Metrics for 2isqrt (example 3.6)

analyze2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
0%	0%	25%	75%	0%	0%	0%	1
50%	12.5%	12.5%	75%	0%	0%	0%	2
75%	18.7%	6.2%	75%	0%	0%	0%	3
87.5%	21.9%	3.1%	75%	0%	0%	0%	4
93.8%	23.4%	1.6%	75%	0%	0%	0%	5
96.9%	24.2%	0.8%	75%	0%	0%	0%	6
98.4%	24.6%	0.4%	75%	0%	0%	0%	7
99.2%	24.8%	0.2%	75%	0%	0%	0%	8
99.6%	24.9%	0.1%	75%	0%	0%	0%	9
99.8%	24.9%	0%	75%	0%	0%	0%	10
99.9%	25%	0%	75%	0%	0%	0%	11
100%	25%	0%	75%	0%	0%	0%	12

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.1s (19.2%)

Memory

43.7MiB live, 2 539.3MiB allocated

Samples

1.3s	6 895×	1	valid
307.0ms	1 073×	2	valid
35.0ms	288×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-sqrt: 365.0ms (27.5% of total)

ival-div: 356.0ms (26.8% of total)

const: 152.0ms (11.4% of total)

ival-add: 119.0ms (9% of total)

ival-sub: 103.0ms (7.8% of total)

adjust: 93.0ms (7% of total)

ival->: 78.0ms (5.9% of total)

ival-and: 21.0ms (1.6% of total)

ival-<: 19.0ms (1.4% of total)

exact: 14.0ms (1.1% of total)

ival-assert: 7.0ms (0.5% of total)

Bogosity

preprocess31.0ms (0.3%)

Memory

23.5MiB live, 62.5MiB allocated

Algorithm

2×	egg-herbie

Rules

112×	`accelerator-lowering-fma.f32`
112×	`accelerator-lowering-fma.f64`
86×	`sub-neg`
80×	`-lowering-.f32`
80×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	38
1	29	36
2	62	35
3	111	35
4	175	35
5	260	35
6	334	35
7	386	35
8	448	35
9	477	35
10	497	35
11	499	35
0	8	11
1	13	11
2	21	11
3	30	11
4	42	11
5	62	11
6	101	11
7	132	11
8	188	11
9	217	11
10	238	11
11	240	11
0	240	11

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(+ (/ 1 (sqrt x)) (/ -1 (sqrt (+ 1 x))))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(+ (/ 1 (sqrt (neg x))) (/ -1 (sqrt (- 1 x))))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))
(+ (/ 1 (sqrt (- 1 x))) (/ -1 (sqrt (neg x))))

explain149.0ms (1.4%)

Memory

-36.5MiB live, 326.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
174	1	(1.0321030055011391e+215)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`	cancellation	175	0

Confusion

	Predicted +	Predicted -
+	174	0
-	1	81

Precision

0.9942857142857143

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	174	0	0
-	1	0	81

Precision?

0.9942857142857143

Recall?

1.0

Freqs

test

number	freq
0	81
1	175

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

66.0ms	440×	1	valid
12.0ms	66×	2	valid
0.0ms	6×	0	valid

Compiler

Compiled 92 to 36 computations (60.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-sqrt: 20.0ms (36.5% of total)

ival-div: 16.0ms (29.2% of total)

ival-add: 7.0ms (12.8% of total)

adjust: 6.0ms (10.9% of total)

ival-sub: 5.0ms (9.1% of total)

exact: 1.0ms (1.8% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

112×	`accelerator-lowering-fma.f32`
112×	`accelerator-lowering-fma.f64`
80×	`-lowering-.f32`
80×	`-lowering-.f64`
52×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	13	32
2	21	32
3	30	32
4	42	32
5	62	32
6	101	32
7	132	32
8	188	32
9	217	32
10	238	32
11	240	32
0	240	32

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize49.0ms (0.5%)

Memory

5.8MiB live, 122.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	39.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

31.0ms	220×	1	valid
6.0ms	33×	2	valid
0.0ms	3×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-sqrt: 10.0ms (37.6% of total)

ival-div: 8.0ms (30.1% of total)

adjust: 3.0ms (11.3% of total)

ival-add: 3.0ms (11.3% of total)

ival-sub: 2.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 x)) x)>
#<alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)>
#<alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))>
#<alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>

Calls

12 calls:

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

rewrite359.0ms (3.3%)

Memory

12.2MiB live, 522.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 400×	`accelerator-lowering-fma.f32`
4 400×	`accelerator-lowering-fma.f64`
3 040×	`-lowering-.f32`
3 040×	`-lowering-.f64`
2 738×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	60	19
2	558	19
3	6710	19
0	8104	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 238

Calls

Call 1

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

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

simplify573.0ms (5.3%)

Memory

26.7MiB live, 1 079.0MiB allocated

Algorithm

1×	egg-herbie

Rules

23 172×	`accelerator-lowering-fma.f32`
23 172×	`accelerator-lowering-fma.f64`
4 828×	`-lowering-.f32`
4 828×	`-lowering-.f64`
3 424×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))

