Metrics for Given's Rotation SVD example, simplified

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample1.9s (25%)

Memory

24.5MiB live, 3 022.8MiB allocated

Samples

897.0ms	2 849×	2	valid
336.0ms	4 190×	0	valid
238.0ms	1 217×	1	valid

Precisions

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

ival-hypot: 433.0ms (36.9% of total)

ival-div: 172.0ms (14.7% of total)

ival-sqrt: 142.0ms (12.1% of total)

adjust: 132.0ms (11.3% of total)

ival-mult: 101.0ms (8.6% of total)

ival-sub: 98.0ms (8.4% of total)

ival-add: 78.0ms (6.7% of total)

exact: 8.0ms (0.7% of total)

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

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

Bogosity

explain211.0ms (2.8%)

Memory

12.7MiB live, 529.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	63	0
-	0	193

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	193
1	63

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

82.0ms	186×	2	valid
22.0ms	246×	0	valid
16.0ms	80×	1	valid

Compiler

Compiled 223 to 40 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-add: 35.0ms (35.9% of total)

ival-hypot: 26.0ms (26.7% of total)

adjust: 9.0ms (9.2% of total)

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

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

ival-mult: 6.0ms (6.2% of total)

ival-sub: 5.0ms (5.1% of total)

exact: 1.0ms (1% of total)

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

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

preprocess16.0ms (0.2%)

Memory

16.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	118	26
4	171	26
5	204	26
6	218	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs x)

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 9 computations (25% saved)

simplify17.0ms (0.2%)

Memory

-34.7MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize65.0ms (0.9%)

Memory

12.4MiB live, 102.6MiB 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	0.0078125	(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	14.812818018488809	(-.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

31.0ms	93×	2	valid
17.0ms	123×	0	valid
7.0ms	40×	1	valid

Compiler

Compiled 130 to 20 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-hypot: 11.0ms (25.1% of total)

ival-mult: 10.0ms (22.9% of total)

ival-sqrt: 9.0ms (20.6% of total)

ival-div: 4.0ms (9.1% of total)

adjust: 3.0ms (6.9% of total)

ival-sub: 3.0ms (6.9% of total)

ival-add: 2.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

-20.7MiB live, 16.4MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	inf	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))
1.0ms	x	@	-inf	((* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))) (/ 1 (sqrt (+ (* 1 1) (* x x)))))

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify168.0ms (2.2%)

Memory

39.7MiB live, 233.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	206	855
1	592	781
2	1668	742
3	4539	701
0	8216	662

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite150.0ms (2%)

Memory

-8.8MiB live, 232.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	18	43
1	78	37
2	562	37
3	5214	37
0	8825	37

Stop Event

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

Counts

5 → 417

Calls

Call 1

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

Outputs
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eval75.0ms (1%)

Memory: -27.4MiB live, 133.2MiB allocated
Compiler: Compiled 10 877 to 1 899 computations (82.5% saved)

prune44.0ms (0.6%)

Memory

17.7MiB live, 54.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	468	9	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	9	478

Accuracy

78.0%

Counts

478 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.6%	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
▶	29.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	30.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))))
▶	29.8%	(-.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)))))
	48.1%	(-.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)))))
	31.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
▶	48.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	76.9%	(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))) #s(literal -1 binary64)))
▶	47.9%	#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))

Compiler

Compiled 222 to 168 computations (24.3% saved)

simplify193.0ms (2.6%)

Memory

0.9MiB live, 153.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(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))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (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)))))
cost-diff	0	(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) 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) (/.f64 #s(literal 1/2 binary64) 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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
cost-diff	0	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
cost-diff	128	(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
cost-diff	192	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	348
0	73	348
1	124	328
2	214	322
3	413	322
4	826	322
5	1465	322
6	2357	322
7	3551	322
8	4084	322
9	4555	322
10	6514	322
0	8074	322

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
#s(literal -1 binary64)
(/.f64 #s(literal 1/2 binary64) 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 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(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))
(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))
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64))
#s(literal -5/32 binary64)
(*.f64 x x)
x
#s(literal 3/16 binary64)
#s(literal -1/4 binary64)

