Metrics for Given's Rotation SVD example, simplified

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample1.7s (20.2%)

Memory

50.2MiB live, 2 170.0MiB allocated

Samples

780.0ms	2 807×	2	valid
360.0ms	4 244×	0	valid
195.0ms	1 205×	1	valid

Precisions

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

ival-hypot: 367.0ms (34.1% of total)

ival-sqrt: 153.0ms (14.2% of total)

ival-mult: 131.0ms (12.2% of total)

ival-div: 126.0ms (11.7% of total)

adjust: 107.0ms (9.9% of total)

ival-sub: 94.0ms (8.7% of total)

ival-add: 78.0ms (7.3% of total)

exact: 8.0ms (0.7% of total)

ival-true: 7.0ms (0.7% of total)

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

Bogosity

explain197.0ms (2.3%)

Memory

6.3MiB live, 287.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
61	-	-	`(-.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	61	0

Confusion

	Predicted +	Predicted -
+	61	0
-	0	195

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	61	0	0
-	0	0	195

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	195
1	61

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

48.0ms	180×	2	valid
21.0ms	278×	0	valid
9.0ms	54×	1	valid

Compiler

Compiled 174 to 31 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-hypot: 22.0ms (37.6% of total)

adjust: 7.0ms (12% of total)

ival-div: 7.0ms (12% of total)

ival-sqrt: 7.0ms (12% of total)

ival-mult: 6.0ms (10.3% of total)

ival-sub: 4.0ms (6.8% of total)

ival-add: 4.0ms (6.8% of total)

exact: 1.0ms (1.7% of total)

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

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

preprocess15.0ms (0.2%)

Memory

21.9MiB live, 21.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	37	27
2	70	27
3	95	27
4	127	27
5	134	27
0	9	12
0	18	12
1	35	10
2	65	10
3	105	10
4	137	10
5	144	10
0	144	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 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Symmetry

(abs x)

Compiler

Compiled 12 to 9 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.2%	(-.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))))))

Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB 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	2	(*.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	35	43
2	65	43
3	105	43
4	137	43
5	144	43
0	144	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 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
#s(literal 1 binary64)
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 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))))
(-.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 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

localize53.0ms (0.6%)

Memory

-1.4MiB live, 94.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
accuracy	0.0078125	(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	0.015625	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	13.967916711288478	(-.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

24.0ms	90×	2	valid
13.0ms	139×	0	valid
7.0ms	27×	1	valid

Compiler

Compiled 81 to 11 computations (86.4% saved)

Precisions

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

ival-hypot: 13.0ms (37.1% of total)

adjust: 6.0ms (17.1% of total)

ival-div: 3.0ms (8.6% of total)

ival-sqrt: 3.0ms (8.6% of total)

ival-add: 3.0ms (8.6% of total)

ival-mult: 3.0ms (8.6% of total)

ival-sub: 2.0ms (5.7% 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

-22.5MiB live, 14.4MiB allocated

Counts

5 → 54

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
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 (* -1/2 (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 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 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 (* 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) (* -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 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))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	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)))))
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)))))

Time

Variable

Point

Expression

5.0ms

-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)))))

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)))))

simplify283.0ms (3.3%)

Memory

22.5MiB live, 382.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	206	845
1	633	767
2	1960	714
3	7820	714
0	8462	676

Stop Event

1×	iter limit
1×	node limit

Counts

54 → 54

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 (* -1/2 (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 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 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 (* 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) (* -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 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 (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/32 binary64) (-.f64 (.f64 #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) x) (/.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 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)))
(-.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))
(*.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 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #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 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.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 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (.f64 #s(literal 3/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 2 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.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 (pow.f64 x #s(literal 4 binary64)) #s(literal -5/16 binary64) (-.f64 (.f64 #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 #s(literal 1/2 binary64) (/.f64 #s(literal -3/16 binary64) (pow.f64 x #s(literal 5 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 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* 1/8 (/ (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 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.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)))))
(-.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3/16 binary64) #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))))
(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 #s(literal -3/16 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 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 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 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.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 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 binary64))))
(/ (- (+ 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 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(- 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 #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))))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 5 binary64))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64))))))
(- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) 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))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (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 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (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 (/.f64 #s(literal -3/16 binary64) x) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x))
(- 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 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x) (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 5 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 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 x))

rewrite192.0ms (2.3%)

Memory

21.6MiB live, 311.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
0	18	33
1	82	33
2	609	33
3	6358	33
0	8243	30

Stop Event

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

Counts

5 → 280

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
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 2 binary64)))) (+.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) (cosh.f64 (atanh.f64 x))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) (-.f64 (-.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (cosh.f64 (atanh.f64 x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)))) (fma.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (tanh.f64 (asinh.f64 x)) #s(literal 2 binary64))) (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
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(*.f64 (+.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
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(*.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cosh.f64 (atanh.f64 x)))
(pow.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (fabs.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
(neg.f64 (neg.f64 (cosh.f64 (atanh.f64 x))))
(fma.f64 (tanh.f64 (asinh.f64 x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cosh.f64 (atanh.f64 x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (acos.f64 (neg.f64 (tanh.f64 (asinh.f64 x)))))
(sin.f64 (acos.f64 (cos.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (atan.f64 x)))))
(sin.f64 (acos.f64 (sin.f64 (neg.f64 (atan.f64 x)))))
(sin.f64 (acos.f64 (fabs.f64 (tanh.f64 (asinh.f64 x)))))
(sin.f64 (acos.f64 (tanh.f64 (asinh.f64 x))))
(sin.f64 (+.f64 (neg.f64 (atan.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (atan.f64 x)))
(cosh.f64 (atanh.f64 (exp.f64 (log.f64 x))))
(cosh.f64 (atanh.f64 (neg.f64 x)))
(cosh.f64 (atanh.f64 x))
(sqrt.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))
(-.f64 (cosh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))) (sinh.f64 (log.f64 (hypot.f64 #s(literal 1 binary64) x))))
(fabs.f64 (neg.f64 (cosh.f64 (atanh.f64 x))))
(fabs.f64 (cosh.f64 (atanh.f64 x)))
(cos.f64 (asin.f64 (neg.f64 (tanh.f64 (asinh.f64 x)))))
(cos.f64 (asin.f64 (cos.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (atan.f64 x)))))
(cos.f64 (asin.f64 (sin.f64 (neg.f64 (atan.f64 x)))))
(cos.f64 (asin.f64 (fabs.f64 (tanh.f64 (asinh.f64 x)))))
(cos.f64 (asin.f64 (tanh.f64 (asinh.f64 x))))
(cos.f64 (atan.f64 (exp.f64 (log.f64 x))))
(cos.f64 (neg.f64 (atan.f64 x)))
(cos.f64 (atan.f64 x))
(exp.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1/2 binary64)))
(exp.f64 (log.f64 (cosh.f64 (atanh.f64 x))))
(+.f64 (cosh.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1/2 binary64))) (sinh.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1/2 binary64))))
(+.f64 (.f64 (tanh.f64 (asinh.f64 x)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cosh.f64 (atanh.f64 x)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (cosh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))) (sinh.f64 (log.f64 (cosh.f64 (atanh.f64 x)))))

