Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Memory

3.5MiB live, 3.5MiB 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 15 to 11 computations (26.7% saved)

sample2.5s (24.8%)

Memory

30.2MiB live, 1 950.9MiB allocated

Samples

2.1s	7 991×	1	valid
16.0ms	265×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-add: 515.0ms (32.1% of total)

adjust: 357.0ms (22.2% of total)

ival-sqrt: 295.0ms (18.4% of total)

const: 243.0ms (15.1% of total)

ival-sub: 77.0ms (4.8% of total)

ival->: 66.0ms (4.1% of total)

ival-<: 19.0ms (1.2% of total)

ival-and: 17.0ms (1.1% of total)

exact: 11.0ms (0.7% of total)

ival-assert: 5.0ms (0.3% of total)

Bogosity

preprocess22.0ms (0.2%)

Memory

15.3MiB live, 53.5MiB allocated

Algorithm

1×	egg-herbie

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
46×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Stop Event

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

Calls

Call 1

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

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

explain115.0ms (1.2%)

Memory

-15.9MiB live, 296.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
253	1	(50.002138655770764)	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	-	`(sqrt.f64 x)`
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 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	254	0

Confusion

	Predicted +	Predicted -
+	253	0
-	1	2

Precision

0.9960629921259843

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	253	0	0
-	1	0	2

Precision?

0.9960629921259843

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms	498×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-sqrt: 18.0ms (49.4% of total)

adjust: 7.0ms (19.2% of total)

ival-add: 6.0ms (16.5% of total)

ival-sub: 4.0ms (11% of total)

exact: 1.0ms (2.7% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory

22.1MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (0.4%)

Memory

-7.2MiB live, 83.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

30.0ms	249×	1	valid
0.0ms	7×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-add: 8.0ms (37.1% of total)

ival-sqrt: 7.0ms (32.4% of total)

adjust: 3.0ms (13.9% of total)

ival-sub: 2.0ms (9.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

-28.1MiB live, 11.0MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (sqrt.f64 x)>

Outputs
#<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 (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)))>

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(- (sqrt (+ x 1)) (sqrt x))
1.0ms	x	@	inf	(- (sqrt (+ x 1)) (sqrt x))
0.0ms	x	@	-inf	(sqrt x)
0.0ms	x	@	0	(- (sqrt (+ x 1)) (sqrt x))
0.0ms	x	@	inf	(+ x 1)

rewrite284.0ms (2.9%)

Memory

42.2MiB live, 429.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 090×	`lower-fma.f64`
5 090×	`lower-fma.f32`
3 260×	`lower-*.f64`
3 260×	`lower-*.f32`
2 676×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16

Stop Event

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

Counts

4 → 357

Calls

Call 1

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

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

simplify415.0ms (4.2%)

Memory

7.0MiB live, 554.2MiB allocated

Algorithm

1×	egg-herbie

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
3 884×	`lower-*.f64`
3 884×	`lower-*.f32`
2 664×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

Inputs
(- 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)))
(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)))

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

eval53.0ms (0.5%)

Memory: -19.3MiB live, 93.0MiB allocated
Compiler: Compiled 8 780 to 1 381 computations (84.3% saved)

prune54.0ms (0.5%)

Memory

35.0MiB live, 109.7MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	395	8	403
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	395	9	404

Accuracy

99.9%

Counts

404 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	7.6%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	4.4%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
▶	6.3%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	3.8%	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	5.4%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
	98.2%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 200 to 126 computations (37% saved)

simplify566.0ms (5.7%)

Memory

-367.2MiB live, 500.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (*.f64 x (sqrt.f64 x))))
✓	cost-diff	320	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	cost-diff	384	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1472	(-.f64 (sqrt.f64 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 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Rules

13 102×	`lower-fma.f32`
13 096×	`lower-fma.f64`
3 256×	`lower--.f32`
3 248×	`lower--.f64`
2 648×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	195
0	51	187
1	86	187
2	172	179
3	564	177
4	1547	177
5	3542	177
6	7339	177
0	8418	175

Stop Event

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

Calls

Call 1

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

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

localize222.0ms (2.2%)

