Metrics for Given's Rotation SVD example, simplified

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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 14 to 11 computations (21.4% saved)

sample1.7s (16.1%)

Memory

42.7MiB live, 3 113.2MiB allocated

Samples

790.0ms	2 817×	2	valid
334.0ms	4 220×	0	valid
253.0ms	1 219×	1	valid

Precisions

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

ival-hypot: 432.0ms (39.8% of total)

ival-mult: 134.0ms (12.3% of total)

ival-sqrt: 125.0ms (11.5% of total)

ival-div: 123.0ms (11.3% of total)

adjust: 94.0ms (8.7% of total)

ival-add: 78.0ms (7.2% of total)

ival-sub: 76.0ms (7% of total)

exact: 14.0ms (1.3% of total)

ival-true: 6.0ms (0.6% of total)

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

Bogosity

preprocess18.0ms (0.2%)

Memory

-11.2MiB live, 26.2MiB allocated

Algorithm

2×	egg-herbie

Rules

38×	`sub-neg`
36×	`+-lowering-+.f64`
36×	`+-lowering-+.f32`
22×	`+-commutative`
20×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	42	32
2	70	32
3	94	32
4	130	32
5	152	32
6	164	32
7	170	32
8	171	32
0	12	15
1	25	13
2	32	13
3	37	13
4	43	13
5	51	13
6	61	13
7	72	13
8	75	13
0	75	12

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

Outputs

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

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

Call 2

Inputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))

Outputs
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x)))))))
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 (neg x))))))
(neg (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 (neg x))))))))
(+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 (neg x))))) -1)

explain173.0ms (1.7%)

Memory

14.1MiB live, 291.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
61	1	(-1.489304771835313e-161)	-	`(-.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	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	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(hypot.f64 #s(literal 1 binary64) x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
0	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	0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
0	0	-	-	`#s(literal 1/2 binary64)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`	cancellation	62	0

Confusion

	Predicted +	Predicted -
+	61	0
-	1	194

Precision

0.9838709677419355

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	61	0	0
-	1	0	194

Precision?

0.9838709677419355

Recall?

1.0

Freqs

test

number	freq
0	194
1	62

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

50.0ms	172×	2	valid
22.0ms	270×	0	valid
12.0ms	70×	1	valid

Compiler

Compiled 128 to 40 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-hypot: 23.0ms (37.4% of total)

ival-sqrt: 9.0ms (14.6% of total)

ival-div: 7.0ms (11.4% of total)

adjust: 7.0ms (11.4% of total)

ival-mult: 5.0ms (8.1% of total)

ival-sub: 4.0ms (6.5% of total)

ival-add: 4.0ms (6.5% of total)

exact: 1.0ms (1.6% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify6.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
✓	cost-diff	320	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
✓	cost-diff	5440	(hypot.f64 #s(literal 1 binary64) x)

Rules

36×	`+-lowering-+.f64`
36×	`+-lowering-+.f32`
18×	`-lowering-.f32`
18×	`--lowering--.f32`
18×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	67
1	25	61
2	32	61
3	37	61
4	43	61
5	51	61
6	61	61
7	72	61
8	75	61
0	75	55

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize64.0ms (0.6%)

Memory

-25.7MiB live, 99.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(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)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
✓	accuracy	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))

Samples

26.0ms	86×	2	valid
13.0ms	135×	0	valid
6.0ms	35×	1	valid

Compiler

Compiled 51 to 11 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-hypot: 10.0ms (31.5% of total)

adjust: 7.0ms (22% of total)

ival-div: 4.0ms (12.6% of total)

ival-sqrt: 3.0ms (9.4% of total)

ival-mult: 3.0ms (9.4% of total)

ival-sub: 2.0ms (6.3% of total)

ival-add: 2.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (sqrt (+ (* 1 1) (* x x)))>
#<alt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))>
#<alt (- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))>
#<alt (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))>
#<alt (/ 1 (sqrt (+ (* 1 1) (* x x))))>
#<alt (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))>

Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1/2 (* 1/2 (/ 1 x))) (/ 1/4 (pow x 3)))>
#<alt (- (+ 1/2 (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5))))) (/ 1/4 (pow x 3)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1/2 (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)))>
#<alt (- 1 (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* (pow x 2) (- (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))) (* -1/4 (/ (sqrt 1/2) (sqrt 2)))))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* -1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* 1/8 (/ (sqrt 1/2) (pow x 2)))) (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (- (+ 1 (* 3/16 (/ (sqrt 1/2) (pow x 3)))) (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/2 (/ (sqrt 1/2) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (- (* -3/16 (/ (sqrt 1/2) x)) (* -1/8 (sqrt 1/2))) x)) (* 1/2 (sqrt 1/2))) x))) (sqrt 1/2))>
#<alt (* (sqrt 1/2) (sqrt 2))>
#<alt (+ (* -1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2))) (* (sqrt 1/2) (sqrt 2)))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* 1/2 (/ (* (pow x 2) (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))))) (sqrt 2))))))>
#<alt (+ (* (sqrt 1/2) (sqrt 2)) (* (pow x 2) (+ (* -1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (* (sqrt 1/2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/2 (/ (sqrt 1/2) x)))>
#<alt (+ (sqrt 1/2) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (+ (sqrt 1/2) (+ (* -3/16 (/ (sqrt 1/2) (pow x 3))) (+ (* -1/8 (/ (sqrt 1/2) (pow x 2))) (* 1/2 (/ (sqrt 1/2) x)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/2 (/ (sqrt 1/2) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/8 (/ (sqrt 1/2) x)) (* 1/2 (sqrt 1/2))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (sqrt 1/2)) (* 3/16 (/ (sqrt 1/2) x))) x)) (* 1/2 (sqrt 1/2))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))>
#<alt (- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))>
#<alt 1>
#<alt (- 1 (/ 1 x))>
#<alt (+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))>

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
0.0ms	x	@	-inf	(/ 1 (sqrt (+ (* 1 1) (* x x))))
0.0ms	x	@	inf	(sqrt (+ (* 1 1) (* x x)))
0.0ms	x	@	inf	(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x))))))))
0.0ms	x	@	inf	(sqrt (* 1/2 (+ 1 (/ 1 (sqrt (+ (* 1 1) (* x x)))))))

rewrite484.0ms (4.6%)

Memory

18.6MiB live, 479.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 098×	`accelerator-lowering-fma.f32`
4 098×	`accelerator-lowering-fma.f64`
3 010×	`-lowering-.f32`
3 010×	`-lowering-.f64`
1 830×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	72	56
2	556	56
3	5199	56
0	8816	50

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 477

Calls

Call 1

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

Outputs
(+.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x x))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (*.f64 x x))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log1p.f64 (*.f64 x x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
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simplify380.0ms (3.6%)

Memory

-4.2MiB live, 588.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 216×	`accelerator-lowering-fma.f32`
12 216×	`accelerator-lowering-fma.f64`
5 034×	`-lowering-.f32`
5 034×	`-lowering-.f64`
2 790×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	232	991
1	674	917
2	1886	877
3	5894	834
0	8222	781

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval98.0ms (0.9%)

Memory: 12.1MiB live, 165.6MiB allocated
Compiler: Compiled 15 917 to 2 298 computations (85.6% saved)

prune84.0ms (0.8%)

Memory

-28.9MiB live, 186.5MiB allocated

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	530	19	549
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	531	19	550

Accuracy

78.5%

Counts

550 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
	53.8%	(/.f64 (-.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) #s(literal -3 binary64)) (pow.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (pow.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))))
	78.1%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
▶	78.2%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
	52.3%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
▶	52.7%	(/.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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
	78.1%	(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
	51.5%	(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))))))
	26.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 3/16 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))))
	25.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))
	51.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))))))
	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
▶	50.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	50.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
	52.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) (fma.f64 x x #s(literal 1 binary64)))))))))
	52.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/2 binary64) x) x))))))
	27.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
▶	51.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	78.2%	(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))