eval45.0ms (0.5%)

Memory: -2.6MiB live, 136.6MiB allocated
Compiler: Compiled 8 248 to 1 577 computations (80.9% saved)

prune19.0ms (0.2%)

Memory

-0.2MiB live, 52.5MiB allocated

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	319	15	334
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	320	15	335

Accuracy

78.6%

Counts

335 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
▶	78.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
	2.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)))) (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64))))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))))))
	25.3%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
▶	52.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
	25.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
	25.3%	(-.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)))))
▶	53.1%	(-.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)))))
	26.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
▶	52.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	3.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
	53.2%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
	53.2%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
▶	52.6%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
	2.3%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))

Compiler

Compiled 846 to 566 computations (33.1% saved)

simplify89.0ms (1%)

Memory

14.5MiB live, 61.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	303
0	62	303
1	96	289
2	152	289
3	244	289
4	409	289
5	513	289
6	534	289
7	558	289
8	599	289
9	710	289
10	900	289
11	1255	289
12	1681	289
13	2303	289
14	2373	289
15	2443	289
16	2749	289
17	2895	289
18	2897	289
19	2897	289
20	2899	289
0	2899	284

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

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

localize187.0ms (2.2%)

Memory

-16.4MiB live, 273.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
accuracy	0.12890625	(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
accuracy	29.821297053934636	#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
accuracy	0.01953125	(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy	0.44140625	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy	1.0	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	29.855241503466484	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	0.0	(+.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	13.967916711288478	(-.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	28.584103381678872	#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	0.0078125	(sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
accuracy	25.43727723988896	#s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))
accuracy	0.00390625	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
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	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Samples

116.0ms	90×	2	valid
30.0ms	139×	0	valid
12.0ms	27×	1	valid

Compiler

Compiled 306 to 26 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-div: 59.0ms (46.6% of total)

ival-sqrt: 25.0ms (19.8% of total)

ival-hypot: 11.0ms (8.7% of total)

adjust: 10.0ms (7.9% of total)

ival-sub: 10.0ms (7.9% of total)

ival-add: 6.0ms (4.7% of total)

ival-mult: 5.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

25.2MiB live, 25.2MiB allocated

Counts

23 → 93

Calls

Call 1

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

Outputs
(* 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 (* -1/8 (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)))
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(- 1 (* (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))))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(* -1/2 (/ (sqrt 1/2) x))
(/ (+ (* -1/2 (sqrt 1/2)) (* x (- 1 (sqrt 1/2)))) x)
(/ (sqrt 1/2) x)
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 (* -1/2 (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 (pow x 2))
(/ -1/2 (pow x 3))
(/ (- (pow x 2) 1/2) (pow x 3))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -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)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(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)))))
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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(- (+ 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) (* 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 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 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -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))) (sqrt 1/2))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(- 1/2 (* 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 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- (+ 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) (* -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 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))
(* -1 (/ (- (* 1/2 (/ 1 (pow x 2))) 1) x))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -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)))))) (+ (/ 1/2 x) 1/2) (+ (* (/ (sqrt 1/2) x) -1/2) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (* 1/2 (+ 1 (/ 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 1/2)) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/ (/ 1/2 x) x) (/ (- 1 (/ (/ 1/2 x) x)) x))
3.0ms	x	@	inf	((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -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)))))) (+ (/ 1/2 x) 1/2) (+ (* (/ (sqrt 1/2) x) -1/2) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (* 1/2 (+ 1 (/ 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 1/2)) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/ (/ 1/2 x) x) (/ (- 1 (/ (/ 1/2 x) x)) x))
3.0ms	x	@	-inf	((- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))) (/ -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)))))) (+ (/ 1/2 x) 1/2) (+ (* (/ (sqrt 1/2) x) -1/2) (- 1 (sqrt 1/2))) (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (/ (sqrt 1/2) x) (sqrt 1/2) (* 1/2 (+ 1 (/ 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 1/2)) (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/ (/ 1/2 x) x) (/ (- 1 (/ (/ 1/2 x) x)) x))

Time

Variable

Point

Expression

3.0ms

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

3.0ms

inf

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

3.0ms

-inf

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

simplify157.0ms (1.9%)

Memory

-24.0MiB live, 265.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	345	1415
1	1054	1316
2	3248	1260
0	8557	1207

Stop Event

1×	iter limit
1×	node limit

Counts

93 → 93

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

rewrite168.0ms (2%)

Memory

30.5MiB live, 258.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	271
0	62	247
1	265	247
2	2039	247
0	8689	237

Stop Event

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

Counts

23 → 429

Calls

Call 1

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

Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))))
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(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(sqrt.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(fabs.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)))
(fabs.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (-.f64 x (.f64 x (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)))) (.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)))) (*.f64 x x))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x)) (.f64 (neg.f64 x) (/.f64 #s(literal -1/2 binary64) x))) (.f64 (neg.f64 x) (*.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) x) (.f64 (neg.f64 x) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (.f64 x x)) (*.f64 (neg.f64 x) (/.f64 #s(literal 1/2 binary64) x))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 (neg.f64 x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 x (neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)))) (*.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x)) (.f64 x (/.f64 #s(literal -1/2 binary64) x))) (.f64 x (*.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 x (/.f64 #s(literal 1/2 binary64) x))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 x #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) (neg.f64 x))
(/.f64 (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))) (+.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))
(/.f64 (-.f64 x (.f64 x (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) (.f64 x x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) #s(literal 1 binary64)) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) (neg.f64 x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))) x))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (neg.f64 x)))
(-.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))))

eval126.0ms (1.5%)