Memory

-4.5MiB live, 400.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	67.8%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	accuracy	52.3%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	6.9%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	6.3%	(-.f64 x (sqrt.f64 (fma.f64 x x x)))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.2%	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	6.2%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Samples

168.0ms

256×

valid

Compiler

Compiled 207 to 31 computations (85% saved)

Precisions

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

adjust: 32.0ms (25.2% of total)

ival-mult: 27.0ms (21.2% of total)

ival-sqrt: 19.0ms (14.9% of total)

ival-div: 18.0ms (14.2% of total)

ival-sub: 16.0ms (12.6% of total)

ival-add: 15.0ms (11.8% of total)

exact: 1.0ms (0.8% of total)

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

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

series14.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Counts

17 → 204

Calls

Call 1

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

Outputs
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 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 (- 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 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<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>
#<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>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)>
#<alt (/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))>
#<alt (/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2))>
#<alt (/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (sqrt x))>
#<alt (- x (sqrt x))>
#<alt (- (* x (+ 1 (* -1/2 (sqrt x)))) (sqrt x))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))) (sqrt x))>
#<alt -1/2>
#<alt (- (* 1/8 (/ 1 x)) 1/2)>
#<alt (- (* 1/8 (/ 1 x)) (+ 1/2 (/ 1/16 (pow x 2))))>
#<alt (- (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))) (+ 1/2 (/ 1/16 (pow x 2))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) 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)))))>

Calls

51 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* (/ (+ x (- 1 x)) (+ (* (+ x 1) (sqrt (+ x 1))) (* x (sqrt x)))) (+ (+ x 1) (- x (sqrt (+ (* x x) x)))))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (* (+ x 1) (sqrt (+ x 1))) (* x (sqrt x))))
1.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
1.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
1.0ms	x	@	0	(* (/ (+ x (- 1 x)) (+ (* (+ x 1) (sqrt (+ x 1))) (* x (sqrt x)))) (+ (+ x 1) (- x (sqrt (+ (* x x) x)))))

rewrite485.0ms (4.9%)

Memory

-1.4MiB live, 341.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 734×	`lower-fma.f32`
5 728×	`lower-fma.f64`
3 984×	`lower-/.f32`
3 976×	`lower-/.f64`
3 220×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	134
0	51	134
1	233	113
2	2300	101
0	8438	95

Stop Event

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

Counts

17 → 739

Calls

Call 1

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

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

simplify461.0ms (4.6%)

Memory

1.7MiB live, 393.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10 696×	`lower-fma.f64`
10 696×	`lower-fma.f32`
5 090×	`lower-*.f64`
5 090×	`lower-*.f32`
3 940×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	396	2527
1	1208	2029
2	4037	1979
0	8617	1848

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 201

Calls

Call 1

Inputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 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)
(- 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)))
0
0
0
0
0
0
0
0
0
0
0
0
(- 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
(+ 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
1
1
1
1
1
1
1
1
1
1
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
1
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2))
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (sqrt x))
(- x (sqrt x))
(- (* x (+ 1 (* -1/2 (sqrt x)))) (sqrt x))
(- (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))) (sqrt x))
-1/2
(- (* 1/8 (/ 1 x)) 1/2)
(- (* 1/8 (/ 1 x)) (+ 1/2 (/ 1/16 (pow x 2))))
(- (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))) (+ 1/2 (/ 1/16 (pow x 2))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) 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)))))

Outputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (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 -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (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 -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (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 -1/8 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)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 #s(literal -1/8 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))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 #s(literal -1/8 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))))
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(fma.f64 x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(-.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64)))) (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) #s(literal 3/8 binary64) (fma.f64 #s(literal -1/16 binary64) (neg.f64 (sqrt.f64 x)) #s(literal -1/16 binary64)))) (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64))))) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(/.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/32 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -3/16 binary64) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) x)
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/.f64 #s(literal 3 binary64) #s(literal 0 binary64))
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64))) x)
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(+.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal -9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (/.f64 #s(literal 1/8 binary64) #s(literal 0 binary64)))) (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)))
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(+.f64 (neg.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 (-.f64 (fma.f64 #s(literal -9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (/.f64 #s(literal 1/8 binary64) #s(literal 0 binary64))) (/.f64 (fma.f64 (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) #s(literal 27/4 binary64) (/.f64 #s(literal 1/16 binary64) #s(literal 0 binary64))) x)) x)) (*.f64 x x)))) (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(fma.f64 x (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(fma.f64 x (fma.f64 x (fma.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal -3/8 binary64)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))) #s(literal 1 binary64))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (+.f64 (fma.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal -3/8 binary64)) #s(literal -3/8 binary64)) #s(literal 1/16 binary64)) (fma.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal -3/8 binary64))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))) #s(literal 1 binary64))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (.f64 x x))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(/.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (.f64 #s(literal -9/32 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64))))) (.f64 (.f64 x (.f64 x x)) x))) (*.f64 x x))
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/.f64 #s(literal 1 binary64) #s(literal 0 binary64))
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))) (*.f64 x x))
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 (sqrt.f64 x) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (fma.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64)) #s(literal 0 binary64)) (/.f64 (.f64 x #s(literal 9/4 binary64)) #s(literal 0 binary64)))) (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(- x (sqrt x))
(-.f64 x (sqrt.f64 x))
(- (* x (+ 1 (* -1/2 (sqrt x)))) (sqrt x))
(-.f64 (fma.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x) x) (sqrt.f64 x))
(- (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))) (sqrt x))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 x)) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(- (* 1/8 (/ 1 x)) (+ 1/2 (/ 1/16 (pow x 2))))
(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(- (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))) (+ 1/2 (/ 1/16 (pow x 2))))
(+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(fma.f64 (neg.f64 x) #s(literal -2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(*.f64 x (+.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)))
(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 #s(literal -1/8 binary64) (sqrt.f64 x))) (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 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64)))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(+.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal -1/2 binary64) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (+.f64 x #s(literal 1/2 binary64))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
(fma.f64 x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) (neg.f64 x))

eval218.0ms (2.2%)

Memory: 38.9MiB live, 411.9MiB allocated
Compiler: Compiled 47 976 to 4 218 computations (91.2% saved)

prune174.0ms (1.7%)

Memory

4.5MiB live, 479.6MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	1 606	7	1 613
Fresh	1	2	3
Picked	5	0	5
Done	0	1	1
Total	1 612	10	1 622

Accuracy

100.0%

Counts

1 622 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	48.8%	(/.f64 (fma.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x x))) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
	98.0%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	4.4%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))) (/.f64 (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
▶	98.2%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 286 to 160 computations (44.1% saved)

simplify315.0ms (3.2%)

Memory

7.6MiB live, 225.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

3 328×	`lower-fma.f32`
3 322×	`lower-fma.f64`
1 260×	`lower-*.f32`
1 254×	`lower-*.f64`
1 178×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	165
0	50	165
1	79	163
2	149	163
3	327	163
4	585	163
5	999	163
6	1706	163
7	2672	163
8	3207	163
9	3382	163
10	3500	163
11	3611	163
12	3892	163
13	4466	163
14	4805	163
15	4926	163
16	5056	163
17	5156	163
18	5174	163
19	5224	163
20	5302	163
21	5302	163
0	5302	161

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize148.0ms (1.5%)

Memory

-21.1MiB live, 210.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (*.f64 x (sqrt.f64 x))))
✓	accuracy	67.8%	(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	accuracy	52.3%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	6.3%	(-.f64 x (sqrt.f64 (fma.f64 x x x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Samples

97.0ms	247×	1	valid
2.0ms	9×	0	valid

Compiler

Compiled 177 to 31 computations (82.5% saved)

Precisions

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

ival-div: 16.0ms (22.3% of total)

ival-add: 14.0ms (19.5% of total)

ival-mult: 14.0ms (19.5% of total)

ival-sqrt: 14.0ms (19.5% of total)

adjust: 11.0ms (15.3% of total)

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

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

16 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

rewrite367.0ms (3.7%)

Memory

24.6MiB live, 537.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 234×	`lower-/.f32`
5 224×	`lower-/.f64`
4 958×	`lower-fma.f32`
4 952×	`lower-fma.f64`
3 148×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	124
0	49	107
1	208	98
2	2015	98
0	8741	96

Stop Event

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

Counts

16 → 802

Calls

Call 1

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

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

simplify344.0ms (3.5%)