Outputs
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(+.f64 (/.f64 (sqrt.f64 x) x) #s(literal -1 binary64))
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -3/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (sqrt.f64 x)) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (.f64 x (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (.f64 x (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

eval88.0ms (0.8%)

Memory: -44.5MiB live, 71.7MiB allocated
Compiler: Compiled 7 388 to 704 computations (90.5% saved)

prune44.0ms (0.4%)

Memory

-4.6MiB live, 114.6MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	273	13	286
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	13	287

Accuracy

83.6%

Counts

287 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.1%	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
	40.8%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	40.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	39.0%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	40.8%	(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	83.1%	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
	40.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
	26.9%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	28.6%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	40.8%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	39.0%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
	82.6%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
▶	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 426 to 256 computations (39.9% saved)

simplify361.0ms (3.3%)

Memory

17.8MiB live, 537.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
✓	cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	640	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(fma.f64 x x x)
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))

Rules

11 378×	`accelerator-lowering-fma.f32`
11 378×	`accelerator-lowering-fma.f64`
3 176×	`-lowering-.f32`
3 176×	`-lowering-.f64`
2 408×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	283
1	87	271
2	203	271
3	466	271
4	1165	271
5	2672	271
6	5011	271
7	7568	271
0	8243	253

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
(fma.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 0 binary64))
(* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 0 binary64))
1/2
#s(literal 1/2 binary64)
(- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))
(-.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(sqrt (/ 1 (* x (* x x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/ 1 (* x (* x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
1
#s(literal 1 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(+ (* x 1/4) 1)
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))
1/4
#s(literal 1/4 binary64)
(sqrt x)
(sqrt.f64 x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(- (sqrt (/ 1 x)) (/ 1 (sqrt (+ x 1))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ 1 (sqrt (+ x 1)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt (+ x 1))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)
(* (/ 1 (sqrt (+ (* x x) x))) (- (sqrt (+ 1 x)) (sqrt x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/ 1 (sqrt (+ (* x x) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))
1
#s(literal 1 binary64)
(sqrt (+ (* x x) x))
(sqrt.f64 (fma.f64 x x x))
(+ (* x x) x)
(fma.f64 x x x)
x
(- (sqrt (+ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(* (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/ 1 (sqrt (+ 1 x))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))) #s(literal 0 binary64)))
(/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))
(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
(- (+ 1 x) x)
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(+ x (sqrt (+ (* x x) x)))
(+.f64 x (sqrt.f64 (fma.f64 x x x)))
(sqrt (+ (* x x) x))
(sqrt.f64 (fma.f64 x x x))
(+ (* x x) x)
(fma.f64 x x x)
(/ 1 (sqrt (+ 1 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))

localize362.0ms (3.4%)

Memory

7.7MiB live, 240.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	52.0%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	6.5%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))
✓	accuracy	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	accuracy	52.0%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	5.4%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	39.0%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	83.5%	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
✓	accuracy	67.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

264.0ms	211×	1	valid
30.0ms	30×	2	valid
8.0ms	12×	3	valid
1.0ms	3×	0	valid

Compiler

Compiled 285 to 36 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 257.0ms

ival-div: 127.0ms (49.5% of total)

ival-add: 55.0ms (21.4% of total)

ival-mult: 34.0ms (13.3% of total)

ival-sqrt: 19.0ms (7.4% of total)

adjust: 11.0ms (4.3% of total)

ival-sub: 9.0ms (3.5% of total)

exact: 1.0ms (0.4% of total)

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

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

series33.0ms (0.3%)

Memory

-8.0MiB live, 33.7MiB allocated

Counts

20 → 240

Calls

Call 1

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

Outputs
#<alt (* 1/2 (sqrt (/ 1 (pow x 7))))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))) x)>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt x) (* x (- (* 1/4 (sqrt x)) (sqrt x)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))>
#<alt (sqrt x)>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<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 (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 x)) x)>
#<alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)>
#<alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/2 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (* (sqrt x) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* (sqrt (/ 1 x)) (- 1 (sqrt x)))>
#<alt (/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)>
#<alt (/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)>
#<alt (/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) x)>
#<alt (/ (+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1/2 (* (sqrt x) (+ 1 (* 1/4 (/ 1 x))))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 2))) (* 1/2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 3/8 (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3))))) x)>
#<alt (/ -1 x)>
#<alt (* -1 (/ (- 1 (* 1/2 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- 1/2 (* 3/8 (/ 1 x))) x))) x))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x))) x))) x))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (sqrt (/ 1 x))>
#<alt (- (sqrt (/ 1 x)) 1)>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)>
#<alt -2>
#<alt (* -1 (+ 2 (* 1/2 (/ 1 x))))>
#<alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)>
#<alt (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 3/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>

Calls

60 calls:

Time	Variable		Point	Expression
15.0ms	x	@	inf	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
2.0ms	x	@	inf	(* (/ 1 (sqrt (+ (* x x) x))) (- (sqrt (+ 1 x)) (sqrt x)))
1.0ms	x	@	-inf	(- (sqrt (+ 1 x)) (sqrt x))
1.0ms	x	@	0	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
1.0ms	x	@	-inf	(* (/ 1 (sqrt (+ (* x x) x))) (- (sqrt (+ 1 x)) (sqrt x)))

rewrite563.0ms (5.2%)

Memory

-20.8MiB live, 489.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 370×	`-lowering-.f32`
4 370×	`-lowering-.f64`
4 206×	`/-lowering-/.f32`
4 206×	`/-lowering-/.f64`
2 398×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	189
1	251	153
2	2328	152
0	8558	136

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 935

Calls

Call 1

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

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

simplify596.0ms (5.5%)

Memory

28.9MiB live, 858.2MiB allocated

Algorithm

1×	egg-herbie

Rules

15 214×	`accelerator-lowering-fma.f32`
15 214×	`accelerator-lowering-fma.f64`
4 678×	`-lowering-.f32`
4 678×	`-lowering-.f64`
4 540×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	555	3441
1	1687	3000
2	5394	2959
0	8597	2776

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 (pow x 7))))
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt x) (* x (- (* 1/4 (sqrt x)) (sqrt x)))) (pow x 2))
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))
(sqrt x)
(* x (- (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))) (sqrt (/ 1 (pow x 3)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
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(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
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(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/2 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (* (sqrt x) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) x)) (* -1/2 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
1
(+ 1 (* -1/2 x))
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(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 5/32 (sqrt x))) x)) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/16 (sqrt x)))) x)) (* 1/4 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1/2 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) x)
(/ (+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1/2 (* (sqrt x) (+ 1 (* 1/4 (/ 1 x))))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 x))) x)
(/ (- (+ 1 (/ 3/8 (pow x 2))) (* 1/2 (/ 1 x))) x)
(/ (- (+ 1 (/ 3/8 (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3))))) x)
(/ -1 x)
(* -1 (/ (- 1 (* 1/2 (/ 1 x))) x))
(* -1 (/ (+ 1 (* -1 (/ (- 1/2 (* 3/8 (/ 1 x))) x))) x))
(* -1 (/ (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x))) x))) x))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
1
1
1
1
1
1
1
1
1
1
1
1
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* -1/2 x))
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(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))

Outputs
(* 1/2 (sqrt (/ 1 (pow x 7))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (.f64 x x) (*.f64 x x)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (.f64 x x) (*.f64 x x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x))) x)
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)) x))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (- (* 1/4 (sqrt (/ 1 x))) (sqrt (/ 1 x))) x)))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(* -1 (/ (+ (* -1/2 (/ (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (- (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) x)) (-.f64 #s(literal 0 binary64) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/ (+ (sqrt x) (* x (- (* 1/4 (sqrt x)) (sqrt x)))) (pow x 2))
(/.f64 (fma.f64 x (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (.f64 x x))
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))
(/.f64 (fma.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 x x))
(/ (+ (sqrt x) (* x (- (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))) (sqrt x)))) (pow x 2))
(/.f64 (fma.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 x x))
(sqrt x)
(sqrt.f64 x)
(* x (- (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3))))) (sqrt (/ 1 (pow x 3)))))
(.f64 x (-.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal -5/128 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/4 binary64) (/.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 x))) (.f64 x (*.f64 x x))))

eval215.0ms (2%)

Memory: 9.2MiB live, 484.1MiB allocated
Compiler: Compiled 46 290 to 4 971 computations (89.3% saved)

prune258.0ms (2.4%)

Memory

16.4MiB live, 612.1MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 634	17	1 651
Fresh	7	1	8
Picked	4	1	5
Done	0	0	0
Total	1 645	19	1 664

Accuracy

100.0%

Counts

1 664 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))) x)
	83.4%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	83.4%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
	99.2%	(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x)
	82.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
▶	83.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
	97.9%	(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/2 binary64) x))))
	83.5%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
	83.5%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	5.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	40.5%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	99.2%	(.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 #s(literal 1/2 binary64) x))
▶	38.7%	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
	83.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
	82.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	98.7%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	82.6%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	66.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 587 to 380 computations (35.3% saved)

simplify282.0ms (2.6%)

Memory

-7.5MiB live, 562.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
✓	cost-diff	1024	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))
✓	cost-diff	0	(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
✓	cost-diff	0	(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x)
✓	cost-diff	448	(.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 #s(literal 1/2 binary64) x))

Rules

7 054×	`accelerator-lowering-fma.f32`
7 054×	`accelerator-lowering-fma.f64`
3 012×	`-lowering-.f32`
3 012×	`-lowering-.f64`
1 690×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	260
1	73	254
2	145	254
3	301	254
4	606	254
5	1307	254
6	2983	254
7	5897	254
0	8239	242