Compiler

Compiled 1 336 to 460 computations (65.6% saved)

simplify294.0ms (2.8%)

Memory

19.3MiB live, 368.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

4 800×	`accelerator-lowering-fma.f32`
4 800×	`accelerator-lowering-fma.f64`
1 844×	`-lowering-.f32`
1 844×	`-lowering-.f64`
1 806×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	334
1	65	333
2	117	333
3	192	333
4	297	333
5	434	333
6	664	333
7	1217	333
8	1903	333
9	3299	333
10	4681	333
11	5403	333
12	5867	333
13	6020	333
14	6054	333
15	6345	333
16	6485	333
17	6852	333
18	7455	333
0	8110	304

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize455.0ms (4.3%)

Memory

-180.4MiB live, 306.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
✓	accuracy	99.5%	(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	79.7%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	accuracy	75.1%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	99.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	98.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓	accuracy	91.1%	(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

Samples

41.0ms	135×	0	valid
26.0ms	34×	2	valid
21.0ms	70×	0	invalid
8.0ms	16×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 308 to 36 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-div: 24.0ms (32.4% of total)

ival-sqrt: 19.0ms (25.6% of total)

ival-add: 13.0ms (17.5% of total)

ival-mult: 6.0ms (8.1% of total)

adjust: 5.0ms (6.7% of total)

ival-sub: 3.0ms (4% of total)

ival-neg: 3.0ms (4% of total)

exact: 1.0ms (1.3% of total)

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

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

series22.0ms (0.2%)

Memory

4.4MiB live, 41.7MiB allocated

Counts

22 → 240

Calls

Call 1

Inputs
#<alt (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))>
#<alt (/ (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))))>
#<alt (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)>
#<alt (/ 1/2 (sqrt (+ (* x x) 1)))>
#<alt (- 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (- 1 (sqrt (+ 1/2 (/ 1/2 x))))>
#<alt (sqrt (+ 1/2 (/ 1/2 x)))>
#<alt (+ 1/2 (/ 1/2 x))>
#<alt (/ 1/2 x)>
#<alt (+ (* (sqrt (+ 1 (sqrt (/ 1 (+ (* x x) 1))))) (neg (sqrt 1/2))) 1)>
#<alt (sqrt (+ 1 (sqrt (/ 1 (+ (* x x) 1)))))>
#<alt (+ 1 (sqrt (/ 1 (+ (* x x) 1))))>
#<alt (sqrt (/ 1 (+ (* x x) 1)))>
#<alt (/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))>
#<alt (+ 1/4 (/ 1/4 (+ (* x x) 1)))>
#<alt (/ 1/4 (+ (* x x) 1))>
#<alt (+ (* x x) 1)>
#<alt (sqrt (+ (* x x) 1))>
#<alt (/ 1 (+ (* x x) 1))>
#<alt (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))>
#<alt (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))>

Outputs
#<alt -2>
#<alt (- (* 1/8 (pow x 2)) 2)>
#<alt (- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)>
#<alt (- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)>
#<alt (* -1 (+ 1 (sqrt 1/2)))>
#<alt (* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))>
#<alt (- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))>
#<alt (* -1 (+ 1 (sqrt 1/2)))>
#<alt (- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))>
#<alt (- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))>
#<alt (- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 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)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* -1/4 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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))))) (+ (* -1/32 (/ (+ (* 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 (/ (+ (* 1/8 (/ 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)))))) (+ (/ 1/4 (* (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)))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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)))) (+ (* -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 (+ 1 (sqrt 1/2))))))) 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))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))>
#<alt -1/2>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))>
#<alt (- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))>
#<alt -1/2>
#<alt (* -1 (+ 1/2 (* 1/2 (/ 1 x))))>
#<alt (- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)>
#<alt (- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))>
#<alt (* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))>
#<alt (/ (- x (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))))>
#<alt (- (+ 1 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 x)) (sqrt 1/2))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt (/ (+ 1/2 (* 1/2 x)) x)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (+ 1/2 (* 1/2 (/ 1 x)))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (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)))))))>
#<alt (+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 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)))))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))>
#<alt (+ 1 (* -1 (sqrt 1/2)))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))>
#<alt (+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ 1 x)))>
#<alt (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))>
#<alt (+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (- 1 (* 1/2 (/ 1 x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))>
#<alt (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) x)))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt 1>
#<alt (+ 1 (/ 1 x))>
#<alt (- (+ 1 (/ 1 x)) (/ 1/2 (pow x 3)))>
#<alt (- (+ 1 (+ (/ 1 x) (* 3/8 (/ 1 (pow x 5))))) (/ 1/2 (pow x 3)))>
#<alt 1>
#<alt (- 1 (/ 1 x))>
#<alt (+ 1 (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt (+ 1 (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 3/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/8 (* -5/16 (pow x 2)))) 1/2)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x))>
#<alt 1/4>
#<alt (+ 1/4 (* -3/64 (pow x 2)))>
#<alt (+ 1/4 (* (pow x 2) (- (* 25/512 (pow x 2)) 3/64)))>
#<alt (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 25/512 (* -739/16384 (pow x 2)))) 3/64)))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/2 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 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)))))))))>
#<alt (- (+ (/ 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 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 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)))) (* 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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 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))))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/64 (/ 1 (* (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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 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)))))>
#<alt (+ (* -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)))) (* 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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 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)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))>
#<alt (- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))>
#<alt 1/4>
#<alt (+ 1/4 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))>
#<alt (- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 (pow x 2)))>
#<alt (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))>
#<alt (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (pow x 2) 1)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* -5/8 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 63/128 (pow x 2)) 5/8)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 63/128 (* -435/1024 (pow x 2)))) 5/8)))>
#<alt (* 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))>
#<alt (- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))>
#<alt 2>
#<alt (+ 2 (* -1/8 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))>
#<alt (- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))>
#<alt (- (+ 1 (+ (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)))))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))>
#<alt (+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))>

Calls

60 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (+ -1 (neg (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))))
2.0ms	x	@	inf	(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))
1.0ms	x	@	-inf	(- 1 (sqrt (+ 1/2 (/ 1/2 x))))
1.0ms	x	@	0	(+ 1/4 (/ 1/4 (+ (* x x) 1)))
1.0ms	x	@	-inf	(/ (+ 1/4 (/ 1/4 (+ (* x x) 1))) (* (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))) (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))

rewrite470.0ms (4.5%)

Memory

8.8MiB live, 700.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 438×	`/-lowering-/.f32`
4 438×	`/-lowering-/.f64`
4 186×	`-lowering-.f32`
4 186×	`-lowering-.f64`
2 752×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	234
1	237	226
2	2149	226
0	8533	206

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 926

Calls

Call 1

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

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

simplify400.0ms (3.8%)

Memory

6.6MiB live, 655.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 334×	`accelerator-lowering-fma.f32`
7 334×	`accelerator-lowering-fma.f64`
4 624×	`-lowering-.f32`
4 624×	`-lowering-.f64`
4 444×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	729	4385
1	2232	4026
2	7135	4013
0	8050	3844