Memory

-25.4MiB live, 415.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 606×	`lower-fma.f64`
9 606×	`lower-fma.f32`
5 324×	`lower-*.f64`
5 324×	`lower-*.f32`
3 038×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	496	2882
1	1549	2380
2	5275	2322
0	8475	2182

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 189

Calls

Call 1

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

Outputs
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.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 x)))))) (/.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.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 x))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.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 x)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) (neg.f64 x) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.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 x))))))) (/.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 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)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (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 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (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)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -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 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 (sqrt.f64 x) #s(literal 1/2 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(/.f64 (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 (sqrt.f64 x) #s(literal 1/2 binary64)))) (.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 x))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 x (fma.f64 #s(literal 2 binary64) (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 (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(.f64 x (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(neg.f64 (.f64 x (fma.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) x)) #s(literal -2 binary64)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (neg.f64 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)))) (* 2 (* (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (neg.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)
(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 (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (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))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 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 (-.f64 (.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))) (neg.f64 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))))))
(neg.f64 (.f64 x (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.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 (* 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 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (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))) (-.f64 (.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))))) (neg.f64 x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 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 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
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(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) (fma.f64 #s(literal -3/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))) (*.f64 x x))
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(-.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (/.f64 (fma.f64 #s(literal 3/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (fma.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64)) #s(literal 0 binary64)) (/.f64 (.f64 x #s(literal -9/4 binary64)) #s(literal 0 binary64)))) (*.f64 x x)))
1
#s(literal 1 binary64)
(+ 1 (* x (+ 3/2 (sqrt x))))
(fma.f64 x (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(fma.f64 x (+.f64 (sqrt.f64 x) (fma.f64 x #s(literal 3/8 binary64) #s(literal 3/2 binary64))) #s(literal 1 binary64))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))
(fma.f64 x (+.f64 (sqrt.f64 x) (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 3/8 binary64)) #s(literal 3/2 binary64))) #s(literal 1 binary64))
(* 2 (sqrt (pow x 3)))
(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 #s(literal 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 3/2 binary64))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 3/2 binary64) (+.f64 (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))))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 3/2 binary64) (+.f64 (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)))))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(literal 0 binary64)
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 3/2 binary64) (*.f64 x x)))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (.f64 #s(literal 3/2 binary64) (+.f64 (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)))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/2 binary64) (fma.f64 x #s(literal -9/4 binary64) #s(literal 1 binary64))) (.f64 (sqrt.f64 x) #s(literal -3/2 binary64))) (.f64 x (.f64 x (neg.f64 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 x))
(neg.f64 (sqrt.f64 x))
(- x (sqrt x))
(-.f64 x (sqrt.f64 x))
(- (* x (+ 1 (* -1/2 (sqrt x)))) (sqrt x))
(-.f64 (fma.f64 x (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) x) (sqrt.f64 x))
(- (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))) (sqrt x))
(-.f64 (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))) x) (sqrt.f64 x))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 x)) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(- (* 1/8 (/ 1 x)) (+ 1/2 (/ 1/16 (pow x 2))))
(+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(- (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3)))) (+ 1/2 (/ 1/16 (pow x 2))))
(+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 2 binary64) #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(*.f64 x (+.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)))
(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 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/8 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)))) (sqrt.f64 x))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (.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 x (+.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)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal -1/2 binary64) (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(neg.f64 (+.f64 (+.f64 x #s(literal 1/2 binary64)) (.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)))))
(fma.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) (neg.f64 x))

eval153.0ms (1.5%)

Memory: 26.5MiB live, 247.1MiB allocated
Compiler: Compiled 43 293 to 3 183 computations (92.6% saved)

prune122.0ms (1.2%)

Memory

7.7MiB live, 213.2MiB allocated

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	1 226	2	1 228
Fresh	1	3	4
Picked	0	5	5
Done	0	1	1
Total	1 227	11	1 238

Accuracy

100.0%

Counts

1 238 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
▶	98.0%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	99.5%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	98.0%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	4.4%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))) (/.f64 (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
✓	98.2%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 215 to 125 computations (41.9% saved)

simplify240.0ms (2.4%)

Memory

-6.0MiB live, 273.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
✓	cost-diff	320	(*.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x))))
✓	cost-diff	1792	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))) (/.f64 (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(sqrt.f64 (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	2112	(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))

