Memory

21.0MiB live, 257.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
62	-	-	`(-.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	62	0

Confusion

	Predicted +	Predicted -
+	62	0
-	0	194

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	0
-	0	0	194

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	194
1	62

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms	178×	2	valid
26.0ms	262×	0	valid
12.0ms	72×	1	valid

Compiler

Compiled 175 to 31 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-div: 30.0ms (35.5% of total)

ival-hypot: 22.0ms (26.1% of total)

ival-sub: 7.0ms (8.3% of total)

ival-sqrt: 7.0ms (8.3% of total)

adjust: 6.0ms (7.1% of total)

ival-mult: 6.0ms (7.1% of total)

ival-add: 5.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess19.0ms (0.3%)

Memory

-8.7MiB live, 29.1MiB allocated

Algorithm

1×	egg-herbie

Rules

36×	`lower-+.f32`
34×	`lower-+.f64`
26×	`associate--r+`
26×	`sub-neg`
24×	`distribute-lft-neg-in`

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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))

Symmetry

(abs x)

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.4%	(-.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 13 to 9 computations (30.8% saved)

simplify5.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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))))
cost-diff	5440	(hypot.f64 #s(literal 1 binary64) x)

Rules

36×	`lower-+.f32`
34×	`lower-+.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
18×	`lower-*.f32`

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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(hypot.f64 #s(literal 1 binary64) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
x

localize57.0ms (0.9%)

Memory

-12.6MiB live, 79.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	0.01171875	(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	14.482037273108205	(-.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

25.0ms	89×	2	valid
10.0ms	131×	0	valid
6.0ms	36×	1	valid

Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-hypot: 10.0ms (32.7% of total)

ival-mult: 5.0ms (16.4% of total)

ival-div: 4.0ms (13.1% of total)

adjust: 3.0ms (9.8% of total)

ival-sqrt: 3.0ms (9.8% of total)

ival-add: 3.0ms (9.8% of total)

ival-sub: 2.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

-24.0MiB live, 13.7MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#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) (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 (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2))))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8))))) (taylor 0 x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#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 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 x (taylor inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (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>) () ())) ())
#s(alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3))) (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)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3))) (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 (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>) () ())) ())
#s(alt (- (+ 1 (* -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>) () ())) ())
#s(alt (- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))) (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>) () ())) ())
#s(alt (- (+ 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))))) (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>) () ())) ())
#s(alt (sqrt 1/2) (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>) () ())) ())
#s(alt (+ (sqrt 1/2) (* 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>) () ())) ())
#s(alt (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 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>) () ())) ())
#s(alt (+ (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))))) (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>) () ())) ())
#s(alt (/ 1 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 (* 1/2 (/ 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 (/ 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 (/ 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>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (hypot.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (hypot.f64 #s(literal 1 binary64) x) (patch (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>) () ())) ())
#s(alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) 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>) () ())) ())
#s(alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) 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>) () ())) ())
#s(alt (- 1 (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>) () ())) ())
#s(alt (- (+ 1 (* 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>) () ())) ())
#s(alt (- (+ 1 (* -1 (/ (- (* -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>) () ())) ())
#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>) () ())) ())
#s(alt (sqrt 1/2) (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>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -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>) () ())) ())
#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>) () ())) ())
#s(alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) 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>) () ())) ())
#s(alt (/ -1 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 (* 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)))) 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
5.0ms	x	@	-inf	((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 (sqrt (+ (* 1 1) (* x x)))))
2.0ms	x	@	0	((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 (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	inf	((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 (sqrt (+ (* 1 1) (* x x)))))

Time

Variable

Point

Expression

5.0ms

-inf

((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 (sqrt (+ (* 1 1) (* x x)))))

2.0ms

((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 (sqrt (+ (* 1 1) (* x x)))))

1.0ms

inf

((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 (sqrt (+ (* 1 1) (* x x)))))

simplify157.0ms (2.4%)

Memory

52.4MiB live, 232.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 216×	`lower-fma.f64`
12 216×	`lower-fma.f32`
5 218×	`lower-*.f64`
5 218×	`lower-*.f32`
2 710×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	219	881
1	640	809
2	1800	769
3	5702	711
0	8163	670