Outputs
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
#s(literal -1/2 binary64)
(hypot.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
#s(literal -1/4 binary64)
#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 #s(literal 1/2 binary64) 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 #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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal -1 binary64) (/.f64 #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 #s(literal 1/2 binary64) x))
#s(literal -1 binary64)
(/.f64 #s(literal 1/2 binary64) 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 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(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))
(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))
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64))
#s(literal -5/32 binary64)
(*.f64 x x)
x
#s(literal 3/16 binary64)
#s(literal -1/4 binary64)

localize198.0ms (2.6%)

Memory

7.5MiB live, 236.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.04296875	(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))
accuracy	0.23820208223310183	(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64))
accuracy	14.812818018488809	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
accuracy	30.282426638071474	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0	(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.71875	(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))
accuracy	32.883548087763295	#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
accuracy	14.812818018488809	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
accuracy	30.313962965559075	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
accuracy	0.0078125	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	14.812818018488809	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy	27.555577671500252	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.0078125	(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	0.01953125	(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
accuracy	14.362079104297454	(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))

Samples

72.0ms	93×	2	valid
36.0ms	123×	0	valid
24.0ms	40×	1	valid

Compiler

Compiled 620 to 72 computations (88.4% saved)

Precisions

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

ival-div: 18.0ms (17.9% of total)

ival-hypot: 17.0ms (16.9% of total)

adjust: 15.0ms (14.9% of total)

ival-add: 13.0ms (12.9% of total)

ival-mult: 13.0ms (12.9% of total)

ival-sub: 11.0ms (10.9% of total)

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

ival-neg: 2.0ms (2% of total)

exact: 1.0ms (1% of total)

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

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

series23.0ms (0.3%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

23 → 264

Calls

Call 1

Inputs
#s(alt (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) (patch (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (patch (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) (patch #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))) (patch #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #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 #s(literal 1/2 binary64) 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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (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))))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64)))) (patch (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))) (patch #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (patch (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())

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

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))
3.0ms	x	@	0	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))
3.0ms	x	@	-inf	((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))

Time

Variable

Point

Expression

5.0ms

inf

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))

3.0ms

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))

3.0ms

-inf

((- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1) (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+ (* (* x x) -1/4) 1) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (+ (* (sqrt 1/2) (- -1 (/ 1/2 x))) 1) (sqrt 1/2) (- -1 (/ 1/2 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)))))) (+ (* (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4) (* x x)) 1) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (* x x) (+ (* -5/32 (* x x)) 3/16) (+ (* (+ (* -5/32 (* x x)) 3/16) (* x x)) -1/4))

simplify337.0ms (4.5%)

Memory

-164.3MiB live, 234.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	392	4030
1	1204	3670
2	3805	3490
0	8153	3317

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

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

rewrite193.0ms (2.6%)

Memory

3.3MiB live, 309.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	307
0	73	307
1	325	276
2	2644	276
0	8607	276

Stop Event

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

Counts

23 → 568

Calls

Call 1

Inputs
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(/.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 #s(literal 1/2 binary64))
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (fma.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(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))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(*.f64 x x)
(fma.f64 #s(literal -5/32 binary64) (*.f64 x x) #s(literal 3/16 binary64))
(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))

Outputs
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eval177.0ms (2.4%)

Memory: 42.3MiB live, 352.6MiB allocated
Compiler: Compiled 25 884 to 3 214 computations (87.6% saved)

prune31.0ms (0.4%)

Memory

-24.7MiB live, 94.7MiB allocated

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	976	7	983
Fresh	3	1	4
Picked	3	2	5
Done	0	0	0
Total	982	10	992

Accuracy

100.0%

Counts

992 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.6%	(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
▶	52.6%	(/.f64 #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64)))
▶	48.1%	(-.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)))))
✓	48.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	49.4%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	52.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
	53.9%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	52.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	54.0%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
✓	47.9%	#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))

Compiler

Compiled 237 to 179 computations (24.5% saved)

simplify196.0ms (2.6%)

Memory

10.2MiB live, 229.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	408
0	85	408
1	144	402
2	240	387
3	482	387
4	1003	387
5	2126	387
6	3310	387
7	4271	387
8	4525	387
9	4787	387
10	6021	387
11	7152	387
12	7905	387
0	8073	387

Stop Event

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

Calls

Call 1

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

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

localize239.0ms (3.2%)