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
-2
(- (* 1/8 (pow x 2)) 2)
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(* -1 (+ 1 (sqrt 1/2)))
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(* -1 (+ 1 (sqrt 1/2)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(/ 1/2 (+ 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 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (+ (* 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)))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 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)) (+ (* -1/4 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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))))) (+ (* -1/32 (/ (+ (* 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 (/ (+ (* 1/8 (/ 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)))))) (+ (/ 1/4 (* (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)))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) x))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (+ (* -1 (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (+ (* 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))))) (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 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)))) (+ (* -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 (+ 1 (sqrt 1/2))))))) 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))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 3/16 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4))
(* (pow x 2) (- (* (pow x 2) (+ 3/16 (* (pow x 2) (- (* 35/256 (pow x 2)) 5/32)))) 1/4))
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1/4 (pow x 3))))
(- (+ (* 1/2 (/ 1 x)) (* 3/16 (/ 1 (pow x 5)))) (+ 1/2 (/ 1/4 (pow x 3))))
-1/2
(* -1 (+ 1/2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
(- (* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)) 1/2)
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 3/16 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 3/16 (* -5/32 (pow x 2)))) 1/4)))
(/ 1/2 x)
(/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x)
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 3/16 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/32 (/ 1 (pow x 6))))) x))
(* -1 (* (sqrt (/ 1 x)) (sqrt 1/2)))
(/ (- x (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt 1/2)))))) (* (sqrt x) (sqrt 1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))))))) (* (sqrt x) (sqrt 1/2))) 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 (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))))
(- 1 (sqrt 1/2))
(- 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (* -1 (/ (- (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))) (sqrt 1/2))
(- (+ 1 (* -1 (/ (+ (* -1 (/ (- (* 1/32 (/ 1 (pow (sqrt 1/2) 3))) (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5))))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt 1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt 1/2)))) (* (sqrt x) (sqrt 1/2))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt 1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt 1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt 1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt 1/2) 5))))))))) x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(- (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2)))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ (sqrt 1/2) (+ (/ 1/4 (* x (sqrt 1/2))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (- (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
(/ (+ 1/2 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
1/2
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(+ 1/2 (* 1/2 (/ 1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ 1 (* -1 (* (sqrt 1/2) (sqrt 2))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* 1/4 (/ (* (pow x 2) (sqrt 1/2)) (sqrt 2)))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (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)))))))
(+ 1 (+ (* -1 (* (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* 1/4 (/ (sqrt 1/2) (sqrt 2))) (* (pow x 2) (+ (* -1/2 (/ (* (sqrt 1/2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 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 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (* 1/8 (/ (sqrt 1/2) (pow x 2))))))
(+ 1 (+ (* -1 (sqrt 1/2)) (+ (* -1/2 (/ (sqrt 1/2) x)) (+ (* 1/8 (/ (sqrt 1/2) (pow x 2))) (* 3/16 (/ (sqrt 1/2) (pow x 3)))))))
(+ 1 (* -1 (sqrt 1/2)))
(+ 1 (+ (* -1 (sqrt 1/2)) (* 1/2 (/ (sqrt 1/2) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1/2 (sqrt 1/2)) (* -1/8 (/ (sqrt 1/2) x))) x))))
(+ 1 (+ (* -1 (sqrt 1/2)) (* -1 (/ (+ (* -1 (/ (+ (* -3/16 (/ (sqrt 1/2) x)) (* 1/8 (sqrt 1/2))) x)) (* -1/2 (sqrt 1/2))) x))))
(sqrt 2)
(+ (sqrt 2) (* -1/4 (/ (pow x 2) (sqrt 2))))
(+ (sqrt 2) (* (pow x 2) (- (* 1/2 (/ (* (pow x 2) (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/4 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow x 2) (- (* (pow x 2) (+ (* -1/2 (/ (* (pow x 2) (+ 5/16 (* -1/4 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 3/8 (* 1/16 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/4 (/ 1 (sqrt 2))))))
1
(+ 1 (* 1/2 (/ 1 x)))
(- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))
(+ 1 (+ (* -1 (/ (+ 1/8 (* 3/16 (/ 1 x))) (pow x 2))) (* 1/2 (/ 1 x))))
1
(- 1 (* 1/2 (/ 1 x)))
(+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
(+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* 3/16 (/ 1 x)) 1/8) x))) 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 (/ 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
(- 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
(+ 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 x)
(/ (- 1 (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 3/8 (pow x 4))) (+ (* 1/2 (/ 1 (pow x 2))) (* 5/16 (/ 1 (pow x 6))))) x)
(/ -1 x)
(* -1 (/ (- 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))
1/4
(+ 1/4 (* -3/64 (pow x 2)))
(+ 1/4 (* (pow x 2) (- (* 25/512 (pow x 2)) 3/64)))
(+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 25/512 (* -739/16384 (pow x 2)))) 3/64)))
(/ 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 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 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)))))))))
(- (+ (/ 1/64 (* (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 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 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)))) (* 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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 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 (sqrt 1/2)))
(+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 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)))) (* 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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))))) (+ 1 (sqrt 1/2))))))) x)) (+ (* 1/64 (/ 1 (* (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))))) (+ 1 (sqrt 1/2)))) (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))
1/2
(+ 1/2 (* -1/4 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))
1/4
(+ 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))
1/4
(+ 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (* 1/4 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(- (+ 1/4 (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (/ 1/4 (pow x 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)))
(/ 1/4 (pow x 2))
(/ (- 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))
(/ 1/4 (pow x 2))
(/ (- 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
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
2
(+ 2 (* -5/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 63/128 (pow x 2)) 5/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 63/128 (* -435/1024 (pow x 2)))) 5/8)))
(* 1/2 (+ 1 (sqrt 1/2)))
(+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))
(- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* 1/2 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
2
(+ 2 (* -1/8 (pow x 2)))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(+ 1 (sqrt 1/2))
(+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(- (+ 1 (+ (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 (sqrt 1/2))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))

Outputs
-2
#s(literal -2 binary64)
(- (* 1/8 (pow x 2)) 2)
(fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2)))) 2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)) #s(literal -2 binary64))
(- (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))) 2)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)) #s(literal -2 binary64))
(* -1 (+ 1 (sqrt 1/2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (+ 1 (+ (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))))
(+.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(+.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(- (+ (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))) (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(* -1 (+ 1 (sqrt 1/2)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (* 1/4 (/ 1 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(- (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2)))) (+ 1 (sqrt 1/2)))
(+.f64 (/.f64 #s(literal 1/32 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(- (* -1 (/ (- (* -1 (/ (+ (* 1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x)) (+ 1 (sqrt 1/2)))
(+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.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 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 1/8 (pow x 2))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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)))))
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(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(+.f64 x (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(.f64 x (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) #s(literal 1 binary64))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* -5/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -5/8 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 63/128 (pow x 2)) 5/8)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 63/128 binary64) #s(literal -5/8 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 63/128 (* -435/1024 (pow x 2)))) 5/8)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -435/1024 binary64) #s(literal 63/128 binary64))) #s(literal -5/8 binary64)) #s(literal 2 binary64))
(* 1/2 (+ 1 (sqrt 1/2)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (/ 1/8 (* x (sqrt 1/2)))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) (/.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(- (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (+.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x))))
(- (+ (* -1/4 (/ (+ 1 (sqrt 1/2)) (pow x 3))) (+ (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (sqrt 1/2)))) (+ (* 1/2 (+ 1 (sqrt 1/2))) (+ (* 1/2 (/ (+ 1 (sqrt 1/2)) x)) (+ (/ 1/8 (* x (sqrt 1/2))) (* 1/8 (/ 1 (* (pow x 2) (sqrt 1/2))))))))) (+ (/ 1/64 (* (pow x 3) (pow (sqrt 1/2) 3))) (* 1/64 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(+.f64 (+.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x)) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -3/64 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64) #s(literal -1/4 binary64)) (.f64 x (.f64 x x))) (-.f64 (/.f64 #s(literal -1/64 binary64) (.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))))
(* 1/2 (+ 1 (sqrt 1/2)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(+ (* -1 (/ (+ (* 1/2 (+ 1 (sqrt 1/2))) (* 1/8 (/ 1 (sqrt 1/2)))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x))
(+ (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (sqrt 1/2))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x))
(+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1/4 (+ 1 (sqrt 1/2))) (* 1/4 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/8 (/ 1 (sqrt 1/2)))) (* 1/64 (/ 1 (pow (sqrt 1/2) 3)))) x)) (+ (* 1/8 (/ 1 (sqrt 1/2))) (* 1/2 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (+ 1 (sqrt 1/2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (+.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal -3/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/32 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x)) x))
2
#s(literal 2 binary64)
(+ 2 (* -1/8 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/8 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* 11/128 (pow x 2)) 1/8)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 11/128 binary64)) #s(literal -1/8 binary64)) #s(literal 2 binary64))
(+ 2 (* (pow x 2) (- (* (pow x 2) (+ 11/128 (* -69/1024 (pow x 2)))) 1/8)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -69/1024 binary64) #s(literal 11/128 binary64)) #s(literal -1/8 binary64)) #s(literal 2 binary64))
(+ 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 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(- (+ 1 (+ (sqrt 1/2) (/ 1/4 (* x (sqrt 1/2))))) (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x))
(- (+ 1 (+ (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 #s(literal 1 binary64) (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -3/32 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(+ 1 (sqrt 1/2))
(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (+ 1 (sqrt 1/2)) (* 1/4 (/ 1 (* x (sqrt 1/2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x))))
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)))
(+ 1 (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* x (sqrt 1/2)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))))
(+.f64 #s(literal 1 binary64) (-.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 #s(literal 3/32 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) x)))

eval263.0ms (2.5%)