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

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

rewrite204.0ms (3.1%)

Memory

-20.7MiB live, 246.6MiB allocated

Rules

4 098×	`lower-fma.f64`
4 098×	`lower-fma.f32`
3 010×	`lower-*.f32`
3 008×	`lower-*.f64`
1 830×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	18	39
1	78	33
2	562	33
3	5208	33
0	8823	33

Stop Event

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

Counts

5 → 376

Calls

Call 1

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

Outputs
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64)))))
(*.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 x x) x) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 0 binary64) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
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(+.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(+.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/2 binary64))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(pow.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))
(/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/8 binary64))) (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 -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
(exp.f64 (.f64 (.f64 (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (fma.f64 (neg.f64 x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (pow.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(pow.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (.f64 x x))))

eval67.0ms (1%)

Memory: 33.5MiB live, 108.6MiB allocated
Compiler: Compiled 12 038 to 1 783 computations (85.2% saved)

prune105.0ms (1.6%)

Memory

-44.6MiB live, 180.8MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	424	11	435
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	425	11	436

Accuracy

78.6%

Counts

436 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.7%	(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
▶	78.2%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64)))
	51.6%	(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))))
▶	52.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))))))
▶	27.4%	(-.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)))))
	51.1%	(-.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)))))
	28.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
▶	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶	51.3%	#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 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64)))

Compiler

Compiled 372 to 230 computations (38.2% saved)

simplify244.0ms (3.7%)

Memory

21.7MiB live, 133.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64))
cost-diff	0	#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 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
cost-diff	320	(+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 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) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))))))
cost-diff	320	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))))
cost-diff	0	(fma.f64 #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 #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 #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 #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)))))) #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) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
cost-diff	0	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64)))
cost-diff	128	(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64))
cost-diff	192	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64))

Rules

8 948×	`lower-fma.f32`
8 942×	`lower-fma.f64`
1 944×	`lower-*.f32`
1 940×	`lower-*.f64`
1 568×	`lower-+.f32`

Iterations

Useful iterations: 13 (0.0ms)

Iter	Nodes	Cost
0	48	416
0	78	403
1	131	383
2	210	377
3	371	377
4	786	377
5	1722	377
6	3554	377
7	4605	377
8	4990	377
9	5142	377
10	5193	377
11	5207	377
12	5775	377
13	6132	369
14	6226	369
15	6501	369
16	7260	369
17	7886	369
0	8081	369

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

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

localize199.0ms (3%)

Memory

15.2MiB live, 274.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
accuracy	0.26449053666779	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
accuracy	0.599941259768442	(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64))
accuracy	30.668893970174956	#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 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
accuracy	0.00390625	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
accuracy	0.01171875	(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))))
accuracy	14.482037273108205	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ ( 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))))))
accuracy	29.821895080570197	#s(approx (sqrt (+ (* 1 1) (* x x))) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(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))))
accuracy	14.482037273108205	(-.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)))))
accuracy	32.216970500153884	#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)))
accuracy	0.01171875	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	14.482037273108205	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy	25.902581304289757	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.01171875	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 1 binary64)))
accuracy	0.01171875	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
accuracy	13.951388253556226	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1 binary64))
accuracy	14.616483134628556	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

Samples

93.0ms	89×	2	valid
57.0ms	131×	0	valid
19.0ms	36×	1	valid

Compiler

Compiled 377 to 36 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-div: 37.0ms (27.3% of total)

ival-hypot: 27.0ms (19.9% of total)

ival-mult: 22.0ms (16.2% of total)

adjust: 14.0ms (10.3% of total)

ival-sub: 12.0ms (8.9% of total)

ival-add: 12.0ms (8.9% of total)

ival-sqrt: 9.0ms (6.6% of total)

ival-neg: 2.0ms (1.5% of total)

exact: 1.0ms (0.7% of total)

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

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

series25.0ms (0.4%)

Memory

-1.6MiB live, 36.4MiB allocated

Counts

25 → 288

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

inf

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

2.0ms

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

2.0ms

-inf

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

simplify203.0ms (3.1%)