Memory

0.6MiB live, 444.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
accuracy	0.05078125	(.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)
accuracy	0.21725154843229053	(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
accuracy	30.34792312617749	#s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x))
accuracy	0.0234375	(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.02734375	(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))
accuracy	0.25756803349764534	(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
accuracy	30.287985098038877	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
accuracy	0.0078125	(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	14.812818018488809	(-.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	31.687888699792172	#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	0.015625	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.0390625	(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.25947162828355264	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	30.346827096038396	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0	(*.f64 x x)
accuracy	0.20182802351313592	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	29.45445142526769	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))

Samples

114.0ms	93×	2	valid
48.0ms	123×	0	valid
35.0ms	40×	1	valid

Compiler

Compiled 740 to 84 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-hypot: 40.0ms (24.8% of total)

ival-mult: 39.0ms (24.2% of total)

ival-div: 29.0ms (18% of total)

adjust: 15.0ms (9.3% of total)

ival-sub: 13.0ms (8.1% of total)

ival-sqrt: 12.0ms (7.5% of total)

ival-add: 10.0ms (6.2% 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)

series24.0ms (0.3%)

Memory

25.5MiB live, 63.7MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify182.0ms (2.4%)

Memory

9.7MiB live, 201.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	5130
1	1199	4831
2	3883	4660
0	8489	4477

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

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))
(* 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)))
(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 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 69/256 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 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 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.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 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 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 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 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 #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))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/2 binary64)) 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 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* x (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x)
(* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -11/128 (pow x 2)))
(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
-2
#s(literal -2 binary64)
(- (* 1/8 (pow x 2)) 2)
(fma.f64 (*.f64 x #s(literal 1/8 binary64)) x #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(fma.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x #s(literal -2 binary64))
(* 1/8 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 69/1024 binary64) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(* -1/4 (pow x 2))
(.f64 #s(literal -1/4 binary64) (.f64 x x))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
(* (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)
(* -1/4 (pow x 2))
(.f64 #s(literal -1/4 binary64) (.f64 x x))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x)
(* (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) (- (* 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)
69/1024
#s(literal 69/1024 binary64)
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 #s(literal -1843/32768 binary64) (*.f64 x x) #s(literal 69/1024 binary64))
-11/128
#s(literal -11/128 binary64)
(- (* 69/1024 (pow x 2)) 11/128)
(fma.f64 #s(literal 69/1024 binary64) (*.f64 x x) #s(literal -11/128 binary64))
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(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))
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(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))
-1/4
#s(literal -1/4 binary64)
(- (* 3/16 (pow x 2)) 1/4)
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(- (* 3/16 (pow x 2)) 1/4)
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(- (* 3/16 (pow x 2)) 1/4)
(fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 #s(literal -1/4 binary64) x)
(* x (- (* 3/16 (pow x 2)) 1/4))
(.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)
(* x (- (* 3/16 (pow x 2)) 1/4))
(.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)
(* x (- (* 3/16 (pow x 2)) 1/4))
(.f64 (fma.f64 #s(literal 3/16 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
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(* -1843/32768 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -1843/32768 binary64))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 1843/32768 binary64)) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 1843/32768 binary64)) (/.f64 #s(literal 11/128 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
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(* -1843/32768 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1843/32768 binary64))
(* -1 (* (pow x 7) (- 1843/32768 (* 69/1024 (/ 1 (pow x 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -69/1024 binary64) (.f64 x x)) #s(literal -1 binary64) #s(literal -1843/32768 binary64)) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (* 69/1024 (/ 1 (pow x 2))))))
(.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -69/1024 binary64) (.f64 x x)) (-.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 11/128 binary64) (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))))))
(.f64 (neg.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 11/128 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1843/32768 binary64)) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 x #s(literal 7 binary64)))
(* -1843/32768 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1843/32768 binary64))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 1843/32768 binary64)))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
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(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
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(* -1 (+ 1 (sqrt 1/2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
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(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
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(/ 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))))))
(fma.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
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(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (-.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -3/64 binary64) (pow.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))) x))) x)) x))
-1/2
#s(literal -1/2 binary64)
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(* 3/16 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3/16 binary64))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* -1843/32768 (pow x 2))
(.f64 #s(literal -1843/32768 binary64) (.f64 x x))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (*.f64 x x)) #s(literal 1843/32768 binary64)) x) x)
(* -1843/32768 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1843/32768 binary64))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 1843/32768 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 1843/32768 binary64)) (/.f64 #s(literal 11/128 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
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(* 3/16 (pow x 2))
(.f64 #s(literal 3/16 binary64) (.f64 x x))
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- 3/16 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x) x)
(* 3/16 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3/16 binary64))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 3/16)))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 3/16)))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 3/16)))
(.f64 (-.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))

rewrite179.0ms (2.4%)