Memory: 30.3MiB live, 575.8MiB allocated
Compiler: Compiled 70 144 to 5 719 computations (91.8% saved)

prune282.0ms (2.7%)

Memory

-9.5MiB live, 498.3MiB allocated

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1 673	16	1 689
Fresh	12	2	14
Picked	2	3	5
Done	0	0	0
Total	1 687	21	1 708

Accuracy

100.0%

Counts

1 708 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.6%	(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))
	50.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
▶	50.5%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	53.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
	78.1%	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
▶	78.2%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
▶	76.2%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	50.8%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))))))))
	37.7%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) #s(literal -2 binary64))
	78.1%	(/.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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
▶	52.3%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓	50.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	50.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓	51.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	78.1%	(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
	48.3%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	49.7%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	48.1%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
	49.9%	(.f64 #s(literal 1/8 binary64) (.f64 x x))
▶	13.8%	#s(literal 1/4 binary64)

Compiler

Compiled 618 to 387 computations (37.4% saved)

simplify115.0ms (1.1%)

Memory

-16.9MiB live, 100.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓	cost-diff	(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓	cost-diff	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
✓	cost-diff	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓	cost-diff	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))

Rules

1 442×	`accelerator-lowering-fma.f32`
1 442×	`accelerator-lowering-fma.f64`
898×	`-lowering-.f32`
898×	`-lowering-.f64`
550×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	195
1	47	194
2	72	194
3	110	194
4	176	194
5	309	194
6	486	194
7	663	194
8	1062	194
9	2182	194
10	2641	194
11	2799	194
12	2879	194
13	2930	194
14	2971	194
15	2979	194
0	2979	180

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize121.0ms (1.2%)

Memory

-2.0MiB live, 274.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
✓	accuracy	99.9%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	87.1%	(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
✓	accuracy	99.9%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
✓	accuracy	99.0%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓	accuracy	87.1%	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

Samples

31.0ms	46×	2	valid
23.0ms	132×	0	valid
11.0ms	54×	0	invalid
8.0ms	21×	1	valid
2.0ms	3×	3	valid

Compiler

Compiled 182 to 29 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-div: 13.0ms (24.8% of total)

ival-add: 13.0ms (24.8% of total)

ival-sqrt: 10.0ms (19% of total)

adjust: 7.0ms (13.3% of total)

ival-mult: 4.0ms (7.6% of total)

ival-sub: 3.0ms (5.7% of total)

exact: 1.0ms (1.9% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

series10.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

15 → 132

Calls

Call 1

Inputs
#<alt (/ (- 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))>
#<alt (- 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))>
#<alt (/ 1/2 (sqrt (+ (* x x) 1)))>
#<alt (sqrt (+ (* x x) 1))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (+ (* (sqrt (+ 1 (/ -1 x))) (neg (sqrt 1/2))) 1)>
#<alt (sqrt (+ 1 (/ -1 x)))>
#<alt (+ 1 (/ -1 x))>
#<alt (/ -1 x)>
#<alt (/ (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (- -1 (sqrt 1/2)))>
#<alt (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2)>
#<alt (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))>
#<alt (neg (sqrt 1/2))>

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

Calls

33 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+ (* (sqrt (+ 1 (/ -1 x))) (neg (sqrt 1/2))) 1)
1.0ms	x	@	inf	(/ (- 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))
1.0ms	x	@	0	(+ (* (sqrt (+ 1 (/ -1 x))) (neg (sqrt 1/2))) 1)
1.0ms	x	@	0	(/ (+ (/ 1/2 (sqrt (+ (* x x) 1))) -1/2) (- -1 (sqrt 1/2)))
0.0ms	x	@	-inf	(/ (- 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))) (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1)))))))

rewrite399.0ms (3.8%)

Memory

20.8MiB live, 612.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 660×	`/-lowering-/.f32`
4 660×	`/-lowering-/.f64`
3 876×	`-lowering-.f32`
3 876×	`-lowering-.f64`
3 430×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	127
1	177	123
2	1518	123
0	8313	115

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 550

Calls

Call 1

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

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

simplify464.0ms (4.4%)

Memory

3.2MiB live, 731.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 930×	`accelerator-lowering-fma.f32`
10 930×	`accelerator-lowering-fma.f64`
5 978×	`-lowering-.f32`
5 978×	`-lowering-.f64`
3 930×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	456	2163
1	1387	2049
2	4269	2021
0	8144	1930

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval149.0ms (1.4%)

Memory: 24.2MiB live, 220.3MiB allocated
Compiler: Compiled 24 436 to 2 681 computations (89% saved)

prune153.0ms (1.5%)

Memory

-23.8MiB live, 296.1MiB allocated

Pruning

22 alts after pruning (15 fresh and 7 done)

	Pruned	Kept	Total
New	819	5	824
Fresh	3	10	13
Picked	1	4	5
Done	0	3	3
Total	823	22	845

Accuracy

100.0%

Counts

845 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.6%	(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))
	50.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	50.5%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	53.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
	78.1%	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
✓	78.2%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
	37.7%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64))
	78.1%	(/.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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
	50.8%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))))))))
▶	51.4%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	51.6%	(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	52.3%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓	50.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
▶	50.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓	51.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	78.2%	(.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 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #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 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
▶	48.3%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	49.7%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	48.1%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
▶	49.9%	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	13.8%	#s(literal 1/4 binary64)

Compiler

Compiled 632 to 376 computations (40.5% saved)

simplify421.0ms (4%)

Memory

0.7MiB live, 617.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64))
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
✓	cost-diff	0	(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (+.f64 (/.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 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	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 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓	cost-diff	384	(.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 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #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 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
✓	cost-diff	1408	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #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 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))

Rules

13 570×	`accelerator-lowering-fma.f32`
13 570×	`accelerator-lowering-fma.f64`
3 648×	`-lowering-.f32`
3 648×	`-lowering-.f64`
2 040×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	445
1	116	441
2	335	437
3	975	437
4	3025	437
5	7164	437
0	8185	395

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize243.0ms (2.3%)

Memory

-18.5MiB live, 474.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64))
✓	accuracy	100.0%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(/.f64 (+.f64 (/.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	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	99.9%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	99.2%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	accuracy	99.9%	(/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
✓	accuracy	99.5%	(/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	87.1%	(-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))))
✓	accuracy	74.5%	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

Samples

63.0ms	54×	0	invalid
51.0ms	45×	2	valid
39.0ms	132×	0	valid
14.0ms	22×	1	valid
3.0ms	3×	3	valid

Compiler

Compiled 405 to 49 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-div: 24.0ms (29% of total)

ival-mult: 16.0ms (19.3% of total)

ival-add: 16.0ms (19.3% of total)

adjust: 9.0ms (10.9% of total)

ival-sqrt: 9.0ms (10.9% of total)

ival-sub: 6.0ms (7.2% of total)

exact: 1.0ms (1.2% of total)

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

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

series31.0ms (0.3%)