Memory

-36.2MiB live, 276.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 042×	`lower-fma.f64`
12 042×	`lower-fma.f32`
5 846×	`lower-*.f64`
5 846×	`lower-*.f32`
4 160×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	462	4316
1	1421	3947
2	4368	3870
0	8756	3648

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 286

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

rewrite176.0ms (2.7%)

Memory

31.6MiB live, 182.2MiB allocated

Rules

3 964×	`lower-/.f32`
3 952×	`lower-/.f64`
3 026×	`lower-*.f32`
3 022×	`lower-*.f64`
2 890×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	351
0	78	338
1	365	305
2	3219	305
0	8676	302

Stop Event

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

Counts

25 → 767

Calls

Call 1

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

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

eval211.0ms (3.2%)

Memory: 5.1MiB live, 356.0MiB allocated
Compiler: Compiled 36 119 to 4 012 computations (88.9% saved)

prune146.0ms (2.2%)

Memory

-16.6MiB live, 303.8MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1 215	4	1 219
Fresh	5	1	6
Picked	4	1	5
Done	0	0	0
Total	1 224	6	1 230

Accuracy

100.0%

Counts

1 230 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.1%	(-.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)))))
✓	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶	52.3%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	49.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	51.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
▶	51.3%	#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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))

Compiler

Compiled 114 to 75 computations (34.2% saved)

simplify163.0ms (2.5%)

Memory

-2.6MiB live, 148.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64))
cost-diff	0	#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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))
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	(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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
cost-diff	0	(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))

Rules

9 488×	`lower-fma.f32`
9 482×	`lower-fma.f64`
2 222×	`lower-*.f32`
2 214×	`lower-*.f64`
1 588×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	352
0	72	352
1	122	344
2	189	335
3	292	335
4	470	335
5	896	335
6	1743	335
7	2702	335
8	3014	335
9	3287	335
10	4298	335
11	5917	335
12	6928	335
13	7785	335
0	8025	325

Stop Event

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

Calls

Call 1

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

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

localize272.0ms (4.1%)

Memory

2.2MiB live, 280.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))
accuracy	0.599941259768442	(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64))
accuracy	14.719245308050535	(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
accuracy	30.668893970174956	#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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))
accuracy	0	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
accuracy	0.01171875	(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	14.482037273108205	(-.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	29.821895135727612	#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	0.03125	(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.0546875	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.06640625	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	32.25628202147979	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	31.245951316604465	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
accuracy	0	(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
accuracy	0	(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	30.496591669732997	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))

Samples

123.0ms	89×	2	valid
52.0ms	131×	0	valid
22.0ms	36×	1	valid

Compiler

Compiled 274 to 43 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-sub: 48.0ms (28.6% of total)

ival-hypot: 33.0ms (19.6% of total)

ival-mult: 30.0ms (17.9% of total)

ival-div: 19.0ms (11.3% of total)

adjust: 15.0ms (8.9% of total)

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

ival-sqrt: 9.0ms (5.4% of total)

ival-neg: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series16.0ms (0.2%)

Memory

35.6MiB live, 35.6MiB allocated

Counts

20 → 204

Calls

Call 1

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

Outputs
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #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 #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #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 #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) #<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 #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<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 #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#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 (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#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 (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#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 (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#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>) () ())) ())
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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 #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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) #s(literal 1 binary64))) (patch #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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (sqrt 1/2))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) #s(literal 1 binary64)) (patch (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x)))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) #s(literal 1 binary64)) (patch (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) #s(literal 1 binary64)) (patch (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) #s(literal 1 binary64)) (patch (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) (patch (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) (patch (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) (patch (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1) (taylor -inf x) (#s(alt (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))) (patch (-.f64 #s(literal -1 binary64) #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x))) (patch #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x))) (patch #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x))) (patch #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)) (taylor -inf x) (#s(alt #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (.f64 x x))) (patch #s(approx (+ (/ 1/2 x) (/ -1/8 ( x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify244.0ms (3.7%)

Memory

-1.5MiB live, 272.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 622×	`lower-fma.f64`
16 622×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
4 250×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	330	3815
1	1013	3543
2	3175	3328
0	8110	3194