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x)))) x) (/ 1/2 x))
(fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (fma.f64 x (sqrt.f64 x) #s(literal 0 binary64)))) (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) x)) #s(literal 0 binary64)))
(/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x)))) x)
(/.f64 (+.f64 (sqrt.f64 x) (-.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 x (sqrt.f64 x) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x)
(+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x))))
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 x (sqrt.f64 x) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/ (+ (* x 1/4) 1) (* x (sqrt x)))
(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 x (sqrt.f64 x) #s(literal 0 binary64)))
(+ (* x 1/4) 1)
(fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))
x
1/4
#s(literal 1/4 binary64)
1
#s(literal 1 binary64)
(* x (sqrt x))
(fma.f64 x (sqrt.f64 x) #s(literal 0 binary64))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (/ -1 (sqrt x)))
(+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/ -1 (sqrt x))
(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
-1
#s(literal -1 binary64)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(/ 1 (sqrt x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)
x
(* (/ 1 (+ 1/2 x)) (- (sqrt (+ 1 x)) (sqrt x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
(/ 1 (+ 1/2 x))
(/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(+ 1/2 x)
(+.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
x
(- (sqrt (+ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(- (sqrt (/ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(sqrt x)
(sqrt.f64 x)
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(/ 1 (/ (sqrt (+ 1 x)) (/ 1 (+ x (sqrt (+ (* x x) x))))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))) #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(/ (sqrt (+ 1 x)) (/ 1 (+ x (sqrt (+ (* x x) x)))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (sqrt.f64 (fma.f64 x x x))) #s(literal 0 binary64))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(/ 1 (+ x (sqrt (+ (* x x) x))))
(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
(+ x (sqrt (+ (* x x) x)))
(+.f64 x (sqrt.f64 (fma.f64 x x x)))
(sqrt (+ (* x x) x))
(sqrt.f64 (fma.f64 x x x))
(+ (* x x) x)
(fma.f64 x x x)

localize214.0ms (2%)

Memory

-13.3MiB live, 459.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	accuracy	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
✓	accuracy	52.0%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.8%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	85.0%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	accuracy	5.4%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.6%	(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x)
✓	accuracy	99.6%	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
✓	accuracy	66.0%	(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))

Samples

123.0ms	249×	1	valid
3.0ms	4×	3	valid
1.0ms	3×	0	valid

Compiler

Compiled 251 to 38 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-div: 31.0ms (34.2% of total)

ival-mult: 18.0ms (19.9% of total)

ival-sqrt: 14.0ms (15.5% of total)

ival-add: 12.0ms (13.3% of total)

adjust: 10.0ms (11% of total)

ival-sub: 4.0ms (4.4% of total)

exact: 1.0ms (1.1% of total)

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

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

series19.0ms (0.2%)

Memory

-12.1MiB live, 34.5MiB allocated

Counts

22 → 264

Calls

Call 1

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

Outputs
#<alt (* 1/2 (sqrt (/ 1 (pow x 7))))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x)>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x)>
#<alt (/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (sqrt (/ 1 (pow x 5)))>
#<alt (/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 3))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))>
#<alt (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)))>
#<alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/4 (sqrt (/ 1 x)))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (* 1/4 (sqrt (/ 1 x)))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- 1 (* 4 (- 1 (sqrt x))))))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* -1 (* x (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* x (- (* x (- 1/8 (* -2 (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (+ (* -1/2 (/ (- (* -1/8 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* -4 x))>
#<alt (+ 2 (* x (- (* 8 x) 4)))>
#<alt (+ 2 (* x (- (* x (+ 8 (* -16 x))) 4)))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 1/2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 1/4 (pow x 2))) (* 1/2 (/ 1 x))) x)>
#<alt (/ (- (+ 1 (/ 1/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 1/8 (/ 1 (pow x 3))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 1/2) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/4) x)) 1/2) x)) 1) x))>
#<alt 1/2>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<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 (sqrt x)>
#<alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))>
#<alt (+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))))>
#<alt (+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (+ (* 1/2 (sqrt (/ 1 x))) (* x (- (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) 1/8))))))))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))>
#<alt (* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (sqrt x)) (* -5/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))>
#<alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (/ -1/2 (pow x 2))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))>
#<alt (sqrt (/ 1 x))>
#<alt (- (sqrt (/ 1 x)) 1)>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)>
#<alt -2>
#<alt (* -1 (+ 2 (* 1/2 (/ 1 x))))>
#<alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)>
#<alt (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)>

Calls

66 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x)))) x)
1.0ms	x	@	-inf	(* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x)))) x) (/ 1/2 x))
1.0ms	x	@	-inf	(* (/ 1 (+ 1/2 x)) (- (sqrt (+ 1 x)) (sqrt x)))
0.0ms	x	@	0	(* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (+ (sqrt x) (/ -1 (sqrt x)))) x) (/ 1/2 x))
0.0ms	x	@	-inf	(/ (sqrt (+ 1 x)) (/ 1 (+ x (sqrt (+ (* x x) x)))))

rewrite142.0ms (1.3%)

Memory

26.6MiB live, 296.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 258×	`/-lowering-/.f32`
1 258×	`/-lowering-/.f64`
1 246×	`-lowering-.f32`
1 246×	`-lowering-.f64`
990×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	197
1	245	182
0	2281	170