Memory

-6.7MiB live, 29.6MiB allocated

Counts

22 → 240

Calls

Call 1

Inputs
#<alt (/ (/ 1 (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (/ 1 (- (+ 1/4 (/ 1/4 (+ (* x x) 1))) (/ 1/4 (sqrt (+ (* x x) 1))))))>
#<alt (* (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (+ 1/8 (/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1)))))) (/ (/ 1 (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (/ 1 (- (+ 1/4 (/ 1/4 (+ (* x x) 1))) (/ 1/4 (sqrt (+ (* x x) 1)))))))>
#<alt (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (+ 1/8 (/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1))))))>
#<alt (- 1/4 (/ 1/4 (+ (* x x) 1)))>
#<alt (* 1/8 (* x x))>
#<alt (* x x)>
#<alt (- 1 (sqrt (+ 1/2 (/ -1/2 x))))>
#<alt (sqrt (+ 1/2 (/ -1/2 x)))>
#<alt (+ 1/2 (/ -1/2 x))>
#<alt (/ -1/2 x)>
#<alt (/ (+ (/ 1/2 x) -1/2) (- -1 (sqrt 1/2)))>
#<alt (+ (/ 1/2 x) -1/2)>
#<alt (/ 1/2 x)>
#<alt (- -1 (sqrt 1/2))>
#<alt (* (* x x) (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) -1843/32768) 69/1024)) -11/128)) 1/8))>
#<alt (+ (* (* x x) (+ (* (* x x) (+ (* (* x x) -1843/32768) 69/1024)) -11/128)) 1/8)>
#<alt (+ (* (* x x) (+ (* (* x x) -1843/32768) 69/1024)) -11/128)>
#<alt (sqrt (+ (* x x) 1))>
#<alt (/ 1/4 (+ (* x x) 1))>
#<alt (/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1))))>
#<alt (sqrt 1/2)>
#<alt (+ (* (* x x) -1843/32768) 69/1024)>

Outputs
#<alt 1/8>
#<alt (+ 1/8 (* -7/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 71/1024 (pow x 2)) 7/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 71/1024 (* -2459/32768 (pow x 2)))) 7/128)))>
#<alt (/ 1/4 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))>
#<alt (- (+ (/ 1/8 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2))))))))))>
#<alt (/ 1/4 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/4 (* x (+ 1 (sqrt 1/2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))))) x)) (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (* -1 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (- (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (+ (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2)))))))>
#<alt (- (+ (/ 3/4 (* (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)))))) (+ (* 4 (/ (+ (* 1/16 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/8 (+ 1 (sqrt 1/2)))) (* (pow x 3) (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))))))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/2 (* x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (* 1/64 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* -1/4 (/ (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/8 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))))>
#<alt (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 3/4 (/ 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))))) (* 4 (/ (+ (* 1/16 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/8 (+ 1 (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)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/4))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 15/64 (pow x 2)) 1/8)) 1/4))))>
#<alt 2>
#<alt (- 2 (* 2 (/ 1 (pow x 2))))>
#<alt (+ 2 (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))))>
#<alt (- (+ 2 (* 2 (/ 1 (pow x 4)))) (+ (* 2 (/ 1 (pow x 2))) (/ 2 (pow x 3))))>
#<alt 2>
#<alt (- 2 (* 2 (/ 1 (pow x 2))))>
#<alt (- (+ 2 (/ 2 (pow x 3))) (* 2 (/ 1 (pow x 2))))>
#<alt (- (+ 2 (+ (* 2 (/ 1 (pow x 4))) (/ 2 (pow x 3)))) (* 2 (/ 1 (pow x 2))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))>
#<alt 1/4>
#<alt (- 1/4 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))>
#<alt 1/4>
#<alt (- 1/4 (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (* (sqrt (/ 1 x)) (sqrt -1/2)))>
#<alt (/ (- x (* (sqrt x) (sqrt -1/2))) x)>
#<alt (/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/2)))))) (* (sqrt x) (sqrt -1/2))) x)>
#<alt (/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))))))) (* (sqrt x) (sqrt -1/2))) x)>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/4 (* x (sqrt 1/2))) (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5))))))) (sqrt 1/2))>
#<alt (- 1 (sqrt 1/2))>
#<alt (- (+ 1 (* 1/4 (/ 1 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (+ (/ 1/32 (* (pow x 2) (pow (sqrt 1/2) 3))) (/ 1/4 (* x (sqrt 1/2))))) (sqrt 1/2))>
#<alt (- (+ 1 (* -1 (/ (- (* -1 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))>
#<alt (* (sqrt (/ 1 x)) (sqrt -1/2))>
#<alt (/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt -1/2)))) (* (sqrt x) (sqrt -1/2))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2))))))) x)>
#<alt (/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1/2) 5))))))))) x)>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (- (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) (pow x 2)))) (/ 1/4 (* x (sqrt 1/2))))>
#<alt (sqrt 1/2)>
#<alt (- (sqrt 1/2) (* 1/4 (/ 1 (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/4 (/ 1 (sqrt 1/2))) (* 1/32 (/ 1 (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (/ 1/128 (* (pow x 2) (pow (sqrt 1/2) 5))) (+ (/ 1/32 (* x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))) x)))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 1/2 x) 1/2) x)>
#<alt (/ (- (* 1/2 x) 1/2) x)>
#<alt (/ (- (* 1/2 x) 1/2) x)>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (- 1/2 (* 1/2 (/ 1 x)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 (* x (+ 1 (sqrt 1/2))))>
#<alt (/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)>
#<alt (/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)>
#<alt (/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (/ 1/2 (+ 1 (sqrt 1/2)))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1/2 x)) x)>
#<alt (/ (+ 1/2 (* -1/2 x)) x)>
#<alt (/ (+ 1/2 (* -1/2 x)) x)>
#<alt -1/2>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt -1/2>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (- (* 1/2 (/ 1 x)) 1/2)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))>
#<alt (* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 8))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt 1/8>
#<alt (+ 1/8 (* -11/128 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))>
#<alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 6))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt -11/128>
#<alt (- (* 69/1024 (pow x 2)) 11/128)>
#<alt (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)>
#<alt (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* -1843/32768 (pow x 4))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))>
#<alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 (pow x 2)))>
#<alt (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))>
#<alt (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4)))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1/4 (pow x 2))>
#<alt (/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 1/8>
#<alt (+ 1/8 (* -3/16 (pow x 2)))>
#<alt (+ 1/8 (* (pow x 2) (- (* 15/64 (pow x 2)) 3/16)))>
#<alt (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 15/64 (* -35/128 (pow x 2)))) 3/16)))>
#<alt (/ 1/8 (pow x 3))>
#<alt (/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3))>
#<alt (/ -1/8 (pow x 3))>
#<alt (* -1 (/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3)))>
#<alt 69/1024>
#<alt (+ 69/1024 (* -1843/32768 (pow x 2)))>
#<alt (+ 69/1024 (* -1843/32768 (pow x 2)))>
#<alt (+ 69/1024 (* -1843/32768 (pow x 2)))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* -1843/32768 (pow x 2))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>
#<alt (* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))>

Calls

60 calls:

Time	Variable		Point	Expression
15.0ms	x	@	0	(/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1))))
1.0ms	x	@	inf	(/ (/ 1 (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (/ 1 (- (+ 1/4 (/ 1/4 (+ (* x x) 1))) (/ 1/4 (sqrt (+ (* x x) 1))))))
1.0ms	x	@	inf	(* (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (+ 1/8 (/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1)))))) (/ (/ 1 (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (/ 1 (- (+ 1/4 (/ 1/4 (+ (* x x) 1))) (/ 1/4 (sqrt (+ (* x x) 1)))))))
1.0ms	x	@	0	(* (/ (- 1/4 (/ 1/4 (+ (* x x) 1))) (+ 1/8 (/ 1/8 (* (+ (* x x) 1) (sqrt (+ (* x x) 1)))))) (/ (/ 1 (+ 1 (sqrt (+ 1/2 (/ 1/2 (sqrt (+ (* x x) 1))))))) (/ 1 (- (+ 1/4 (/ 1/4 (+ (* x x) 1))) (/ 1/4 (sqrt (+ (* x x) 1)))))))
1.0ms	x	@	0	(/ (+ (/ 1/2 x) -1/2) (- -1 (sqrt 1/2)))

rewrite365.0ms (3.5%)