Rules

7 246×	`lower-fma.f32`
7 238×	`lower-fma.f64`
3 734×	`lower-*.f32`
3 726×	`lower-*.f64`
1 900×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	251
0	56	235
1	105	231
2	221	231
3	759	219
4	2775	219
5	5229	219
0	8202	211

Stop Event

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

Calls

Call 1

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

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

localize195.0ms (2%)

Memory

6.3MiB live, 205.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x))))
✓	accuracy	66.5%	(/.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
✓	accuracy	52.3%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	6.3%	(-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x x x)))
✓	accuracy	100.0%	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(sqrt.f64 (sqrt.f64 x))
✓	accuracy	99.7%	(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Samples

132.0ms	246×	1	valid
2.0ms	10×	0	valid

Compiler

Compiled 267 to 34 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 43.0ms (40.5% of total)

ival-add: 20.0ms (18.8% of total)

ival-div: 14.0ms (13.2% of total)

adjust: 14.0ms (13.2% of total)

ival-sqrt: 11.0ms (10.4% of total)

ival-sub: 4.0ms (3.8% of total)

exact: 1.0ms (0.9% of total)

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

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

series52.0ms (0.5%)

Memory

0.9MiB live, 74.8MiB allocated

Counts

15 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	(sqrt (sqrt x))
12.0ms	x	@	inf	(sqrt (sqrt x))
2.0ms	x	@	-inf	(sqrt (sqrt x))
1.0ms	x	@	-inf	(/ 1 (/ (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x)))) (* 1 (+ (+ x -1) x))))
1.0ms	x	@	-inf	(/ (+ (* x (sqrt x)) (* (+ 1 x) (sqrt (+ 1 x)))) (* 1 (+ (+ x -1) x)))

rewrite371.0ms (3.7%)

Memory

9.6MiB live, 533.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 472×	`lower-/.f32`
5 460×	`lower-/.f64`
4 992×	`lower-*.f32`
4 984×	`lower-*.f64`
3 506×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	157
0	56	110
1	267	102
2	2271	102
0	9517	100

Stop Event

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

Counts

15 → 1 107

Calls

Call 1

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

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

simplify340.0ms (3.4%)

Memory

13.1MiB live, 438.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 140×	`lower-fma.f64`
8 140×	`lower-fma.f32`
5 740×	`lower-*.f64`
5 740×	`lower-*.f32`
2 996×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	514	2584
1	1615	2066
2	6509	2037
0	8029	1911

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 179

Calls

Call 1

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

Outputs
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(fma.f64 x #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(neg.f64 (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (neg.f64 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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (neg.f64 x))
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.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 x)))))) (/.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (fma.f64 x (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.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 x))))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.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 x)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))))) (/.f64 #s(literal 1/4 binary64) (.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 x)))))) (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/16 binary64)))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.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 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(/.f64 (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))) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(/.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.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)))))) (neg.f64 x))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(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 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
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(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (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))))
(* x (- (+ (sqrt (/ 1 x)) (* 3/4 (sqrt (/ 1 (pow x 3))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/4 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* 3/4 (sqrt (/ 1 (pow x 3)))) (* 3/4 (sqrt (/ 1 (pow x 5)))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (/ (- (* 3/4 (sqrt x)) (* -1/4 (sqrt (/ 1 x)))) (pow x 3))) (* -1/4 (sqrt (/ 1 (pow x 5))))))))
(.f64 x (-.f64 (fma.f64 #s(literal 3/4 binary64) (+.f64 (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) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64) (.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (.f64 (sqrt.f64 x) #s(literal 3/4 binary64))) (.f64 x (*.f64 x x))))))))
(* 1/2 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x #s(literal 0 binary64))
(* -1 (* x (+ (* -1/2 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1/4 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)))))
#s(literal 0 binary64)
(* -1 (* x (+ (* -1 (/ (- (+ (* 1/4 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 3/4 (sqrt (/ 1 x)))) (* -1/8 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))) x)) (* -1/2 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64) (/.f64 #s(literal 0 binary64) x)) (neg.f64 x)))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (- (* 3/4 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -3/4 (sqrt (/ 1 x)))) (* 1/2 (/ (- (* 3/4 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x))) x)) (* 1/4 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* -1/2 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (/.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/4 binary64) #s(literal 0 binary64)) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/4 binary64) (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 3/4 binary64) #s(literal 0 binary64))))) (neg.f64 x)) (neg.f64 x)))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 x) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x)))
(- (+ 1 (* x (+ 1 (* -1/2 (sqrt x))))) (sqrt x))
(-.f64 (fma.f64 x (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) (sqrt.f64 x))
(- (+ 1 (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (sqrt x))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(- (+ 1/2 (* 1/8 (/ 1 x))) (/ 1/16 (pow x 2)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(- (+ 1/2 (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) (/ 1/16 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 3/2 (/ 1 x))))
(fma.f64 x #s(literal 2 binary64) #s(literal 3/2 binary64))
(* -1 (* x (- (* -1 (/ (- 3/2 (* 1/8 (/ 1 x))) x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* -1 (* x (- (* -1 (/ (+ 3/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 #s(literal 3/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) 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 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/8 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)))) (sqrt.f64 x))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (.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 x (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(+.f64 (neg.f64 x) #s(literal -1/2 binary64))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (neg.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))