Memory: -17.6MiB live, 173.7MiB allocated
Compiler: Compiled 20 505 to 2 416 computations (88.2% saved)

prune42.0ms (0.5%)

Memory

1.4MiB live, 47.8MiB allocated

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	521	13	534
Fresh	9	1	10
Picked	1	4	5
Done	0	0	0
Total	531	18	549

Accuracy

99.9%

Counts

549 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.1%	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
▶	79.0%	(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
	53.4%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
	52.3%	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
✓	78.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
	52.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
✓	53.1%	(-.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)))))
✓	52.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	27.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
	25.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	27.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
▶	26.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
	3.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
▶	48.3%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
▶	46.7%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
	48.4%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
▶	53.3%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
✓	52.6%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 976 to 605 computations (38% saved)

simplify235.0ms (2.8%)

Memory

14.7MiB live, 192.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	285
0	75	281
1	120	279
2	238	279
3	554	279
4	1267	279
5	2332	279
6	3049	279
7	3431	279
8	3891	279
9	5011	279
0	8066	279

Stop Event

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

Calls

Call 1

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

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

localize959.0ms (11.3%)

Memory

-199.9MiB live, 269.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	0.01953125	(fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
accuracy	0.44140625	(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
accuracy	29.855241503466484	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
accuracy	0.03125	(.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.05859375	(fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	0.3495679147233557	(.f64 #s(literal 69/1024 binary64) (.f64 x x))
accuracy	33.05634826580851	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	0.0390625	(.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x)
accuracy	0.04296875	(.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x)
accuracy	0.0703125	(fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
accuracy	34.09990307681092	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
accuracy	27.677466334116325	#s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x 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	0.01171875	(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
accuracy	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	13.481324395306684	(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Samples

806.0ms	139×	0	valid
78.0ms	90×	2	valid
25.0ms	27×	1	valid

Compiler

Compiled 314 to 40 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 871.0ms

ival-mult: 753.0ms (86.4% of total)

ival-sub: 51.0ms (5.9% of total)

ival-div: 21.0ms (2.4% of total)

adjust: 14.0ms (1.6% of total)

ival-hypot: 12.0ms (1.4% of total)

ival-sqrt: 10.0ms (1.1% of total)

ival-add: 10.0ms (1.1% of total)

exact: 1.0ms (0.1% of total)

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

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

series12.0ms (0.1%)

Memory

38.7MiB live, 38.7MiB allocated

Counts

20 → 98

Calls

Call 1

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

Outputs
(* 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))))
(* 1/8 (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)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(+ 1 (* -1/8 (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)))
(* 1/8 x)
(* x (+ 1/8 (* -11/128 (pow x 2))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(* x (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(- 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)) (* 1/2 (/ x (+ 1 (sqrt 1/2))))) x)
(/ (sqrt 1/2) x)
(* 69/1024 (pow x 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 (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 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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -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)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(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)))))
(* -11/128 (pow x 4))
(* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 3))
(* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* -11/128 (pow x 2))
(* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 11/128))
(* 69/1024 (pow x 6))
(* (pow x 6) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 5))
(* (pow x 5) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(* 69/1024 (pow x 4))
(* (pow x 4) (- 69/1024 (* 11/128 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 69/1024 (/ 1/8 (pow x 4))) (* 11/128 (/ 1 (pow x 2)))))
(- (+ 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)))))
(+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ 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)))
(+ (/ 1/8 (* 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 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -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))) (sqrt 1/2))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(* -1 (* (pow x 3) (- 11/128 (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) 69/1024)))
(* -1 (* (pow x 5) (- (* 11/128 (/ 1 (pow x 2))) (+ 69/1024 (/ 1/8 (pow x 4))))))
(- (+ 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))

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

inf

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

3.0ms

-inf

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

3.0ms

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

simplify232.0ms (2.7%)

Memory

-39.9MiB live, 345.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	392	1881
1	1228	1731
2	4292	1687
0	8373	1632

Stop Event

1×	iter limit
1×	node limit

Counts

98 → 98

Calls

Call 1

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

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

rewrite173.0ms (2%)

Memory

43.3MiB live, 325.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	233
0	75	227
1	289	215
2	2109	215
0	8169	214

Stop Event

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

Counts

20 → 313

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (neg.f64 (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
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(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(fabs.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))) (sinh.f64 (log.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))))
(.f64 (fabs.f64 (.f64 #s(literal 69/1024 binary64) (neg.f64 x))) x)
(.f64 (fabs.f64 (.f64 #s(literal 69/1024 binary64) x)) x)
(.f64 (.f64 #s(literal 69/1024 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 69/1024 binary64) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 69/1024 binary64)))
(.f64 #s(literal 69/1024 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 69/1024 binary64))
(.f64 x (fabs.f64 (.f64 (neg.f64 x) #s(literal 69/1024 binary64))))
(.f64 x (fabs.f64 (.f64 #s(literal 69/1024 binary64) x)))
(.f64 x (.f64 #s(literal 69/1024 binary64) x))
(sqrt.f64 (*.f64 #s(literal 4761/1048576 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (neg.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x))))
(fabs.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)))

eval103.0ms (1.2%)

Memory: -26.1MiB live, 160.0MiB allocated
Compiler: Compiled 19 484 to 2 176 computations (88.8% saved)

prune45.0ms (0.5%)

Memory

15.6MiB live, 79.4MiB allocated

Pruning

20 alts after pruning (13 fresh and 7 done)

	Pruned	Kept	Total
New	496	6	502
Fresh	2	7	9
Picked	2	3	5
Done	0	4	4
Total	500	20	520

Accuracy

100.0%

Counts

520 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.0%	(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
	79.0%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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 (sqrt.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 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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)))))
	53.1%	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
	79.0%	(/.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)))
▶	52.3%	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
✓	78.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
▶	52.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
✓	53.1%	(-.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)))))
✓	52.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	27.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
	25.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	27.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	26.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
	3.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
▶	53.4%	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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))))
▶	48.4%	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
	46.7%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	48.3%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	53.3%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
✓	52.6%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 1 145 to 630 computations (45% saved)

simplify131.0ms (1.5%)