Memory

14.1MiB live, 676.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 144×	`/-lowering-/.f32`
4 144×	`/-lowering-/.f64`
3 302×	`-lowering-.f32`
3 302×	`-lowering-.f64`
2 386×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	277
1	357	254
2	3446	234
0	8553	212

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 705

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal -1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
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(/.f64 (-.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64))) (-.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x #s(literal -1843/32768 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -6260024107/35184372088832 binary64) #s(literal 328509/1073741824 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) (-.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 x x) #s(literal -127167/33554432 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) #s(literal -4761/1048576 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal -1843/32768 binary64)) #s(literal -69/1024 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64)))) (neg.f64 (-.f64 #s(literal 69/1024 binary64) (.f64 x (.f64 x #s(literal -1843/32768 binary64))))))
(pow.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) (-.f64 #s(literal 4761/1048576 binary64) (.f64 (.f64 x x) #s(literal -127167/33554432 binary64)))) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -6260024107/35184372088832 binary64) #s(literal 328509/1073741824 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1843/32768 binary64)) #s(literal -69/1024 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) #s(literal -4761/1048576 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -6260024107/35184372088832 binary64) #s(literal 328509/1073741824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) (-.f64 #s(literal 4761/1048576 binary64) (.f64 (*.f64 x x) #s(literal -127167/33554432 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 3396649/1073741824 binary64) #s(literal -4761/1048576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1843/32768 binary64)) #s(literal -69/1024 binary64))))

simplify443.0ms (4.2%)

Memory

33.4MiB live, 705.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 592×	`accelerator-lowering-fma.f32`
7 592×	`accelerator-lowering-fma.f64`
4 890×	`-lowering-.f32`
4 890×	`-lowering-.f64`
4 668×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	483	3572
1	1452	3409
2	4699	3385
0	8366	3248

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
1/8
(+ 1/8 (* -7/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 71/1024 (pow x 2)) 7/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 71/1024 (* -2459/32768 (pow x 2)))) 7/128)))
(/ 1/4 (+ 1 (sqrt 1/2)))
(+ (* -1 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(- (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))
(- (+ (/ 1/8 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2))))))))))
(/ 1/4 (+ 1 (sqrt 1/2)))
(+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/4 (* x (+ 1 (sqrt 1/2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))))) x)) (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(/ 1/2 (+ 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)))))))
(- (+ (/ 3/4 (* (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)))))) (+ (* 4 (/ (+ (* 1/16 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/8 (+ 1 (sqrt 1/2)))) (* (pow x 3) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/8 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/2 (* x (+ 1 (sqrt 1/2))))))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(+ (/ 1/8 (* 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 (/ (- (* 3/4 (/ 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))))) (* 4 (/ (+ (* 1/16 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (sqrt 1/2))) (* 1/8 (+ 1 (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)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* 15/64 (pow x 2)) 1/8)) 1/4))))
2
(- 2 (* 2 (/ 1 (pow x 2))))
(+ 2 (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))))
(- (+ 2 (* 2 (/ 1 (pow x 4)))) (+ (* 2 (/ 1 (pow x 2))) (/ 2 (pow x 3))))
2
(- 2 (* 2 (/ 1 (pow x 2))))
(- (+ 2 (/ 2 (pow x 3))) (* 2 (/ 1 (pow x 2))))
(- (+ 2 (+ (* 2 (/ 1 (pow x 4))) (/ 2 (pow x 3)))) (* 2 (/ 1 (pow x 2))))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* (pow x 2) (+ 1/4 (* -1/4 (pow x 2)))) 1/4))))
1/4
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
1/4
(- 1/4 (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))
(- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6)))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* (sqrt (/ 1 x)) (sqrt -1/2)))
(/ (- x (* (sqrt x) (sqrt -1/2))) x)
(/ (- (* x (+ 1 (* -1/4 (* (sqrt x) (/ 1 (sqrt -1/2)))))) (* (sqrt x) (sqrt -1/2))) x)
(/ (- (* x (+ 1 (* x (- (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))))))) (* (sqrt x) (sqrt -1/2))) x)
(- 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 (+ (/ 1/4 (* x (sqrt 1/2))) (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) (* 1/128 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5))))))) (sqrt 1/2))
(- 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 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/4 (/ 1 (sqrt 1/2)))) x))) (sqrt 1/2))
(* (sqrt (/ 1 x)) (sqrt -1/2))
(/ (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (sqrt -1/2)))) (* (sqrt x) (sqrt -1/2))) x)
(/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2))))))) x)
(/ (+ (* (sqrt x) (sqrt -1/2)) (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1/2)))) (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1/2) 3)))) (* 1/128 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1/2) 5))))))))) 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 (/ (+ (* 1/128 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/32 (/ 1 (pow (sqrt 1/2) 3)))) (pow x 2)))) (/ 1/4 (* x (sqrt 1/2))))
(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 (/ (+ (/ 1/128 (* (pow x 2) (pow (sqrt 1/2) 5))) (+ (/ 1/32 (* x (pow (sqrt 1/2) 3))) (* 1/4 (/ 1 (sqrt 1/2))))) x)))
(/ -1/2 x)
(/ (- (* 1/2 x) 1/2) x)
(/ (- (* 1/2 x) 1/2) x)
(/ (- (* 1/2 x) 1/2) x)
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
1/2
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
(- 1/2 (* 1/2 (/ 1 x)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 (* x (+ 1 (sqrt 1/2))))
(/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)
(/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)
(/ (- (* 1/2 (/ x (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (+ 1 (sqrt 1/2))))) x)
(/ 1/2 (+ 1 (sqrt 1/2)))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(/ 1/2 (+ 1 (sqrt 1/2)))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(- (* 1/2 (/ 1 (+ 1 (sqrt 1/2)))) (* 1/2 (/ 1 (* x (+ 1 (sqrt 1/2))))))
(/ 1/2 x)
(/ (+ 1/2 (* -1/2 x)) x)
(/ (+ 1/2 (* -1/2 x)) x)
(/ (+ 1/2 (* -1/2 x)) x)
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) 1/2)
-1/2
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) 1/2)
(- (* 1/2 (/ 1 x)) 1/2)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -11/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 8))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 8) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 8) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
1/8
(+ 1/8 (* -11/128 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 6))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 6) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 6) (- (+ (* 69/1024 (/ 1 (pow x 2))) (* 1/8 (/ 1 (pow x 6)))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
-11/128
(- (* 69/1024 (pow x 2)) 11/128)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128)
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* -1843/32768 (pow x 4))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
1/4
(+ 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)))
(/ 1/4 (pow x 2))
(/ (- 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))
(/ 1/4 (pow x 2))
(/ (- 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))
1/8
(+ 1/8 (* -3/16 (pow x 2)))
(+ 1/8 (* (pow x 2) (- (* 15/64 (pow x 2)) 3/16)))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 15/64 (* -35/128 (pow x 2)))) 3/16)))
(/ 1/8 (pow x 3))
(/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3))
(/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3))
(/ -1/8 (pow x 3))
(* -1 (/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3)))
69/1024
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* -1843/32768 (pow x 2))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))