Memory

-35.1MiB live, 222.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	345
0	85	345
1	319	339
2	2257	309
0	8411	309

Stop Event

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

Counts

23 → 375

Calls

Call 1

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

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eval101.0ms (1.3%)

Memory: 34.9MiB live, 186.9MiB allocated
Compiler: Compiled 19 332 to 2 535 computations (86.9% saved)

prune119.0ms (1.6%)

Memory

-9.1MiB live, 184.2MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	761	5	766
Fresh	2	1	3
Picked	3	2	5
Done	0	2	2
Total	766	10	776

Accuracy

100.0%

Counts

776 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.8%	(/.f64 (-.f64 #s(literal 1 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 (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)))
	52.3%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x))))
✓	48.1%	(-.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)))))
✓	48.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
▶	49.4%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	52.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	52.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	53.9%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	54.0%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
✓	47.9%	#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))

Compiler

Compiled 215 to 155 computations (27.9% saved)

simplify226.0ms (3%)

Memory

20.0MiB live, 135.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
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	(-.f64 #s(literal 1 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))))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 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 (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)))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(approx (+ ( -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
cost-diff	0	(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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x)
cost-diff	0	(.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
cost-diff	0	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	507
0	77	507
1	142	495
2	240	483
3	496	483
4	1003	479
5	1629	479
6	2393	479
7	3341	479
8	3669	479
9	4059	479
10	5328	479
11	6762	479
12	7034	479
13	7285	479
14	7576	479
15	7638	479
0	8583	451

Stop Event

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

Calls

Call 1

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

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

localize226.0ms (3%)

Memory

-47.4MiB live, 334.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(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	0.01953125	(/.f64 (-.f64 #s(literal 1 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 (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)))
accuracy	14.362079104297454	(-.f64 #s(literal 1 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))))
accuracy	31.687888699792172	#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	0.0234375	(.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.02734375	(fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (*.f64 x x) #s(literal -11/128 binary64))
accuracy	30.287985098038877	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	30.4312486330533	#s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64))
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	32.40728298982483	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
accuracy	0	(*.f64 x x)
accuracy	0.03515625	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x))
accuracy	0.25947162828355264	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	30.346827096038396	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
accuracy	0.01953125	(.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x)
accuracy	0.0234375	(.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)
accuracy	30.287985098038877	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
accuracy	30.47493085664223	#s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64))

Samples

76.0ms	92×	2	valid
50.0ms	124×	0	valid
23.0ms	40×	1	valid

Compiler

Compiled 635 to 73 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 115.0ms

ival-mult: 31.0ms (27% of total)

ival-div: 21.0ms (18.3% of total)

adjust: 18.0ms (15.7% of total)

ival-hypot: 12.0ms (10.5% of total)

ival-add: 12.0ms (10.5% of total)

ival-sub: 9.0ms (7.8% of total)

ival-sqrt: 8.0ms (7% of total)

ival-neg: 2.0ms (1.7% of total)

exact: 1.0ms (0.9% of total)

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

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

series26.0ms (0.4%)

Memory

13.4MiB live, 49.7MiB allocated

Counts

23 → 240

Calls

Call 1

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

Outputs
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #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 (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x) (patch (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/8 x) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))) (taylor 0 x) (#s(alt (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/8 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* -11/128 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) (patch #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (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 (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (+ ( 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 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 (* 1/8 (pow x 2)) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 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 (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (patch #s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

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

3.0ms

inf

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

2.0ms

-inf

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

simplify238.0ms (3.2%)

Memory

11.3MiB live, 232.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	428	5773
1	1355	5459
2	4843	5417
0	8597	5153