Memory

-36.3MiB live, 151.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64)))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
cost-diff	2	(.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) 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 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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	(.f64 #s(literal 1/8 binary64) (.f64 x x))
cost-diff	0	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
cost-diff	0	(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
cost-diff	0	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.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: 0 (0.0ms)

Iter	Nodes	Cost
0	55	537
0	94	533
1	136	528
2	227	528
3	372	528
4	660	528
5	1109	528
6	2483	528
7	4832	528
0	8044	523

Stop Event

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

Calls

Call 1

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

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

localize222.0ms (2.6%)

Memory

44.6MiB live, 318.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.4609375	(sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
accuracy	0.484375	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64)))))
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
accuracy	29.821297053934636	#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))
accuracy	0.03515625	(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
accuracy	0.5456215747966553	(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
accuracy	13.967916711288478	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
accuracy	29.820981640629533	#s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.0	(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	29.804180060256858	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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	0.0	(*.f64 x x)
accuracy	0.0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
accuracy	33.023815731876155	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
accuracy	0.015625	(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
accuracy	0.0234375	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))))
accuracy	0.5065590747966553	(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
accuracy	13.409119314006071	(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))

Samples

99.0ms	90×	2	valid
48.0ms	139×	0	valid
17.0ms	27×	1	valid

Compiler

Compiled 517 to 44 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 124.0ms

ival-div: 30.0ms (24.3% of total)

ival-add: 24.0ms (19.4% of total)

ival-sqrt: 17.0ms (13.8% of total)

adjust: 15.0ms (12.1% of total)

ival-sub: 14.0ms (11.3% of total)

ival-mult: 12.0ms (9.7% of total)

ival-hypot: 10.0ms (8.1% of total)

exact: 1.0ms (0.8% of total)

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

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

series27.0ms (0.3%)

Memory

-12.9MiB live, 30.8MiB allocated

Counts

23 → 133

Calls

Call 1

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

Outputs
(* 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) (+ 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))))
(* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))
1/4
(+ 1/4 (* -1/4 (pow x 2)))
(+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
(pow x 2)
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
1/2
(+ 1/2 (* -1/8 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/32 (pow x 2)) 1/8)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/32 (* -5/64 (pow x 2)))) 1/8)))
(- 1 (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* 1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2)))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* (pow x 2) (- (* -11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(* (pow 2 1/4) (sqrt (sqrt 1/2)))
(+ (* -1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* 11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* (pow x 2) (+ (* -69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))))))
(sqrt (sqrt 1/2))
(+ (sqrt (sqrt 1/2)) (* -1/16 (* (pow x 2) (sqrt (sqrt 1/2)))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* 21/512 (* (pow x 2) (sqrt (sqrt 1/2)))))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -255/8192 (* (pow x 2) (sqrt (sqrt 1/2)))) (* 21/512 (sqrt (sqrt 1/2))))))))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(+ 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 (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)))))
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(- (+ (/ 1/64 (* (pow x 3) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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))))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (* (pow x 3) (+ 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))))) (+ (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 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)))))
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 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 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -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)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(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)))))
(+ 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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(+ 1/4 (* 1/4 (/ 1 x)))
(- (+ 1/4 (* 1/4 (/ 1 x))) (/ 1/8 (pow x 3)))
(- (+ 1/4 (+ (* 1/4 (/ 1 x)) (* 3/32 (/ 1 (pow x 5))))) (/ 1/8 (pow x 3)))
(- 1 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* 1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2)))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(- (+ 1 (* 3/16 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2)))))) (+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(* (pow 1/2 1/4) (sqrt (sqrt 1/2)))
(+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(+ (* -3/16 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2))))) (+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -3/32 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(+ (* -3/32 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* -9/128 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2))))) (+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(+ (/ 1/8 (* 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)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 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 (/ (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (+ 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)))) (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ 1 (sqrt 1/2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 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 (/ (- (* 1/4 (/ 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 (/ (- (* -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 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -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))) (sqrt 1/2))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- 1/4 (* 1/4 (/ 1 x)))
(+ 1/4 (* -1 (/ (- 1/4 (* 1/8 (/ 1 (pow x 2)))) x)))
(+ 1/4 (* -1 (/ (- (+ 1/4 (/ 3/32 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)))
(- (+ 1 (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1 (/ (- (* -1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* 1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* 3/32 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 9/128 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(* -1 (/ (- 1/2 (* 1/4 (/ 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))

Calls

3 calls:

Time

Variable

Point

Expression

14.0ms

inf

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

6.0ms

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

4.0ms

-inf

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

simplify226.0ms (2.7%)

Memory

-10.7MiB live, 285.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	562	3580
1	1883	3332
2	7293	3214
0	8525	3101