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

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))))
(* 1/8 (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)
(* 1/8 (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 (* (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)))
(- (+ 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)))
(* 1/8 (/ (sqrt 1/2) (pow x 2)))
(/ (+ (* -1/2 (* x (sqrt 1/2))) (* 1/8 (sqrt 1/2))) (pow x 2))
(/ (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ 1 (* -1 (sqrt 1/2))))))) (pow x 2))
(/ (+ (* 1/8 (sqrt 1/2)) (* x (+ (* -1/2 (sqrt 1/2)) (* x (+ 1 (* -1 (sqrt 1/2))))))) (pow x 2))
(/ 1/8 (pow x 2))
(/ (+ 1/8 (* -1/2 x)) (pow x 2))
(/ (+ 1/8 (* x (- (* -1 x) 1/2))) (pow x 2))
(/ (+ 1/8 (* x (- (* -1 x) 1/2))) (pow x 2))
(/ -1/8 (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ -1/8 (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 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 (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))))))))))
(* 1/8 (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)
(/ 1/2 (+ 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))))))))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(- 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)))
1/2
(+ 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 (* 1/8 (/ (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)))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x))))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ 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 (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)
(/ 1/2 (+ 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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(- 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))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
-1
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) 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)
(* 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))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* 1/8 (pow x 2))
(.f64 (.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)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 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 (* (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 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (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) (- (* -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)))
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(- (+ 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)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 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 (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) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64))) 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 (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) #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 (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)))
(+ 1 (* -1 (sqrt 1/2)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(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 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) x))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))))
(-.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 1/2 (/ 1 x))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x))

rewrite197.0ms (3%)

Memory

3.3MiB live, 323.4MiB allocated

Rules

5 510×	`lower-/.f32`
5 504×	`lower-/.f64`
3 462×	`lower-*.f32`
3 454×	`lower-*.f64`
3 080×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	322
0	72	322
1	346	268
2	2900	268
0	8917	257

Stop Event

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

Counts

20 → 322

Calls

Call 1

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

Outputs
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal -2 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(pow.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(neg.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 3/2 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 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 3/2 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 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/2 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 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (neg.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.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(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(.f64 (.f64 #s(literal 1/8 binary64) x) x)
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* 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 #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)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)))
(.f64 x (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x))
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(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (neg.f64 x)))
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(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) (*.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (*.f64 x x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (*.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) x))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) (.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))) x))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))) (.f64 x x)))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))) (.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (*.f64 x #s(literal -1/16 binary64))))) x))
(.f64 (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) #s(literal -1/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))))
(.f64 (pow.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))))
(.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x))
(.f64 (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x)))
(.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal 1 binary64))
(.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (.f64 x x)))
(pow.f64 (/.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (.f64 (neg.f64 x) x))
(/.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))))) (neg.f64 (neg.f64 (*.f64 (neg.f64 x) x))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)) (.f64 x x))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64)))) (*.f64 x x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64)))))
(/.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64))) (neg.f64 (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64))) (neg.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64)))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)) (.f64 x x)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64)))) (*.f64 x x)))
(/.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x) x)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/64 binary64)) (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) #s(literal -1/512 binary64)) (.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))) (*.f64 (neg.f64 x) x))
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))) (*.f64 x x)))
(neg.f64 (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (*.f64 (neg.f64 x) x)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) x)) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (.f64 (neg.f64 x) x)))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (.f64 x x)) (/.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1/8 binary64))) (.f64 x x)))
(exp.f64 (.f64 (log.f64 (.f64 x (/.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64))))) #s(literal -1 binary64)))
#s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (*.f64 x x)))

eval81.0ms (1.2%)

Memory: 8.1MiB live, 188.0MiB allocated
Compiler: Compiled 12 506 to 1 348 computations (89.2% saved)

prune124.0ms (1.9%)

Memory

12.7MiB live, 195.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	582	1	583
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	583	6	589

Accuracy

100.0%

Counts

589 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(-.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)))))
✓	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓	52.3%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	49.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	51.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
✓	51.3%	#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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))

Compiler

Compiled 60 to 39 computations (35% saved)

simplify285.0ms (4.3%)

Memory

-32.5MiB live, 231.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 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)) (*.f64 x x))
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