Outputs
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -7/128 (pow x 2)))
(fma.f64 #s(literal -7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* 71/1024 (pow x 2)) 7/128)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 71/1024 binary64)) #s(literal -7/128 binary64)) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 71/1024 (* -2459/32768 (pow x 2)))) 7/128)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -2459/32768 binary64) #s(literal 71/1024 binary64)) #s(literal -7/128 binary64))) #s(literal 1/8 binary64))
(/ 1/4 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* -1 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(- (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2)))))))
(+.f64 (/.f64 #s(literal 1/128 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (+.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))) (/.f64 #s(literal -1/4 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x))))
(- (+ (/ 1/8 (* (pow x 3) (+ 1 (sqrt 1/2)))) (+ (* 1/128 (/ 1 (* (pow x 2) (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ 1 (* (pow x 2) (+ 1 (sqrt 1/2))))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))) (+ (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 2) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow x 3) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2)))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (pow x 3) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2))))) (+ (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (pow x 3) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (/ 1/4 (* x (+ 1 (sqrt 1/2))))))))))
(-.f64 (+.f64 (/.f64 #s(literal 1/128 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)))))) (+.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 (.f64 x x) (.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))) (/.f64 #s(literal -3/128 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (.f64 x x)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/128 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))))
(/ 1/4 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (/ 1/16 (* x (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (+ (/ 1/4 (* x (+ 1 (sqrt 1/2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) x))))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/128 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ 1 (+ 1 (sqrt 1/2)))) (+ (* 1/32 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (pow (sqrt 1/2) 3) (+ 1 (sqrt 1/2))))) (+ (* 1/8 (/ (- (* 1/64 (/ 1 (pow (sqrt 1/2) 4))) 1/4) (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ (- (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))))) x)) (+ (* 1/128 (/ 1 (* (pow (sqrt 1/2) 3) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2))))) (* (sqrt 1/2) (+ 1 (sqrt 1/2)))))) x)) (+ (* 1/16 (/ 1 (* (sqrt 1/2) (pow (+ 1 (sqrt 1/2)) 2)))) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))) x)) (* 1/4 (/ 1 (+ 1 (sqrt 1/2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 (-.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/128 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/128 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 #s(literal 1/32 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal -3/128 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))) x)) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
(* 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 x x) (fma.f64 x (*.f64 x #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* 69/1024 (pow x 2)) 11/128))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64))) #s(literal 1/8 binary64))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 69/1024 (* -1843/32768 (pow x 2)))) 11/128))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
(/ 1/2 (+ 1 (sqrt 1/2)))
(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))) x))
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(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1843/32768 binary64))))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(.f64 (+.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (/.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- (* 69/1024 (/ 1 (pow x 2))) (+ 1843/32768 (/ 11/128 (pow x 4)))))
(.f64 (+.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (.f64 x x))) (/.f64 #s(literal -11/128 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x)
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) x)
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) x))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))))) x))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1/4 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/4 binary64))
(+ 1/4 (* (pow x 2) (- (* 1/4 (pow x 2)) 1/4)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #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 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/4 binary64))) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))) (*.f64 x x))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (- 1/4 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (* 1/4 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 1/4 (/ 1/4 (pow x 4))) (+ (* 1/4 (/ 1 (pow x 2))) (* 1/4 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* -3/16 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -3/16 binary64)) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* 15/64 (pow x 2)) 3/16)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 15/64 binary64)) #s(literal -3/16 binary64)) #s(literal 1/8 binary64))
(+ 1/8 (* (pow x 2) (- (* (pow x 2) (+ 15/64 (* -35/128 (pow x 2)))) 3/16)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -35/128 binary64)) #s(literal 15/64 binary64))) #s(literal -3/16 binary64)) #s(literal 1/8 binary64))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))
(/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x x))) (.f64 x (*.f64 x x)))
(/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3))
(/.f64 (+.f64 (/.f64 #s(literal 15/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x x)))) (.f64 x (.f64 x x)))
(/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3))
(/.f64 (+.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 15/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (/.f64 #s(literal -3/16 binary64) (.f64 x x)) (/.f64 #s(literal -35/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (.f64 x x)))
(/ -1/8 (pow x 3))
(/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (- 1/8 (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x x))) (.f64 x (*.f64 x (neg.f64 x))))
(* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (* 3/16 (/ 1 (pow x 2)))) (pow x 3)))
(/.f64 (+.f64 (/.f64 #s(literal 15/64 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -3/16 binary64) (.f64 x x)))) (.f64 x (.f64 x (neg.f64 x))))
(* -1 (/ (- (+ 1/8 (/ 15/64 (pow x 4))) (+ (* 3/16 (/ 1 (pow x 2))) (* 35/128 (/ 1 (pow x 6))))) (pow x 3)))
(/.f64 (+.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 15/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (/.f64 #s(literal -3/16 binary64) (.f64 x x)) (/.f64 #s(literal -35/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 x (.f64 x (neg.f64 x))))
69/1024
#s(literal 69/1024 binary64)
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64))
(+ 69/1024 (* -1843/32768 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1843/32768 binary64)) #s(literal 69/1024 binary64))
(* -1843/32768 (pow x 2))
(.f64 x (.f64 x #s(literal -1843/32768 binary64)))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)
(* -1843/32768 (pow x 2))
(.f64 x (.f64 x #s(literal -1843/32768 binary64)))
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (- (* 69/1024 (/ 1 (pow x 2))) 1843/32768))
(.f64 (.f64 (+.f64 #s(literal -1843/32768 binary64) (/.f64 #s(literal 69/1024 binary64) (*.f64 x x))) x) x)

eval201.0ms (1.9%)

Memory: -50.5MiB live, 416.1MiB allocated
Compiler: Compiled 49 211 to 3 857 computations (92.2% saved)

prune147.0ms (1.4%)

Memory

22.9MiB live, 292.2MiB allocated

Pruning

22 alts after pruning (11 fresh and 11 done)

	Pruned	Kept	Total
New	1 167	1	1 168
Fresh	0	10	10
Picked	1	4	5
Done	0	7	7
Total	1 168	22	1 190

Accuracy

100.0%

Counts

1 190 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.6%	(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))
	50.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	50.5%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
✓	53.1%	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
	78.1%	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
✓	78.2%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
	37.7%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64))
	78.1%	(/.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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
	50.8%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))))))))
✓	51.4%	(/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	51.6%	(/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	52.3%	(/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	77.4%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))))
✓	50.1%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
✓	50.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
✓	51.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	78.1%	(*.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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))
✓	48.3%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	49.7%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64)))
	48.1%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
✓	49.9%	(.f64 #s(literal 1/8 binary64) (.f64 x x))
✓	13.8%	#s(literal 1/4 binary64)

Compiler

Compiled 1 399 to 392 computations (72% saved)

regimes75.0ms (0.7%)

Memory

19.9MiB live, 178.2MiB allocated

Counts

42 → 2

Calls

Call 1

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

Outputs

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

Calls

7 calls:

12.0ms	(hypot.f64 #s(literal 1 binary64) x)
11.0ms	x
11.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
10.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
10.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	3	`x`
100.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
100.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
100.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
100.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
100.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes61.0ms (0.6%)

Memory

-27.0MiB live, 188.4MiB allocated

Counts

37 → 2

Calls

Call 1

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

Outputs

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

Calls

6 calls:

13.0ms	(hypot.f64 #s(literal 1 binary64) x)
10.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
10.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
9.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
9.0ms	(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
100.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
100.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
100.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
100.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
100.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes53.0ms (0.5%)

Memory

11.4MiB live, 123.8MiB allocated

Counts

33 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

10.0ms	(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	(hypot.f64 #s(literal 1 binary64) x)
9.0ms	(/.f64 #s(literal 1 binary64) (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
100.0%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
100.0%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
100.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
100.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
100.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
100.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes79.0ms (0.8%)

Memory

14.4MiB live, 90.1MiB allocated

Counts

26 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

41.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
12.0ms	(hypot.f64 #s(literal 1 binary64) x)
7.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
6.0ms	(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))
6.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

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

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes88.0ms (0.8%)

Memory

-22.8MiB live, 86.8MiB allocated

Counts

24 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

31.0ms	(hypot.f64 #s(literal 1 binary64) x)
23.0ms	(-.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))))))
14.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
7.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
6.0ms	(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))

Results

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

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes61.0ms (0.6%)