Stop Event

1×	iter limit
1×	node limit

Counts

133 → 133

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))))
(* 1/4 (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))))
(* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))
1/4
(+ 1/4 (* -1/4 (pow x 2)))
(+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
(pow x 2)
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
1/2
(+ 1/2 (* -1/8 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/32 (pow x 2)) 1/8)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/32 (* -5/64 (pow x 2)))) 1/8)))
(- 1 (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* 1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2)))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* (pow x 2) (- (* -11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(* (pow 2 1/4) (sqrt (sqrt 1/2)))
(+ (* -1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* 11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* (pow x 2) (+ (* -69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))))))
(sqrt (sqrt 1/2))
(+ (sqrt (sqrt 1/2)) (* -1/16 (* (pow x 2) (sqrt (sqrt 1/2)))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* 21/512 (* (pow x 2) (sqrt (sqrt 1/2)))))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -255/8192 (* (pow x 2) (sqrt (sqrt 1/2)))) (* 21/512 (sqrt (sqrt 1/2))))))))
(/ 1/4 (pow x 2))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(+ 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 (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))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))))))))
(- (+ (/ 1/64 (* (pow x 3) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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))))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (* (pow x 3) (+ 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))))) (+ (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (* (pow x 3) (+ 1 (sqrt 1/2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 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)))))
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 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 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(- (+ 1 (+ (* -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)))))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))
(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)))))
(+ 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 x)
(/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x)
(+ 1/4 (* 1/4 (/ 1 x)))
(- (+ 1/4 (* 1/4 (/ 1 x))) (/ 1/8 (pow x 3)))
(- (+ 1/4 (+ (* 1/4 (/ 1 x)) (* 3/32 (/ 1 (pow x 5))))) (/ 1/8 (pow x 3)))
(- 1 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* 1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2)))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(- (+ 1 (* 3/16 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2)))))) (+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(* (pow 1/2 1/4) (sqrt (sqrt 1/2)))
(+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(+ (* -3/16 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2))))) (+ (* -1/8 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -3/32 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))))
(+ (* -3/32 (* (pow 1/2 1/4) (* (/ 1 (pow x 2)) (sqrt (sqrt 1/2))))) (+ (* -9/128 (* (pow 1/2 1/4) (* (/ 1 (pow x 3)) (sqrt (sqrt 1/2))))) (+ (* 1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))))
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(+ (/ 1/8 (* 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)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 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 (/ (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3))))) (+ 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)))) (* 2 (/ (* (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))) (+ 1 (sqrt 1/2))))))) x)) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 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 (/ (- (* 1/4 (/ 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 (/ (- (* -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 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(- (+ 1 (* -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))) (sqrt 1/2))
(- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(- 1/4 (* 1/4 (/ 1 x)))
(+ 1/4 (* -1 (/ (- 1/4 (* 1/8 (/ 1 (pow x 2)))) x)))
(+ 1/4 (* -1 (/ (- (+ 1/4 (/ 3/32 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)))
(- (+ 1 (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1 (/ (- (* -1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* 1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* 3/32 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 9/128 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(* -1 (/ (- 1/2 (* 1/4 (/ 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
(* 1/8 (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 (-.f64 (.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 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(* 1/4 (pow x 2))
(.f64 #s(literal 1/4 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4 (* -3/16 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16))))
(.f64 (.f64 (fma.f64 (-.f64 (.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) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 5/32 (* -35/256 (pow x 2)))) 3/16))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -35/256 binary64) (.f64 x x) #s(literal 5/32 binary64)) x) x) #s(literal 3/16 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x))
(* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))
(.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x)
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal 1/4 binary64)) (.f64 x x))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1/4 (pow x 2)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x x) #s(literal 1/4 binary64))
(+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(fma.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1/4 binary64))
(+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal 1/4 binary64))
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #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 (-.f64 (.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 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -5/32 binary64) (.f64 x x) #s(literal 3/16 binary64)) x) x) #s(literal 1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -3/16 (pow x 2)))) 1/2)
(-.f64 (.f64 (.f64 (fma.f64 #s(literal -3/16 binary64) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 5/32 (pow x 2)) 3/16)))) 1/2)
(-.f64 (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 5/32 binary64) (.f64 x x)) #s(literal 3/16 binary64)) (*.f64 x x) #s(literal 1/4 binary64)) x) x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 (pow x 2)))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 3/32 (pow x 2)) 1/8)))
(fma.f64 (-.f64 (.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/32 (* -5/64 (pow x 2)))) 1/8)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -5/64 binary64) (.f64 x x) #s(literal 3/32 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(- 1 (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(- (+ 1 (* 1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2)))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (*.f64 x x)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* -11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -11/128 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))) (.f64 x x) #s(literal 1 binary64)))
(- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))) (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2))))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -11/128 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 69/1024 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))) (.f64 x x))) (*.f64 x x) #s(literal 1 binary64)))
(* (pow 2 1/4) (sqrt (sqrt 1/2)))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+ (* -1/8 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* (pow 2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* 11/128 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))))))
(fma.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 11/128 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))) (.f64 x x) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(+ (* (pow 2 1/4) (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -1/8 (* (pow 2 1/4) (sqrt (sqrt 1/2)))) (* (pow x 2) (+ (* -69/1024 (* (pow 2 1/4) (* (pow x 2) (sqrt (sqrt 1/2))))) (* 11/128 (* (pow 2 1/4) (sqrt (sqrt 1/2)))))))))
(fma.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -69/1024 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 11/128 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 x x))) (.f64 x x) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(sqrt (sqrt 1/2))
(sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(+ (sqrt (sqrt 1/2)) (* -1/16 (* (pow x 2) (sqrt (sqrt 1/2)))))
(.f64 (fma.f64 #s(literal -1/16 binary64) (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* 21/512 (* (pow x 2) (sqrt (sqrt 1/2)))))))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 21/512 binary64) (.f64 x x) #s(literal -1/16 binary64))) (*.f64 x x) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt (sqrt 1/2)) (* (pow x 2) (+ (* -1/16 (sqrt (sqrt 1/2))) (* (pow x 2) (+ (* -255/8192 (* (pow x 2) (sqrt (sqrt 1/2)))) (* 21/512 (sqrt (sqrt 1/2))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal -255/8192 binary64) (.f64 x x) #s(literal 21/512 binary64))) (.f64 x x) (.f64 #s(literal -1/16 binary64) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 x x) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ 1/4 (pow x 3))
(/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.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 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -5/16 binary64) (.f64 x x) #s(literal 3/8 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(-.f64 (/.f64 (-.f64 (/.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 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (neg.f64 x)) (/.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -2 (/ (* (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2))))) (* (pow x 2) (+ 1 (sqrt 1/2))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (+ (* 1/8 (/ 1 (* (pow x 2) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))))))))
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(- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))
(-.f64 (+.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (* -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))) (sqrt 1/2))
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -3/32 binary64) x)) (sqrt.f64 #s(literal 1/2 binary64))) x) #s(literal -1 binary64) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (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) x) #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 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) #s(literal -1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/2) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6)))) (+ 1/2 (/ 3/16 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/32 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (+.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64))) (neg.f64 x))
(- 1/4 (* 1/4 (/ 1 x)))
(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) x))
(+ 1/4 (* -1 (/ (- 1/4 (* 1/8 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(+ 1/4 (* -1 (/ (- (+ 1/4 (/ 3/32 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)))
(-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(- (+ 1 (* 1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x) (fma.f64 (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(- (+ 1 (* -1 (/ (- (* -1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (neg.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (fma.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -3/16 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x))) (neg.f64 x)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(+ (* -1/2 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(-.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x)))
(+ (* -1 (/ (+ (* 1/8 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x))) (neg.f64 x)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 3/16 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/2 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 5/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 3/16 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x))) (neg.f64 x))) (neg.f64 x)))
(+ (* -1/4 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* -1 (/ (+ (* 3/32 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2))))) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 3/32 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 (*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 x)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -3/32 (* (pow 1/2 1/4) (sqrt (sqrt 1/2)))) (* 9/128 (* (pow 1/2 1/4) (* (/ 1 x) (sqrt (sqrt 1/2)))))) x)) (* 1/4 (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))) x)) (* (pow 1/2 1/4) (sqrt (sqrt 1/2))))
(fma.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 9/128 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))) x) (.f64 (.f64 #s(literal -3/32 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 x))) (neg.f64 x)))
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 x))
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (neg.f64 x))
(* -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))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (neg.f64 x))
(* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 3/8 binary64) (pow.f64 x #s(literal 4 binary64))) #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)))) (neg.f64 x))