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* 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)
(* 1/8 (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))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* x (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* 1/4 (/ (pow x 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))
(* (pow x 2) (+ (* -1 (* (pow x 2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(* (pow x 2) (+ (* (pow x 2) (- (* (pow x 2) (- (+ (* -1 (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (* (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/4 (/ (* (sqrt 1/2) (- (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* -1/8 (/ (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 35/256 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))))) (* 5/32 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))) (+ (* 1/8 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 1/4 (/ (* (sqrt 1/2) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2))))))) (* (sqrt 2) (+ 1 (* (sqrt 1/2) (sqrt 2))))))))) (+ (* -1/16 (/ (sqrt 1/2) (* (sqrt 2) (pow (+ 1 (* (sqrt 1/2) (sqrt 2))) 2)))) (* 3/16 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))) (* 1/4 (/ 1 (+ 1 (* (sqrt 1/2) (sqrt 2)))))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
1
(+ 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)
69/1024
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
-11/128
(- (* 69/1024 (pow x 2)) 11/128)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(* (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))))))))
(/ 1/2 (+ 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))))))))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 7))
(* (pow x 7) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 7) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 7) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(/ 1/2 (+ 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 (/ (+ (* 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))))))))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 7))
(* (pow x 7) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 7) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 7) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/4 (/ (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 (/ (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (pow x 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))
(- (+ (/ 1/4 (* (pow x 3) (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (* -3/32 (/ (sqrt 1/2) (* (pow x 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -1/16 (/ (sqrt 1/2) (* (pow x 2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* 1/8 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))))))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (* 1/2 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 3))) (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))))
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)))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(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 (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)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 7))
(* -1 (* (pow x 7) (- 1843/32768 (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(/ 1/2 (+ 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)
(/ 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)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 7))
(* -1 (* (pow x 7) (- 1843/32768 (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (* 69/1024 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1843/32768 (/ 11/128 (pow x 4))) (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (* 1/4 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* x (+ 1 (sqrt 1/2))))) (* -1/16 (/ (sqrt 1/2) (* x (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ (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)))) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ 1 (sqrt 1/2)))) (+ (* -3/32 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/8 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* -1/2 (/ (* (sqrt 1/2) (+ (* 1/4 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (+ 1 (sqrt 1/2)))) (* -1/16 (/ (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) x)) (+ (* 1/4 (/ (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 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)))
(+ 1/2 (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)))
1/2
(- 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)))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(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)))

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

rewrite203.0ms (2.7%)

Memory

-6.1MiB live, 307.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	466
0	77	466
1	351	433
2	2711	381
0	8643	355

Stop Event

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

Counts

23 → 348

Calls

Call 1

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

Outputs
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eval142.0ms (1.9%)

Memory: 24.7MiB live, 252.5MiB allocated
Compiler: Compiled 17 960 to 2 182 computations (87.9% saved)

prune48.0ms (0.6%)

Memory

13.5MiB live, 135.0MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	719	1	720
Fresh	0	1	1
Picked	1	4	5
Done	0	4	4
Total	720	10	730

Accuracy

100.0%

Counts

730 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	48.8%	(/.f64 #s(approx (- 1 (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 (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)))
	52.3%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(approx (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) x))))
✓	48.1%	(-.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)))))
✓	48.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
✓	49.4%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
✓	52.6%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	52.7%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	53.9%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 (fma.f64 (fma.f64 #s(approx (+ (* -1843/32768 (* x x)) 69/1024) #s(literal 69/1024 binary64)) (.f64 x x) #s(literal -11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	54.0%	#s(approx (/ (- (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) 1) (- (neg (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) 1)) (.f64 (.f64 #s(approx (+ (* (+ (* (+ (* -1843/32768 (* x x)) 69/1024) (* x x)) -11/128) (* x x)) 1/8) #s(literal 1/8 binary64)) x) x))
✓	47.9%	#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 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))

Compiler

Compiled 447 to 205 computations (54.1% saved)

regimes83.0ms (1.1%)

Memory

-33.2MiB live, 69.8MiB allocated

Counts

23 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

44.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
7.0ms	(hypot.f64 #s(literal 1 binary64) x)
7.0ms	x
7.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
6.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

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

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes35.0ms (0.5%)

Memory

-10.8MiB live, 64.3MiB allocated

Counts

15 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

7.0ms	x
6.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
5.0ms	(/.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 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	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))))))`
99.4%	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)))))`
99.4%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.4%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.4%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.4%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes30.0ms (0.4%)

Memory

25.4MiB live, 62.6MiB allocated

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	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))))))`
99.4%	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)))))`
99.4%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.4%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.4%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.4%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes28.0ms (0.4%)

Memory

2.4MiB live, 42.7MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

8.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
4.0ms	x
3.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms	(hypot.f64 #s(literal 1 binary64) x)
3.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
99.3%	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))))))`
99.3%	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)))))`
99.3%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.3%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.3%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.3%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes20.0ms (0.3%)