Memory

15.0MiB live, 88.9MiB allocated

Counts

19 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

19.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
16.0ms	x
5.0ms	(/.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 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Results

Accuracy	Segments	Branch
98.3%	3	`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	`(sqrt.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 1/2 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) (/.f64 #s(literal 1 binary64) (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	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes78.0ms (0.7%)

Memory

-15.7MiB live, 71.2MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

29.0ms	(-.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))))))
29.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
5.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
5.0ms	(hypot.f64 #s(literal 1 binary64) x)
4.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Results

Accuracy	Segments	Branch
98.2%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
98.2%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
98.2%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.2%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.2%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.2%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes31.0ms (0.3%)

Memory

35.4MiB live, 68.9MiB allocated

Counts

12 → 2

Calls

Call 1

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

Outputs

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

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

Calls

6 calls:

13.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))
4.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
4.0ms	(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	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))

Results

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

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes44.0ms (0.4%)

Memory

-28.8MiB live, 49.2MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

6 calls:

17.0ms	(hypot.f64 #s(literal 1 binary64) x)
14.0ms	(-.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	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
3.0ms	(*.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
98.0%	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))))))`
98.0%	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)))))`
98.0%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
98.0%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
98.0%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
98.0%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes15.0ms (0.1%)

Memory

36.9MiB live, 36.9MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1/4 binary64)
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64))))

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

Calls

6 calls:

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	(-.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	(*.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
97.2%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
97.2%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
97.2%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.2%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.2%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.2%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes35.0ms (0.3%)

Memory

-9.8MiB live, 32.0MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 1/4 binary64)
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1 binary64)))

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

Calls

6 calls:

25.0ms	(hypot.f64 #s(literal 1 binary64) x)
2.0ms	(/.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)))))
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	(*.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
97.1%	2	`(-.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))))`
97.1%	2	`(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))))`
97.1%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
97.1%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
97.1%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
97.1%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 52 to 36 computations (30.8% saved)

regimes32.0ms (0.3%)

Memory

-9.9MiB live, 29.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 1/4 binary64)
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(fma.f64 (*.f64 x x) #s(literal -3/64 binary64) #s(literal 1/4 binary64))

Outputs
(.f64 #s(literal 1/8 binary64) (.f64 x x))
#s(literal 1/4 binary64)

Calls

7 calls:

22.0ms	(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))
2.0ms	x
2.0ms	(hypot.f64 #s(literal 1 binary64) x)
1.0ms	(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))
1.0ms	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
59.3%	3	`x`
59.3%	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))))))`
59.3%	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)))))`
59.3%	2	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
59.3%	2	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
59.3%	2	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
59.3%	2	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

regimes21.0ms (0.2%)

Memory

-17.9MiB live, 21.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/4 binary64)

Outputs
#s(literal 1/4 binary64)

Calls

7 calls:

14.0ms	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
13.8%	1	`x`
13.8%	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)))))`
13.8%	1	`(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))))`
13.8%	1	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x)))`
13.8%	1	`(/.f64 #s(literal 1 binary64) (hypot.f64 #s(literal 1 binary64) x))`
13.8%	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))))))`
13.8%	1	`(hypot.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 54 to 37 computations (31.5% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000033378569566	1.022995515014577

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000033378569566	1.022995515014577

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000033378569566	1.022995515014577

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000033378569566	1.022995515014577

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.000033378569566	1.022995515014577

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2133951002469252	1.7236668476907901

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2133951002469252	1.7236668476907901

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2133951002469252	1.7236668476907901

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2133951002469252	1.7236668476907901

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2133951002469252	1.7236668476907901

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.7236668476907901	22.776054979935388

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.7236668476907901	22.776054979935388

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify14.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated

Algorithm

1×	egg-herbie

Rules

46×	`+-commutative_binary64`
32×	`*-commutative_binary64`
30×	`sub-neg_binary64`
18×	`neg-sub0_binary64`
18×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	441
1	117	441
2	143	441
3	160	441
4	172	441
5	176	441

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 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 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #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 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)

Outputs
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 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 1/8 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #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 1/4 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 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 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2296835809958953/2251799813685248 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1843/32768 binary64) #s(literal 69/1024 binary64)) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 69/1024 binary64) #s(literal -11/128 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -11/128 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/4 binary64))
(if (<=.f64 (hypot.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/8 binary64)) #s(literal 1/4 binary64))
#s(literal 1/4 binary64)

soundness1.3s (12.1%)

Memory

-45.3MiB live, 1 217.6MiB allocated

Rules

12 216×	`accelerator-lowering-fma.f32`
12 216×	`accelerator-lowering-fma.f64`
10 930×	`accelerator-lowering-fma.f32`
10 930×	`accelerator-lowering-fma.f64`
7 334×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	232	991
1	674	917
2	1886	877
3	5894	834
0	8222	781
0	456	2163
1	1387	2049
2	4269	2021
0	8144	1930
0	26	127
1	177	123
2	1518	123
0	8313	115
0	729	4385
1	2232	4026
2	7135	4013
0	8050	3844
0	47	277
1	357	254
2	3446	234
0	8553	212
0	12	64
1	72	56
2	556	56
3	5199	56
0	8816	50
0	34	234
1	237	226
2	2149	226
0	8533	206

Stop Event

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

Compiler

Compiled 766 to 284 computations (62.9% saved)

preprocess69.0ms (0.7%)

Memory: 15.0MiB live, 171.7MiB allocated
Compiler: Compiled 910 to 180 computations (80.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	17	39
1	42	32
2	70	32
3	94	32
4	130	32
5	152	32
6	164	32
7	170	32
8	171	32
0	12	15
1	25	13
2	32	13
3	37	13
4	43	13
5	51	13
6	61	13
7	72	13
8	75	13
0	75	12

Iter	Nodes	Cost
0	17	39
1	42	32
2	70	32
3	94	32
4	130	32
5	152	32
6	164	32
7	170	32
8	171	32
0	12	15
1	25	13
2	32	13
3	37	13
4	43	13
5	51	13
6	61	13
7	72	13
8	75	13
0	75	12

analyze0.0ms (0%)

sample1.7s (16.1%)

preprocess18.0ms (0.2%)

explain173.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize64.0ms (0.6%)

series6.0ms (0.1%)

rewrite484.0ms (4.6%)

simplify380.0ms (3.6%)

eval98.0ms (0.9%)

prune84.0ms (0.8%)

simplify294.0ms (2.8%)

localize455.0ms (4.3%)

series22.0ms (0.2%)

rewrite470.0ms (4.5%)

simplify400.0ms (3.8%)

eval263.0ms (2.5%)

prune282.0ms (2.7%)

simplify115.0ms (1.1%)

localize121.0ms (1.2%)

series10.0ms (0.1%)

rewrite399.0ms (3.8%)

simplify464.0ms (4.4%)

eval149.0ms (1.4%)

prune153.0ms (1.5%)

simplify421.0ms (4%)

localize243.0ms (2.3%)

series31.0ms (0.3%)

rewrite365.0ms (3.5%)

simplify443.0ms (4.2%)

eval201.0ms (1.9%)

prune147.0ms (1.4%)

regimes75.0ms (0.7%)

regimes61.0ms (0.6%)

regimes53.0ms (0.5%)

regimes79.0ms (0.8%)

regimes88.0ms (0.8%)

regimes61.0ms (0.6%)

regimes78.0ms (0.7%)

regimes31.0ms (0.3%)

regimes44.0ms (0.4%)

regimes15.0ms (0.1%)

regimes35.0ms (0.3%)

regimes32.0ms (0.3%)

regimes21.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify14.0ms (0.1%)

soundness1.3s (12.1%)

preprocess69.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	17	39
1	42	32
2	70	32
3	94	32
4	130	32
5	152	32
6	164	32
7	170	32
8	171	32
0	12	15
1	25	13
2	32	13
3	37	13
4	43	13
5	51	13
6	61	13
7	72	13
8	75	13
0	75	12