rewrite190.0ms (2.2%)

Memory

31.4MiB live, 260.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	362
0	94	342
1	331	315
2	2318	290
0	8260	286

Stop Event

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

Counts

23 → 320

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
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(.f64 (neg.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64))))
(.f64 (fabs.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64))) (fabs.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64))))
(.f64 (sqrt.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (+.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(pow.f64 (.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64))) (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(fabs.f64 (pow.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (/.f64 (log.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (+.f64 (log1p.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))) (log.f64 #s(literal 1/4 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (hypot.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))
(/.f64 (fabs.f64 (/.f64 #s(literal 1/4 binary64) (neg.f64 x))) x)
(/.f64 (fabs.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x))) x)
(/.f64 (fabs.f64 (/.f64 #s(literal 1/4 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1/4 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1/4 binary64) x) x)
(/.f64 #s(literal -1/4 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(sqrt.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(fabs.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(fabs.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(/.f64 (-.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) (neg.f64 x))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (neg.f64 x)) (.f64 x #s(literal -1/2 binary64))) (.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) x) (.f64 x #s(literal 1/2 binary64))) (.f64 x x))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/8 binary64)) (.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(neg.f64 (/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x))
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x))
(.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)))
#s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))

eval84.0ms (1%)

Memory: -1.0MiB live, 100.8MiB allocated
Compiler: Compiled 23 715 to 2 406 computations (89.9% saved)

prune39.0ms (0.5%)

Memory

-10.4MiB live, 78.1MiB allocated

Pruning

23 alts after pruning (13 fresh and 10 done)

	Pruned	Kept	Total
New	485	7	492
Fresh	2	6	8
Picked	2	3	5
Done	0	7	7
Total	489	23	512

Accuracy

100.0%

Counts

512 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.0%	(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
	38.4%	(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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)))
	79.0%	(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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 (sqrt.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 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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)))))
	53.1%	(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64)))
	79.0%	(/.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)))
	79.0%	(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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))))
	52.3%	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
	51.6%	(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
✓	78.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	52.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
✓	53.1%	(-.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)))))
✓	52.7%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
	27.4%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
	25.8%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
	27.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	26.6%	(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
	46.9%	#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
✓	53.4%	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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))))
✓	48.4%	#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
	46.7%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
✓	48.3%	#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
✓	53.3%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
✓	52.6%	#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))

Compiler

Compiled 2 183 to 712 computations (67.4% saved)

regimes103.0ms (1.2%)

Memory

3.4MiB live, 101.3MiB allocated

Counts

42 → 2

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x 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) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.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 1/4 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.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 binary64) (.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 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 (sqrt.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 1/8 binary64) (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 3 binary64))))) (.f64 (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)))) (cosh.f64 (asinh.f64 (pow.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64))))) (*.f64 (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (-.f64 (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64)) (cosh.f64 (atanh.f64 x)) #s(literal 1 binary64))))))))

Outputs

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

(/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))

Calls

7 calls:

37.0ms	(-.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))))))
20.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
11.0ms	x
8.0ms	(hypot.f64 #s(literal 1 binary64) x)
8.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

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

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes66.0ms (0.8%)

Memory

21.1MiB live, 109.2MiB allocated

Counts

39 → 2

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x 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) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.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 1/4 binary64) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))

Outputs

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

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

Calls

7 calls:

13.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
11.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
10.0ms	x
8.0ms	(hypot.f64 #s(literal 1 binary64) x)
7.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

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

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes83.0ms (1%)

Memory

-14.9MiB live, 90.8MiB allocated

Counts

37 → 2

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x 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) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.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 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (*.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))

Outputs

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

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

Calls

7 calls:

30.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
13.0ms	x
9.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
8.0ms	(hypot.f64 #s(literal 1 binary64) x)
7.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Results

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

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes71.0ms (0.8%)

Memory

-17.4MiB live, 117.8MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x 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) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))

Outputs

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

(/.f64 (+.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)))

Calls

7 calls:

14.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
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))))))
10.0ms	(hypot.f64 #s(literal 1 binary64) x)
9.0ms	x
9.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))

Results

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

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes64.0ms (0.8%)

Memory

6.7MiB live, 150.7MiB allocated

Counts

34 → 2

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (*.f64 x x)))
#s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (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) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 11/128 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x 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) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 #s(literal 3/16 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -69/1024 binary64) (.f64 x x) #s(literal 11/128 binary64)) x) x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
#s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #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 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64) (.f64 (.f64 (.f64 #s(literal -11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))))) (sqrt.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))))))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))) (fma.f64 (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal -69/512 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) x (.f64 #s(literal 11/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x) (.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))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
(-.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 #s(approx (/ 1 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x)) #s(literal 1 binary64))))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))

Outputs

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

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

Calls

7 calls:

13.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
9.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
9.0ms	x
9.0ms	(hypot.f64 #s(literal 1 binary64) x)
8.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.6%	2	`(hypot.f64 #s(literal 1 binary64) x)`
99.6%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.6%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.6%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.6%	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)))))`
99.6%	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))))))`
99.6%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes40.0ms (0.5%)