Rules

12 670×	`lower-fma.f32`
12 668×	`lower-fma.f64`
2 612×	`lower-*.f32`
2 608×	`lower-*.f64`
1 982×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	60
0	24	60
1	47	60
2	92	57
3	163	57
4	300	57
5	610	57
6	1121	57
7	1580	57
8	2066	57
9	2694	57
10	3910	57
11	5582	57
12	6668	57
13	7139	57
14	7484	57
15	7745	57
0	8218	55

Stop Event

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

Calls

Call 1

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

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

localize101.0ms (1.5%)

Memory

9.3MiB live, 131.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.04296875	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy	0.06640625	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	32.25628202147979	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))

Samples

61.0ms	88×	2	valid
14.0ms	131×	0	valid
8.0ms	37×	1	valid

Compiler

Compiled 53 to 20 computations (62.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

adjust: 36.0ms (49.8% of total)

ival-hypot: 12.0ms (16.6% of total)

ival-div: 7.0ms (9.7% of total)

ival-sub: 6.0ms (8.3% of total)

ival-mult: 4.0ms (5.5% of total)

ival-sqrt: 3.0ms (4.2% of total)

ival-neg: 2.0ms (2.8% of total)

ival-add: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<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 #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#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 (+ 1/8 (* -11/128 (pow x 2))) (taylor 0 x) (#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 (+ 1/8 (* -11/128 (pow x 2))) (taylor 0 x) (#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 (+ 1/8 (* -11/128 (pow x 2))) (taylor 0 x) (#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 (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 (+ 1 (sqrt 1/2))) (taylor inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))))) (taylor inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* 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))))))) (taylor inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (/ 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)))))))))) (taylor inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -11/128 (pow x 4)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -11/128 (pow x 2)) (taylor inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor inf x) (#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 (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 (/ 1/2 (+ 1 (sqrt 1/2))) (taylor -inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 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)))))) (taylor -inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))))) (taylor -inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))))) (taylor -inf x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ ( x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -11/128 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) (patch (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -11/128 (pow x 2)) (taylor -inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#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 (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128)) (taylor -inf x) (#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 (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify179.0ms (2.7%)

Memory

-9.1MiB live, 219.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 342×	`lower-fma.f64`
12 342×	`lower-fma.f32`
4 078×	`lower-/.f32`
4 078×	`lower-/.f64`
4 066×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	126	922
1	399	872
2	1481	818
3	7229	816
0	8414	794

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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))))
(* 1/8 (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
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* -11/128 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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))))))))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(pow x 2)
(pow x 2)
(pow x 2)
(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)
(* 1/8 (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
#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))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ (* -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)))))
(+.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(- (+ (* 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)))))))
(-.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/32 binary64) (.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)))) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/32 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))))
(- (+ (/ 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))))))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) x) x)) (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) x) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/2 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 #s(literal 1/8 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) x)) (/.f64 #s(literal -1/4 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) x)) (+.f64 (/.f64 #s(literal -3/16 binary64) (.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)))) (/.f64 (-.f64 (/.f64 #s(literal 1/32 binary64) (.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)))) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/32 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))))))
(* -11/128 (pow x 4))
(.f64 (.f64 #s(literal -11/128 binary64) x) (.f64 (.f64 x x) x))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* -11/128 (pow x 2))
(.f64 #s(literal -11/128 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) x) x)
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) x) x)
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 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)
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.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 #s(literal 1/8 binary64) (*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 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 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/32 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (.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))))) (.f64 x x))) (-.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))))
(+ (* -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 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/32 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (-.f64 (/.f64 #s(literal 1/32 binary64) (.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)))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -3/64 binary64) (.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))))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/32 binary64) (.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)))) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/32 binary64) (.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))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #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 1/256 binary64) (.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)))) (/.f64 #s(literal 1/64 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64))))) x))) (.f64 x x))) (-.f64 (/.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x)) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) x x) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))))
(* -11/128 (pow x 4))
(.f64 (.f64 #s(literal -11/128 binary64) x) (.f64 (.f64 x x) x))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)))
(* -11/128 (pow x 2))
(.f64 #s(literal -11/128 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) x) x)
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 binary64)) x) x)
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 11/128 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)

rewrite183.0ms (2.8%)