Stop Event

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

Counts

22 → 486

Calls

Call 1

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

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

simplify552.0ms (5.1%)

Memory

-14.8MiB live, 870.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 644×	`accelerator-lowering-fma.f32`
12 644×	`accelerator-lowering-fma.f64`
4 800×	`-lowering-.f32`
4 800×	`-lowering-.f64`
3 594×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	539	3442
1	1663	3002
2	5315	2934
0	8184	2770

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 (pow x 7))))
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))))) (pow x 4))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 3))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))
(+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1 (sqrt (/ 1 (pow x 3)))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3))))))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* -1 (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))))) x)))
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt x) (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x))))) (pow x 2))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 2))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* 1/4 (sqrt (/ 1 x))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
(* 1/4 (sqrt (/ 1 x)))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(* 1/4 (sqrt (/ 1 x)))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 2 (- 1 (sqrt x)))
(+ (* 2 (- 1 (sqrt x))) (* x (- 1 (* 4 (- 1 (sqrt x))))))
(+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* -1 (* x (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))
(+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* x (- (* x (- 1/8 (* -2 (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (+ (* -1/2 (/ (- (* -1/8 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) (pow x 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
2
(+ 2 (* -4 x))
(+ 2 (* x (- (* 8 x) 4)))
(+ 2 (* x (- (* x (+ 8 (* -16 x))) 4)))
(/ 1 x)
(/ (- 1 (* 1/2 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/4 (pow x 2))) (* 1/2 (/ 1 x))) x)
(/ (- (+ 1 (/ 1/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 1/8 (/ 1 (pow x 3))))) x)
(/ 1 x)
(* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 1/2) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/4) x)) 1/2) x)) 1) x))
1/2
(+ 1/2 x)
(+ 1/2 x)
(+ 1/2 x)
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt x)
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))))
(+ (sqrt x) (* x (+ 1 (+ (* 1/2 (sqrt x)) (* x (+ 1/2 (+ (* -1/8 (sqrt x)) (+ (* 1/2 (sqrt (/ 1 x))) (* x (- (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) 1/8))))))))))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (sqrt x)) (* -5/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (sqrt x)) (* -1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(/ -1/2 (pow x 2))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)

Outputs
(* 1/2 (sqrt (/ 1 (pow x 7))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))
(/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (+ (* -1 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 4))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (.f64 x (.f64 (sqrt.f64 x) #s(literal -3/8 binary64)))) (.f64 (.f64 x x) (*.f64 x x)))
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(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (+.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (sqrt (/ 1 (pow x 5))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 x))) (.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 x))) (.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 x))) (.f64 x (*.f64 x x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) #s(literal 1/2 binary64)))) (sqrt.f64 x))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) x)
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 #s(literal 1/2 binary64) x) (.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) x) (.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
(-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) #s(literal 1 binary64)) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(- (sqrt (/ 1 x)) 1)
(+.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))) #s(literal -1 binary64)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) x)
-2
#s(literal -2 binary64)
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal -2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(+.f64 #s(literal -2 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
(+.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x))

eval117.0ms (1.1%)

Memory: 19.8MiB live, 223.9MiB allocated
Compiler: Compiled 19 339 to 2 333 computations (87.9% saved)

prune121.0ms (1.1%)

Memory

-31.9MiB live, 203.7MiB allocated

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	893	13	906
Fresh	10	3	13
Picked	3	2	5
Done	0	1	1
Total	906	19	925

Accuracy

100.0%

Counts

925 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	83.4%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	99.1%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))
▶	38.7%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
▶	99.3%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
	82.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
▶	98.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))))
✓	83.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
	97.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)))
	83.5%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	66.1%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
✓	5.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	98.6%	(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))
	98.7%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	98.7%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	82.5%	(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	98.6%	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
▶	2.1%	(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	66.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 423 to 292 computations (31% saved)

simplify414.0ms (3.8%)

Memory

12.0MiB live, 245.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))))
✓	cost-diff	1024	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	-64	(.f64 x (.f64 x x))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x x)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64))
✓	cost-diff	320	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
✓	cost-diff	320	(.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x))))

Rules

3 776×	`accelerator-lowering-fma.f32`
3 776×	`accelerator-lowering-fma.f64`
2 340×	`-lowering-.f32`
2 340×	`-lowering-.f64`
1 332×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	181
1	69	175
2	147	175
3	288	171
4	448	171
5	716	171
6	1094	171
7	1563	171
8	2145	171
9	2554	171
10	2955	171
11	3875	171
12	5135	171
13	5914	171
14	6415	171
15	6533	171
16	6667	171
17	6741	171
18	6799	171
19	7015	171
20	7111	171
21	7111	171
22	7111	171
23	7129	171
24	7129	171
25	7129	171
0	7129	166