Memory

33.0MiB live, 79.0MiB allocated

Counts

24 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

7.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
6.0ms	x
6.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms	(hypot.f64 #s(literal 1 binary64) x)
5.0ms	(-.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
99.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`
99.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
99.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
99.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
99.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
99.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
99.0%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes42.0ms (0.5%)

Memory

-23.7MiB live, 75.0MiB allocated

Counts

20 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

11.0ms	x
8.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms	(hypot.f64 #s(literal 1 binary64) x)
4.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
4.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
98.8%	2	`(hypot.f64 #s(literal 1 binary64) x)`
98.8%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.8%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.8%	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)))))`
98.8%	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))))))`
98.8%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes35.0ms (0.4%)

Memory

20.6MiB live, 65.7MiB allocated

Counts

19 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
98.5%	2	`(hypot.f64 #s(literal 1 binary64) x)`
98.5%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.5%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.5%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
98.5%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.5%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes33.0ms (0.4%)

Memory

9.7MiB live, 54.5MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
98.5%	2	`(hypot.f64 #s(literal 1 binary64) x)`
98.5%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.5%	2	`x`
98.5%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.5%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.5%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.5%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes31.0ms (0.4%)

Memory

0.3MiB live, 50.7MiB allocated

Counts

14 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

10.0ms	x
4.0ms	(/.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))))))
3.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

Accuracy	Segments	Branch
98.3%	2	`(hypot.f64 #s(literal 1 binary64) x)`
98.3%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.3%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.3%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.3%	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)))))`
98.3%	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))))))`
98.3%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes22.0ms (0.3%)

Memory

-7.7MiB live, 38.6MiB allocated

Counts

11 → 2

Calls

Call 1

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

Outputs

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

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

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

Results

Accuracy	Segments	Branch
97.7%	2	`(hypot.f64 #s(literal 1 binary64) x)`
97.7%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.7%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.7%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.7%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
97.7%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
97.7%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes41.0ms (0.5%)

Memory

-21.6MiB live, 24.6MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

26.0ms	(-.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))))))
3.0ms	x
3.0ms	(/.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
97.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`
97.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.0%	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)))))`
97.0%	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))))))`
97.0%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes15.0ms (0.2%)

Memory

24.0MiB live, 24.0MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
97.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`
97.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.0%	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)))))`
97.0%	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))))))`
97.0%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes28.0ms (0.3%)

Memory

-33.2MiB live, 13.5MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
96.8%	2	`(hypot.f64 #s(literal 1 binary64) x)`
96.8%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
96.8%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
96.8%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
96.8%	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)))))`
96.8%	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))))))`
96.8%	2	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes10.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

1.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
1.0ms	(hypot.f64 #s(literal 1 binary64) x)
1.0ms	(-.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
48.4%	1	`(hypot.f64 #s(literal 1 binary64) x)`
48.4%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
48.4%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
48.4%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
48.4%	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)))))`
48.4%	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))))))`
48.4%	1	`x`

Compiler

Compiled 47 to 37 computations (21.3% saved)

regimes7.0ms (0.1%)

Memory

19.2MiB live, 19.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

7 calls:

1.0ms	x
1.0ms	(/.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)))))
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))))))

Results

Accuracy	Segments	Branch
26.6%	1	`(hypot.f64 #s(literal 1 binary64) x)`
26.6%	1	`x`
26.6%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
26.6%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
26.6%	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)))))`
26.6%	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))))))`
26.6%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 47 to 37 computations (21.3% saved)

bsearch54.0ms (0.6%)

Memory

-62.9MiB live, 17.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
52.0ms	0.0010236833586042074	0.02965885320230699

Samples

8.0ms

112×

valid

Compiler

Compiled 566 to 328 computations (42% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-hypot: 2.0ms (36.3% of total)

ival-div: 1.0ms (18.2% of total)

ival-add: 1.0ms (18.2% of total)

ival-mult: 1.0ms (18.2% of total)

ival-sub: 1.0ms (18.2% of total)

ival-sqrt: 1.0ms (18.2% of total)

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

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

exact: 0.0ms (0% of total)

bsearch5.0ms (0.1%)

Memory

7.9MiB live, 7.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	0.0010236833586042074	0.02965885320230699

Samples

2.0ms

32×

valid

Compiler

Compiled 433 to 286 computations (33.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-hypot: 1.0ms (65.5% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0010236833586042074	0.02965885320230699

Compiler

Compiled 447 to 300 computations (32.9% saved)

bsearch7.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	0.0010236833586042074	0.02965885320230699

Samples

3.0ms

48×

valid

Compiler

Compiled 370 to 258 computations (30.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-hypot: 1.0ms (42% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

bsearch21.0ms (0.2%)

Memory

-9.0MiB live, 32.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.6445078854318006	908.0244455783775

Samples

13.0ms

128×

valid

Compiler

Compiled 900 to 437 computations (51.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 5.0ms (48.1% of total)

ival-hypot: 2.0ms (19.2% of total)

ival-div: 1.0ms (9.6% of total)

ival-add: 1.0ms (9.6% of total)

ival-sub: 1.0ms (9.6% of total)

ival-sqrt: 1.0ms (9.6% of total)

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

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

exact: 0.0ms (0% of total)

bsearch5.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	0.6445078854318006	908.0244455783775

Samples

2.0ms

32×

valid

Compiler

Compiled 740 to 437 computations (40.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-hypot: 1.0ms (66.9% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

bsearch2.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.6445078854318006	908.0244455783775

Compiler

Compiled 700 to 421 computations (39.9% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.7074960393064355	0.9593088015007294

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.7074960393064355	0.9593088015007294

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch3.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.6445078854318006	908.0244455783775

Samples

1.0ms

16×

valid

Compiler

Compiled 412 to 309 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.6445078854318006	908.0244455783775

Compiler

Compiled 524 to 333 computations (36.5% saved)

bsearch16.0ms (0.2%)

Memory

-41.5MiB live, 2.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.6445078854318006	908.0244455783775

Compiler

Compiled 380 to 293 computations (22.9% saved)

bsearch1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.6445078854318006	908.0244455783775

Compiler

Compiled 380 to 301 computations (20.8% saved)

bsearch7.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	0.6445078854318006	908.0244455783775