Memory

-1.0MiB live, 34.7MiB allocated

Counts

6 → 2

Calls

Call 1

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

5.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
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	(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 47 to 37 computations (21.3% saved)

regimes18.0ms (0.2%)

Memory

-4.2MiB live, 31.9MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

4.0ms	(*.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	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)))))

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 47 to 37 computations (21.3% saved)

regimes16.0ms (0.2%)

Memory

-7.2MiB live, 28.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

5.0ms	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) (/.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
98.4%	2	`x`
98.4%	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))))))`
98.4%	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)))))`
98.4%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.4%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.4%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.4%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes10.0ms (0.1%)

Memory

23.0MiB live, 23.0MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

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

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

Outputs

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

Calls

7 calls:

2.0ms	x
2.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms	(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
54.0%	1	`x`
54.0%	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))))))`
54.0%	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)))))`
54.0%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
54.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
54.0%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
54.0%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes21.0ms (0.3%)

Memory

-17.8MiB live, 20.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

13.0ms	(-.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	x
1.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms	(hypot.f64 #s(literal 1 binary64) x)
1.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

Accuracy	Segments	Branch
54.0%	1	`x`
54.0%	1	`(hypot.f64 #s(literal 1 binary64) x)`
54.0%	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))))))`
54.0%	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)))))`
54.0%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
54.0%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
54.0%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 47 to 37 computations (21.3% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0000060551365069	21920702.20350115

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify91.0ms (1.2%)

Memory

17.1MiB live, 52.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	609
1	136	599
2	237	587
3	513	587
4	1180	587
5	2546	587
6	5917	587

Stop Event

1×	node limit

Calls

Call 1

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

soundness1.2s (15.6%)

Memory

-25.8MiB live, 967.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	394	5130
1	1199	4831
2	3883	4660
0	8489	4477
0	9	43
0	18	43
1	78	37
2	562	37
3	5214	37
0	8825	37
0	428	5773
1	1355	5459
2	4843	5417
0	8597	5153
0	206	855
1	592	781
2	1668	742
3	4539	701
0	8216	662
0	53	345
0	85	345
1	319	339
2	2257	309
0	8411	309
0	392	4030
1	1204	3670
2	3805	3490
0	8153	3317

Stop Event

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

Compiler

Compiled 349 to 176 computations (49.6% saved)

preprocess54.0ms (0.7%)

Memory: 1.6MiB live, 124.1MiB allocated
Compiler: Compiled 518 to 182 computations (64.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	118	26
4	171	26
5	204	26
6	218	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	118	26
4	171	26
5	204	26
6	218	26
0	9	12
0	18	12
1	31	10
2	38	10
3	43	10
4	49	10
5	57	10
6	67	10
7	78	10
8	81	10
0	81	10

start0.0ms (0%)

analyze0.0ms (0%)

sample1.9s (25%)

explain211.0ms (2.8%)

preprocess16.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify17.0ms (0.2%)

localize65.0ms (0.9%)

series9.0ms (0.1%)

simplify168.0ms (2.2%)

rewrite150.0ms (2%)

eval75.0ms (1%)

prune44.0ms (0.6%)

simplify193.0ms (2.6%)

localize198.0ms (2.6%)

series23.0ms (0.3%)

simplify337.0ms (4.5%)

rewrite193.0ms (2.6%)

eval177.0ms (2.4%)

prune31.0ms (0.4%)

simplify196.0ms (2.6%)

localize239.0ms (3.2%)

series24.0ms (0.3%)

simplify182.0ms (2.4%)

rewrite179.0ms (2.4%)

eval101.0ms (1.3%)

prune119.0ms (1.6%)

simplify226.0ms (3%)

localize226.0ms (3%)

series26.0ms (0.4%)

simplify238.0ms (3.2%)

rewrite203.0ms (2.7%)

eval142.0ms (1.9%)

prune48.0ms (0.6%)

regimes83.0ms (1.1%)

regimes35.0ms (0.5%)

regimes30.0ms (0.4%)

regimes28.0ms (0.4%)

regimes20.0ms (0.3%)

regimes18.0ms (0.2%)

regimes16.0ms (0.2%)

regimes10.0ms (0.1%)

regimes21.0ms (0.3%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify91.0ms (1.2%)

soundness1.2s (15.6%)

preprocess54.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	31
1	37	26
2	75	26
3	118	26
4	171	26
5	204	26
6	218	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