eval505.0ms (5.1%)

Memory: -74.0MiB live, 322.0MiB allocated
Compiler: Compiled 54 312 to 3 732 computations (93.1% saved)

prune149.0ms (1.5%)

Memory

-11.0MiB live, 275.5MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	1 503	2	1 505
Fresh	0	0	0
Picked	2	3	5
Done	0	6	6
Total	1 505	11	1 516

Accuracy

100.0%

Counts

1 516 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
✓	98.0%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	99.5%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	98.0%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	4.4%	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.7%	(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
	67.5%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal -1 binary64))))) (+.f64 x (+.f64 x #s(literal -1 binary64))))
✓	98.2%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 381 to 145 computations (61.9% saved)

regimes12.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes11.0ms (0.1%)

Memory

-26.6MiB live, 10.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.0%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.4%	1	`x`
4.4%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated

Accuracy

Total -1.5b remaining (-2.4%)

Threshold costs -1.5b (-2.4%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))

Outputs
#s(literal 0 binary64)

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
3.8%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
3.8%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify39.0ms (0.4%)

Memory

-29.1MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	23	26
2	27	26
3	29	26
4	30	26

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness900.0ms (9%)

Memory

10.7MiB live, 529.7MiB allocated

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
8 140×	`lower-fma.f64`
8 140×	`lower-fma.f32`
5 740×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	134
0	51	134
1	233	113
2	2300	101
0	8438	95
0	25	124
0	49	107
1	208	98
2	2015	98
0	8741	96
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	514	2584
1	1615	2066
2	6509	2037
0	8029	1911
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398

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

Compiler

Compiled 82 to 55 computations (32.9% saved)

preprocess49.0ms (0.5%)

Memory: 1.6MiB live, 115.7MiB allocated
Compiler: Compiled 102 to 66 computations (35.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

analyze2.0ms (0%)

sample2.5s (24.8%)

preprocess22.0ms (0.2%)

explain115.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize40.0ms (0.4%)

series6.0ms (0.1%)

rewrite284.0ms (2.9%)

simplify415.0ms (4.2%)

eval53.0ms (0.5%)

prune54.0ms (0.5%)

simplify566.0ms (5.7%)

localize222.0ms (2.2%)

series14.0ms (0.1%)

rewrite485.0ms (4.9%)

simplify461.0ms (4.6%)

eval218.0ms (2.2%)

prune174.0ms (1.7%)

simplify315.0ms (3.2%)

localize148.0ms (1.5%)

series10.0ms (0.1%)

rewrite367.0ms (3.7%)

simplify344.0ms (3.5%)

eval153.0ms (1.5%)

prune122.0ms (1.2%)

simplify240.0ms (2.4%)

localize195.0ms (2%)

series52.0ms (0.5%)

rewrite371.0ms (3.7%)

simplify340.0ms (3.4%)

eval505.0ms (5.1%)

prune149.0ms (1.5%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify39.0ms (0.4%)

soundness900.0ms (9%)

preprocess49.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18