Samples

3.0ms

48×

valid

Compiler

Compiled 340 to 277 computations (18.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-hypot: 1.0ms (44.2% of total)

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

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

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

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

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

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

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

exact: 0.0ms (0% of total)

simplify66.0ms (0.8%)

Memory

9.0MiB live, 54.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	961
1	202	947
2	324	945
3	482	945
4	739	945
5	1305	945
6	2826	945
7	5251	945

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 3170534137668829/288230376151711744 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (+.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))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 2589569785738035/2251799813685248 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) #s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))))
(if (<=.f64 (sqrt.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 3602879701896397/4503599627370496 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 (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))))
(if (<=.f64 (sqrt.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 3602879701896397/4503599627370496 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 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)))
(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #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)))))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))))))
(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) (.f64 x x))) #s(approx (/ (- 1 (- 1/2 (/ -1/2 (sqrt (+ ( 1 1) (* x x)))))) (+ (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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.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)))))) #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))

Outputs
(if (<=.f64 x #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 5764607523034235/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)) #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))) (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 5476377146882523/576460752303423488 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))) (.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) (hypot.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))))
(if (<=.f64 x #s(literal 3170534137668829/288230376151711744 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (+.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))))
(if (<=.f64 x #s(literal 3170534137668829/288230376151711744 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 69/1024 binary64) (.f64 x x)) #s(literal 11/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (+.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))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)))) (+.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ ( 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))) #s(literal 1 binary64))))
(if (<=.f64 x #s(literal 2589569785738035/2251799813685248 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) #s(approx (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(if (<=.f64 x #s(literal 1 binary64)) #s(approx (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) #s(approx (/ -1/2 (sqrt (+ (* 1 1) (* x x)))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))))))
(if (<=.f64 (sqrt.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 3602879701896397/4503599627370496 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 (/ (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) (+ (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) 1)) (.f64 (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1843/32768 binary64) (.f64 x x) #s(literal 69/1024 binary64)) x) x) #s(literal 11/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))))
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(if (<=.f64 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #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 x #s(literal 2476979795053773/2251799813685248 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 (fma.f64 #s(literal -11/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) x) x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx ( 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal 6980579422424269/4503599627370496 binary64)) #s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.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)))))) #s(literal 1/2 binary64)))))
#s(approx (- 1 (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x))))))) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (sqrt (- 1/2 (/ -1/2 (sqrt (+ (* 1 1) (* x x)))))) #s(literal 1 binary64)))

soundness1.5s (17.3%)

Memory

22.5MiB live, 1 171.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	392	1881
1	1228	1731
2	4292	1687
0	8373	1632
0	9	43
0	18	33
1	82	33
2	609	33
3	6358	33
0	8243	30
0	206	845
1	633	767
2	1960	714
3	7820	714
0	8462	676
0	345	1415
1	1054	1316
2	3248	1260
0	8557	1207
0	55	362
0	94	342
1	331	315
2	2318	290
0	8260	286
0	562	3580
1	1883	3332
2	7293	3214
0	8525	3101
0	47	233
0	75	227
1	289	215
2	2109	215
0	8169	214
0	39	271
0	62	247
1	265	247
2	2039	247
0	8689	237

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
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 2 375 to 953 computations (59.9% saved)

preprocess136.0ms (1.6%)

Memory: -12.3MiB live, 130.2MiB allocated
Compiler: Compiled 2 234 to 394 computations (82.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	14	31
1	37	27
2	70	27
3	95	27
4	127	27
5	134	27
0	9	12
0	18	12
1	35	10
2	65	10
3	105	10
4	137	10
5	144	10
0	144	10

Iter	Nodes	Cost
0	14	31
1	37	27
2	70	27
3	95	27
4	127	27
5	134	27
0	9	12
0	18	12
1	35	10
2	65	10
3	105	10
4	137	10
5	144	10
0	144	10

start0.0ms (0%)

analyze0.0ms (0%)

sample1.7s (20.2%)

explain197.0ms (2.3%)

preprocess15.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize53.0ms (0.6%)

series9.0ms (0.1%)

simplify283.0ms (3.3%)

rewrite192.0ms (2.3%)

eval45.0ms (0.5%)

prune19.0ms (0.2%)

simplify89.0ms (1%)

localize187.0ms (2.2%)

series11.0ms (0.1%)

simplify157.0ms (1.9%)

rewrite168.0ms (2%)

eval126.0ms (1.5%)

prune42.0ms (0.5%)

simplify235.0ms (2.8%)

localize959.0ms (11.3%)

series12.0ms (0.1%)

simplify232.0ms (2.7%)

rewrite173.0ms (2%)

eval103.0ms (1.2%)

prune45.0ms (0.5%)

simplify131.0ms (1.5%)

localize222.0ms (2.6%)

series27.0ms (0.3%)

simplify226.0ms (2.7%)

rewrite190.0ms (2.2%)

eval84.0ms (1%)

prune39.0ms (0.5%)

regimes103.0ms (1.2%)

regimes66.0ms (0.8%)

regimes83.0ms (1%)

regimes71.0ms (0.8%)

regimes64.0ms (0.8%)

regimes40.0ms (0.5%)

regimes42.0ms (0.5%)

regimes35.0ms (0.4%)

regimes33.0ms (0.4%)

regimes31.0ms (0.4%)

regimes22.0ms (0.3%)

regimes41.0ms (0.5%)

regimes15.0ms (0.2%)

regimes28.0ms (0.3%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch54.0ms (0.6%)

bsearch5.0ms (0.1%)

bsearch2.0ms (0%)

bsearch7.0ms (0.1%)

bsearch21.0ms (0.2%)

bsearch5.0ms (0.1%)

bsearch2.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch3.0ms (0%)

bsearch1.0ms (0%)

bsearch16.0ms (0.2%)

bsearch1.0ms (0%)

bsearch7.0ms (0.1%)

simplify66.0ms (0.8%)

soundness1.5s (17.3%)

preprocess136.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	31
1	37	27
2	70	27
3	95	27
4	127	27
5	134	27
0	9	12
0	18	12
1	35	10
2	65	10
3	105	10
4	137	10
5	144	10
0	144	10