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))
1/2
(* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))
(sqrt (/ 1 x))
(/ 1 x)
1
x
(+ 1 (/ -3/4 x))
(/ -3/4 x)
-3/4
(* 2 (- 1 (sqrt x)))
2
(- 1 (sqrt x))
1
(sqrt x)
x
(/ 1 (* (sqrt (* x (* x x))) 2))
1
(* (sqrt (* x (* x x))) 2)
(sqrt (* x (* x x)))
(* x (* x x))
x
(* x x)
2
(/ (- (sqrt (+ x 1)) (sqrt x)) (+ x 1/2))
(- (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
x
1
(sqrt x)
(+ x 1/2)
1/2
(/ 1 (/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x)))))
1
(/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x))))
(sqrt (+ 1 x))
(+ 1 x)
x
(/ 1 (+ x (+ 1/2 x)))
(+ x (+ 1/2 x))
(+ 1/2 x)
1/2

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

localize166.0ms (1.5%)

Memory

1.9MiB live, 315.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
✓	accuracy	5.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	98.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
✓	accuracy	68.3%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x))))
✓	accuracy	100.0%	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)

Samples

113.0ms	253×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 191 to 34 computations (82.2% saved)

Precisions

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

ival-div: 23.0ms (27.8% of total)

ival-sqrt: 16.0ms (19.4% of total)

ival-add: 15.0ms (18.2% of total)

ival-mult: 14.0ms (16.9% of total)

adjust: 8.0ms (9.7% of total)

ival-sub: 5.0ms (6.1% of total)

exact: 1.0ms (1.2% of total)

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

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

series11.0ms (0.1%)

Memory

24.6MiB live, 24.6MiB allocated

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))>
#<alt (/ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))) x)>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (- 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ 1 (* (sqrt (* x (* x x))) 2))>
#<alt (* (sqrt (* x (* x x))) 2)>
#<alt (sqrt (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (/ (- (sqrt (+ x 1)) (sqrt x)) (+ x 1/2))>
#<alt (- (sqrt (+ x 1)) (sqrt x))>
#<alt (sqrt (+ x 1))>
#<alt (+ x 1)>
#<alt (/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x))))>
#<alt (/ 1 (/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x)))))>
#<alt (sqrt (+ 1 x))>
#<alt (+ 1 x)>
#<alt (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))>
#<alt (* x x)>
#<alt (+ 1/2 x)>

Outputs
#<alt (* -3/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* -3/8 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<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 (* 2 (- 1 (sqrt x)))>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (* -2 (sqrt x))>
#<alt (* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))>
#<alt (* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))>
#<alt (* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))>
#<alt (* 2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 2 (- 1 (sqrt x)))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- 1 (* 4 (- 1 (sqrt x))))))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* -1 (* x (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))>
#<alt (+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* x (- (* x (- 1/8 (* -2 (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (/ (- (+ (* -1/2 (/ (- (* -1/8 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 9/4 x))>
#<alt (+ 1/2 (* x (+ 9/4 (* 15/16 x))))>
#<alt (+ 1/2 (* x (+ 9/4 (* x (+ 15/16 (* -7/32 x))))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))))>
#<alt (* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt x)) (* -1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))))>
#<alt 2>
#<alt (+ 2 (* -9 x))>
#<alt (+ 2 (* x (- (* 147/4 x) 9)))>
#<alt (+ 2 (* x (- (* x (+ 147/4 (* -1181/8 x))) 9)))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -1/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt x))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt x)))) x)) (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* -3/4 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))>
#<alt (/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))>
#<alt (/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 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 1/2>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>

Calls

66 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))
1.0ms	x	@	0	(* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))
0.0ms	x	@	inf	(* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))
0.0ms	x	@	-inf	(* (sqrt (* x (* x x))) 2)
0.0ms	x	@	-inf	(/ 1 (/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x)))))

rewrite460.0ms (4.3%)

Memory

-12.2MiB live, 737.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 140×	`/-lowering-/.f32`
5 140×	`/-lowering-/.f64`
4 634×	`-lowering-.f32`
4 634×	`-lowering-.f64`
3 316×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	140
1	215	123
2	1720	122
0	9012	122

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 900

Calls

Call 1

Inputs
(* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x))))
(/ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))) x)
(sqrt (/ 1 x))
(/ 1 x)
(* 2 (- 1 (sqrt x)))
(- 1 (sqrt x))
(sqrt x)
(/ 1 (* (sqrt (* x (* x x))) 2))
(* (sqrt (* x (* x x))) 2)
(sqrt (* x (* x x)))
(* x (* x x))
(/ (- (sqrt (+ x 1)) (sqrt x)) (+ x 1/2))
(- (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
(/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x))))
(/ 1 (/ (sqrt (+ 1 x)) (/ 1 (+ x (+ 1/2 x)))))
(sqrt (+ 1 x))
(+ 1 x)
(* (sqrt (/ 1 x)) (+ 1 (/ -3/4 x)))
(* x x)
(+ 1/2 x)

Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)))
(+.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)))
(+.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(+.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -27/64 binary64) (.f64 x (*.f64 x x))))) (fma.f64 (/.f64 #s(literal -3/4 binary64) x) (-.f64 (/.f64 #s(literal -3/4 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 9/16 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -27/64 binary64) (.f64 x (*.f64 x x)))))) (neg.f64 (fma.f64 (/.f64 #s(literal -3/4 binary64) x) (-.f64 (/.f64 #s(literal -3/4 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 9/16 binary64) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x))))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))))))))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 (.f64 (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x))) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) (-.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))) (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/4 binary64) x)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (-.f64 (.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (.f64 (.f64 (/.f64 #s(literal -3/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))
(*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))
(.f64 (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) (/.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (sqrt.f64 x) (/.f64 x (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))))))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) x))
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(/.f64 (fma.f64 x (.f64 x x) #s(literal 1/8 binary64)) (-.f64 (fma.f64 x x #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1/4 binary64)) (+.f64 x #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 x (+.f64 x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1/2 binary64) x)))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1/4 binary64))) (neg.f64 (+.f64 x #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) x)) (.f64 (-.f64 #s(literal 1/2 binary64) x) (.f64 x x))) (.f64 (-.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -1/2 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (+.f64 x #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 (fma.f64 x (+.f64 x #s(literal -1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) x)) (fma.f64 x (.f64 x x) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x #s(literal -1/2 binary64)) (fma.f64 x x #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) x))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) x)))
(*.f64 (fma.f64 x x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1/2 binary64))))

simplify451.0ms (4.2%)

Memory

35.3MiB live, 710.3MiB allocated

Algorithm

1×	egg-herbie

Rules

10 562×	`accelerator-lowering-fma.f32`
10 562×	`accelerator-lowering-fma.f64`
4 052×	`+-lowering-+.f64`
4 052×	`+-lowering-+.f32`
3 448×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	340	2857
1	957	2418
2	2819	2366
3	7248	2366
0	8137	2227

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(* -3/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -3/8 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 2 (- 1 (sqrt x)))
(* 2 (- 1 (sqrt x)))
(* 2 (- 1 (sqrt x)))
(* 2 (- 1 (sqrt x)))
(* -2 (sqrt x))
(* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))
(* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))
(* x (+ (* -2 (sqrt (/ 1 x))) (* 2 (/ 1 x))))
(* 2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))
(* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))
(* -1 (* x (- (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 2 (/ 1 x)))))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 2 (- 1 (sqrt x)))
(+ (* 2 (- 1 (sqrt x))) (* x (- 1 (* 4 (- 1 (sqrt x))))))
(+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* -1 (* x (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))
(+ (* 2 (- 1 (sqrt x))) (* x (- (+ 1 (* x (- (* x (- 1/8 (* -2 (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (+ 1/4 (* 2 (- 1 (* 4 (- 1 (sqrt x))))))))) (* 4 (- 1 (sqrt x))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (+ (* -1/2 (/ (- (* -1/8 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))) (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/4 (sqrt (/ 1 x))))) (pow x 2))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))) (pow x 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (- (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/8 (sqrt x))) x)) (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* 1/8 (sqrt x))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (sqrt x))) (pow x 2))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1/2
(+ 1/2 (* 9/4 x))
(+ 1/2 (* x (+ 9/4 (* 15/16 x))))
(+ 1/2 (* x (+ 9/4 (* x (+ 15/16 (* -7/32 x))))))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))))
(* (pow x 2) (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (sqrt x)) (* -1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))))
2
(+ 2 (* -9 x))
(+ 2 (* x (- (* 147/4 x) 9)))
(+ 2 (* x (- (* x (+ 147/4 (* -1181/8 x))) 9)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -1/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt x))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt x)))) x)) (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -3/4 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))
(/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))
(/ (+ (sqrt (pow x 3)) (* -3/4 (sqrt x))) (pow x 2))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (* -3/4 (sqrt (/ 1 (pow x 3)))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -3/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 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)
1/2
(+ 1/2 x)
(+ 1/2 x)
(+ 1/2 x)
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))

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

eval421.0ms (3.9%)

Memory: -143.1MiB live, 312.3MiB allocated
Compiler: Compiled 22 682 to 3 477 computations (84.7% saved)

prune134.0ms (1.2%)

Memory

-2.5MiB live, 313.9MiB allocated

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	1 181	10	1 191
Fresh	6	5	11
Picked	4	1	5
Done	2	1	3
Total	1 193	17	1 210

Accuracy

100.0%

Counts

1 210 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	83.4%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	99.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	99.2%	(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
	98.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
	82.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	39.3%	(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
	7.7%	(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
✓	83.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
	83.5%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.1%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	66.1%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
	97.5%	(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
	98.6%	(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))
	82.5%	(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	98.1%	(.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64))
	66.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
	4.5%	#s(literal 2 binary64)

Compiler

Compiled 903 to 277 computations (69.3% saved)

regimes55.0ms (0.5%)

Memory

-14.2MiB live, 64.0MiB allocated

Counts

54 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64))
(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))) x)
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x)
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 x (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/2 binary64) x))))

Outputs
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)

Calls

2 calls:

40.0ms	x
13.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes20.0ms (0.2%)

Memory

25.1MiB live, 25.1MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 1/2 binary64))
(/.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes32.0ms (0.3%)

Memory

-21.7MiB live, 16.9MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x #s(literal 1/2 binary64)))

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

Calls

2 calls:

26.0ms	x
5.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes9.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1/2 binary64) x))

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

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes9.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))

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

Calls

2 calls:

5.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes14.0ms (0.1%)

Memory

-26.5MiB live, 11.2MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))

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

Calls

2 calls:

11.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))

Outputs
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
39.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
39.3%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))

Outputs
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
7.7%	1	`x`
7.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)

Outputs
#s(literal 2 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
4.5%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify8.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	76
1	46	76

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
#s(literal 2 binary64)

Outputs
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 15/16 binary64) #s(literal 9/4 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 9/4 binary64) #s(literal 1/2 binary64)))
#s(literal 2 binary64)

soundness1.2s (11.4%)

Memory

4.2MiB live, 1 149.5MiB allocated

Rules

23 172×	`accelerator-lowering-fma.f32`
23 172×	`accelerator-lowering-fma.f64`
12 644×	`accelerator-lowering-fma.f32`
12 644×	`accelerator-lowering-fma.f64`
10 562×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	539	3442
1	1663	3002
2	5315	2934
0	8184	2770
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416
0	34	189
1	251	153
2	2328	152
0	8558	136
0	340	2857
1	957	2418
2	2819	2366
3	7248	2366
0	8137	2227
0	32	140
1	215	123
2	1720	122
0	9012	122
0	8	23
1	60	19
2	558	19
3	6710	19
0	8104	19

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

Compiler

Compiled 340 to 210 computations (38.2% saved)

preprocess122.0ms (1.1%)

Memory: -24.6MiB live, 223.2MiB allocated
Compiler: Compiled 230 to 116 computations (49.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	38
1	29	36
2	62	35
3	111	35
4	175	35
5	260	35
6	334	35
7	386	35
8	448	35
9	477	35
10	497	35
11	499	35
0	8	11
1	13	11
2	21	11
3	30	11
4	42	11
5	62	11
6	101	11
7	132	11
8	188	11
9	217	11
10	238	11
11	240	11
0	240	11

Iter	Nodes	Cost
0	8	32
1	13	32
2	21	32
3	30	32
4	42	32
5	62	32
6	101	32
7	132	32
8	188	32
9	217	32
10	238	32
11	240	32
0	240	32

Iter	Nodes	Cost
0	16	38
1	29	36
2	62	35
3	111	35
4	175	35
5	260	35
6	334	35
7	386	35
8	448	35
9	477	35
10	497	35
11	499	35
0	8	11
1	13	11
2	21	11
3	30	11
4	42	11
5	62	11
6	101	11
7	132	11
8	188	11
9	217	11
10	238	11
11	240	11
0	240	11

Iter	Nodes	Cost
0	8	32
1	13	32
2	21	32
3	30	32
4	42	32
5	62	32
6	101	32
7	132	32
8	188	32
9	217	32
10	238	32
11	240	32
0	240	32

analyze2.0ms (0%)

sample2.1s (19.2%)

preprocess31.0ms (0.3%)

explain149.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize49.0ms (0.5%)

series5.0ms (0%)

rewrite359.0ms (3.3%)

simplify573.0ms (5.3%)

eval88.0ms (0.8%)

prune44.0ms (0.4%)

simplify361.0ms (3.3%)

localize362.0ms (3.4%)

series33.0ms (0.3%)

rewrite563.0ms (5.2%)

simplify596.0ms (5.5%)

eval215.0ms (2%)

prune258.0ms (2.4%)

simplify282.0ms (2.6%)

localize214.0ms (2%)

series19.0ms (0.2%)

rewrite142.0ms (1.3%)

simplify552.0ms (5.1%)

eval117.0ms (1.1%)

prune121.0ms (1.1%)

simplify414.0ms (3.8%)

localize166.0ms (1.5%)

series11.0ms (0.1%)

rewrite460.0ms (4.3%)

simplify451.0ms (4.2%)

eval421.0ms (3.9%)

prune134.0ms (1.2%)

regimes55.0ms (0.5%)

regimes20.0ms (0.2%)

regimes32.0ms (0.3%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes14.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes3.0ms (0%)

simplify8.0ms (0.1%)

soundness1.2s (11.4%)

preprocess122.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	38
1	29	36
2	62	35
3	111	35
4	175	35
5	260	35
6	334	35
7	386	35
8	448	35
9	477	35
10	497	35
11	499	35
0	8	11
1	13	11
2	21	11
3	30	11
4	42	11
5	62	11
6	101	11
7	132	11
8	188	11
9	217	11
10	238	11
11	240	11
0	240	11

Iter	Nodes	Cost
0	8	32
1	13	32
2	21	32
3	30	32
4	42	32
5	62	32
6	101	32
7	132	32
8	188	32
9	217	32
10	238	32
11	240	32
0	240	32