Memory

-15.8MiB live, 134.6MiB allocated

Rules

5 650×	`lower-fma.f32`
5 648×	`lower-fma.f64`
3 740×	`lower-/.f64`
3 740×	`lower-/.f32`
3 598×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	57
0	24	57
1	124	57
2	1011	43
0	9209	42

Stop Event

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

Counts

4 → 86

Calls

Call 1

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

Outputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x) x))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (.f64 x x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))
(.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))))
(.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(.f64 x (.f64 (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) x))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)))) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))))) (-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x))) (.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) #s(literal 1/8 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (.f64 x x))) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (.f64 x x))) (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)))) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (.f64 x x)) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64))) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)))
(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)) (.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))) (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)))))
(fma.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) (.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/8 binary64) (.f64 x x) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 (*.f64 x x) #s(literal 1/8 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal -11/128 binary64))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal -11/128 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal -11/1024 binary64)))))))
(.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (.f64 (*.f64 x x) #s(literal 11/1024 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (*.f64 x x) #s(literal -11/1024 binary64))))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)))) (.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))))) (+.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (fma.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))) (.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)))) (neg.f64 (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)) #s(literal 1/64 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x))) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64))) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 x x) #s(literal 11/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64))))))
(/.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 x x) #s(literal 11/1024 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64))) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 x x) #s(literal 11/1024 binary64)))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64))) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64))) (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64))))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) #s(literal -1/64 binary64)) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))))
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) #s(literal -1331/2097152 binary64)) #s(literal 1/512 binary64)) (neg.f64 (fma.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal -11/1024 binary64)))))))
(fma.f64 (*.f64 #s(literal -11/128 binary64) x) x #s(literal 1/8 binary64))
(fma.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))) (neg.f64 (/.f64 #s(literal -1/64 binary64) (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))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 x (*.f64 #s(literal -11/128 binary64) x) #s(literal 1/8 binary64))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))) (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64))))
(+.f64 (/.f64 (.f64 (.f64 #s(literal 121/16384 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal -1/8 binary64))) (neg.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal 11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)))))
(+.f64 (.f64 (.f64 x x) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))
(+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) #s(literal -11/128 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval22.0ms (0.3%)

Memory: -7.0MiB live, 31.6MiB allocated
Compiler: Compiled 3 731 to 375 computations (89.9% saved)

prune22.0ms (0.3%)

Memory

10.7MiB live, 49.0MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	154	6	160

Accuracy

100.0%

Counts

160 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(-.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)))))
✓	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓	52.3%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
✓	49.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	51.2%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
✓	51.3%	#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) #s(approx (+ (/ 1/2 x) (/ -1/8 (* x x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1/8 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))

Compiler

Compiled 299 to 117 computations (60.9% saved)

regimes38.0ms (0.6%)

Memory

-19.1MiB live, 67.0MiB allocated

Counts

17 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

7.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
7.0ms	x
5.0ms	(hypot.f64 #s(literal 1 binary64) x)
5.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
4.0ms	(-.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 54 to 37 computations (31.5% saved)

regimes31.0ms (0.5%)

Memory

10.8MiB live, 47.7MiB allocated

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

6.0ms	(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	x
4.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms	(hypot.f64 #s(literal 1 binary64) x)
4.0ms	(-.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
99.5%	2	`x`
99.5%	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))))))`
99.5%	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)))))`
99.5%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.5%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.5%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes16.0ms (0.2%)

Memory

-7.6MiB live, 31.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

3.0ms	x
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) 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))))))
2.0ms	(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
98.7%	2	`x`
98.7%	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))))))`
98.7%	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)))))`
98.7%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.7%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.7%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.7%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes16.0ms (0.2%)

Memory

-7.8MiB live, 34.7MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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:

4.0ms	x
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms	(hypot.f64 #s(literal 1 binary64) x)
2.0ms	(*.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) (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
98.7%	2	`x`
98.7%	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))))))`
98.7%	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)))))`
98.7%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.7%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.7%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.7%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes12.0ms (0.2%)

Memory

32.7MiB live, 32.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 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:

2.0ms	x
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms	(hypot.f64 #s(literal 1 binary64) x)
2.0ms	(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) (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
98.6%	2	`x`
98.6%	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))))))`
98.6%	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)))))`
98.6%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.6%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.6%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes10.0ms (0.2%)

Memory

-14.4MiB live, 23.9MiB 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 (+ (* x x) 1)))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* x x) 1)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))

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

Calls

7 calls:

3.0ms	(hypot.f64 #s(literal 1 binary64) x)
1.0ms	x
1.0ms	(/.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))))))
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)))))

Results

Accuracy	Segments	Branch
51.2%	1	`x`
51.2%	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))))))`
51.2%	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)))))`
51.2%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
51.2%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
51.2%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
51.2%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000034368999	1008411.5564385739

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000034368999	1008411.5564385739

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000034368999	1008411.5564385739

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000034368999	1008411.5564385739

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000000034368999	1008411.5564385739

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify13.0ms (0.2%)

Memory

-17.8MiB live, 21.6MiB allocated

Algorithm

1×	egg-herbie

Rules

164×	`unsub-neg_binary64`
88×	`neg-mul-1_binary64`
50×	`*-commutative_binary64`
40×	`+-commutative_binary64`
36×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	358
1	73	358
2	91	357
3	115	357
4	148	357
5	204	357
6	235	357
7	266	357
8	300	357
9	362	357
10	405	357

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness622.0ms (9.5%)

Memory

15.3MiB live, 490.2MiB allocated

Rules

12 216×	`lower-fma.f64`
12 216×	`lower-fma.f32`
12 042×	`lower-fma.f64`
12 042×	`lower-fma.f32`
5 846×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	18	39
1	78	33
2	562	33
3	5208	33
0	8823	33
0	462	4316
1	1421	3947
2	4368	3870
0	8756	3648
0	51	322
0	72	322
1	346	268
2	2900	268
0	8917	257
0	219	881
1	640	809
2	1800	769
3	5702	711
0	8163	670

Stop Event

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

Compiler

Compiled 247 to 111 computations (55.1% saved)

preprocess95.0ms (1.4%)

Memory: 16.2MiB live, 96.4MiB allocated
Remove: (abs x)
Compiler: Compiled 376 to 128 computations (66% 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	55	358
1	73	358
2	91	357
3	115	357
4	148	357
5	204	357
6	235	357
7	266	357
8	300	357
9	362	357
10	405	357

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	55	358
1	73	358
2	91	357
3	115	357
4	148	357
5	204	357
6	235	357
7	266	357
8	300	357
9	362	357
10	405	357

start0.0ms (0%)

analyze0.0ms (0%)

sample1.8s (27.3%)

explain200.0ms (3.1%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize57.0ms (0.9%)

series10.0ms (0.2%)

simplify157.0ms (2.4%)

rewrite204.0ms (3.1%)

eval67.0ms (1%)

prune105.0ms (1.6%)

simplify244.0ms (3.7%)

localize199.0ms (3%)

series25.0ms (0.4%)

simplify203.0ms (3.1%)

rewrite176.0ms (2.7%)

eval211.0ms (3.2%)

prune146.0ms (2.2%)

simplify163.0ms (2.5%)

localize272.0ms (4.1%)

series16.0ms (0.2%)

simplify244.0ms (3.7%)

rewrite197.0ms (3%)

eval81.0ms (1.2%)

prune124.0ms (1.9%)

simplify285.0ms (4.3%)

localize101.0ms (1.5%)

series4.0ms (0.1%)

simplify179.0ms (2.7%)

rewrite183.0ms (2.8%)

eval22.0ms (0.3%)

prune22.0ms (0.3%)

regimes38.0ms (0.6%)

regimes31.0ms (0.5%)

regimes16.0ms (0.2%)

regimes16.0ms (0.2%)

regimes12.0ms (0.2%)

regimes10.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify13.0ms (0.2%)

soundness622.0ms (9.5%)

preprocess95.0ms (1.4%)

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

Iter	Nodes	Cost
0	55	358
1	73	358
2	91	357
3	115	357
4	148	357
5	204	357
6	235	357
7	266	357
8	300	357
9	362	357
10	405	357