Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.4s (15.4%)

Memory

100.0MiB live, 2 464.5MiB allocated

Samples

1.0s	7 983×	1	valid
17.0ms	273×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 805.0ms

ival-sqrt: 265.0ms (32.9% of total)

const: 141.0ms (17.5% of total)

adjust: 120.0ms (14.9% of total)

ival-add: 105.0ms (13% of total)

ival-sub: 82.0ms (10.2% of total)

ival->: 38.0ms (4.7% of total)

ival-and: 19.0ms (2.4% of total)

ival-<: 19.0ms (2.4% of total)

exact: 11.0ms (1.4% of total)

ival-assert: 7.0ms (0.9% of total)

Bogosity

preprocess30.0ms (0.3%)

Memory

-28.8MiB live, 48.3MiB allocated

Algorithm

2×	egg-herbie

Rules

80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
74×	`sub-neg`
48×	`-lowering-.f32`
48×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	25	24
2	51	23
3	90	23
4	145	23
5	214	23
6	268	23
7	299	23
8	342	23
9	357	23
10	365	23
0	6	7
1	11	7
2	15	7
3	21	7
4	29	7
5	44	7
6	76	7
7	101	7
8	143	7
9	158	7
10	166	7
0	166	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain128.0ms (1.4%)

Memory

-13.8MiB live, 185.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
255	-	1	(17.08854619702328)	`(-.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	1

Confusion

	Predicted +	Predicted -
+	254	1
-	0	1

Precision

1.0

Recall

0.996078431372549

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	1	0
-	0	0	1

Precision?

1.0

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

53.0ms	496×	1	valid
1.0ms	16×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

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

ival-sqrt: 17.0ms (48.4% of total)

adjust: 7.0ms (19.9% of total)

ival-add: 5.0ms (14.2% of total)

ival-sub: 4.0ms (11.4% of total)

exact: 1.0ms (2.8% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify42.0ms (0.5%)

Memory

-31.0MiB live, 9.0MiB 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×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
48×	`-lowering-.f32`
48×	`-lowering-.f64`
36×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	21	18
4	29	18
5	44	18
6	76	18
7	101	18
8	143	18
9	158	18
10	166	18
0	166	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize53.0ms (0.6%)

Memory

0.6MiB live, 38.6MiB 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	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

24.0ms	248×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sqrt: 7.0ms (44.6% of total)

adjust: 3.0ms (19.1% of total)

ival-add: 3.0ms (19.1% of total)

ival-sub: 2.0ms (12.8% of total)

exact: 0.0ms (0% of total)

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

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

series5.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- (sqrt (+ x 1)) (sqrt x))>
#<alt (sqrt (+ x 1))>
#<alt (+ x 1)>
#<alt (sqrt 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
1.0ms	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)

rewrite534.0ms (6%)

Memory

39.4MiB live, 422.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 090×	`accelerator-lowering-fma.f32`
5 090×	`accelerator-lowering-fma.f64`
3 260×	`-lowering-.f32`
3 260×	`-lowering-.f64`
2 676×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	39	16
2	286	16
3	3385	16
0	8673	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 357

Calls

Call 1

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

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

simplify552.0ms (6.2%)

Memory

-7.5MiB live, 708.2MiB allocated

Algorithm

1×	egg-herbie

Rules

17 328×	`accelerator-lowering-fma.f32`
17 328×	`accelerator-lowering-fma.f64`
3 884×	`-lowering-.f32`
3 884×	`-lowering-.f64`
2 664×	`--lowering--.f32`

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 → 48

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))))))
(fma.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))) #s(literal 0 binary64))
(* 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)))))
(fma.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))) #s(literal 0 binary64))
(* -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))))))
(fma.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)))) #s(literal 0 binary64))
(* -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)))))))
(fma.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))))) #s(literal 0 binary64))
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)

eval50.0ms (0.6%)

Memory: 27.3MiB live, 100.7MiB allocated
Compiler: Compiled 8 900 to 1 375 computations (84.6% saved)

prune60.0ms (0.7%)

Memory

3.4MiB live, 125.0MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	395	10	405
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	395	11	406

Accuracy

99.9%

Counts

406 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.1%	(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	98.6%	(/.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)
	98.3%	(/.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)
▶	8.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	8.7%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	8.7%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	7.0%	(-.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))
	97.6%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 312 to 192 computations (38.5% saved)

simplify616.0ms (6.9%)

Memory

-447.1MiB live, 664.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	384	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	1152	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	cost-diff	0	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	cost-diff	384	(+.f64 x (-.f64 #s(literal 1 binary64) 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)) (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))))
✓	cost-diff	0	(/.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)

Rules

10 362×	`accelerator-lowering-fma.f32`
10 362×	`accelerator-lowering-fma.f64`
3 804×	`+-lowering-+.f64`
3 804×	`+-lowering-+.f32`
3 680×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	207
1	76	207
2	215	187
3	687	187
4	3920	187
0	8264	179

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
(+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2)))
-1/8
(sqrt (/ 1 x))
(/ 1 x)
1
x
(+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))
1/16
(sqrt (/ 1 (* x (* x x))))
(/ 1 (* x (* x x)))
(* x (* x x))
(* x x)
(* (sqrt x) 1/2)
(sqrt x)
1/2
(- 1 (sqrt x))
1
(sqrt x)
x
(- (sqrt x) (sqrt x))
(sqrt x)
x
(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
(+ x (- 1 x))
x
(- 1 x)
1
(+ (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
(sqrt x)
(/ (* (+ x (+ x 1)) (+ x (- 1 x))) (* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1))))
(* (+ x (+ x 1)) (+ x (- 1 x)))
(+ x (+ x 1))
x
(+ x 1)
1
(+ x (- 1 x))
(- 1 x)
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1)))
(+ (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(sqrt x)

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

localize273.0ms (3.1%)

Memory

-1.5MiB live, 359.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	99.7%	(*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	68.0%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	8.0%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	accuracy	8.0%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 x) (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	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)) (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)
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	65.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

178.0ms

256×

valid

Compiler

Compiled 234 to 32 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

adjust: 25.0ms (22.2% of total)

ival-div: 22.0ms (19.5% of total)

ival-mult: 22.0ms (19.5% of total)

ival-sqrt: 19.0ms (16.9% of total)

ival-add: 15.0ms (13.3% of total)

ival-sub: 9.0ms (8% of total)

exact: 1.0ms (0.9% of total)

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

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

series13.0ms (0.1%)

Memory

19.8MiB live, 19.8MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)>
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (- 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (- (sqrt x) (sqrt x))>
#<alt (+ x (- 1 x))>
#<alt (/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))>
#<alt (- 1 x)>
#<alt (+ (sqrt (+ x 1)) (sqrt x))>
#<alt (/ (* (+ x (+ x 1)) (+ x (- 1 x))) (* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1))))>
#<alt (* (+ x (+ x 1)) (+ x (- 1 x)))>
#<alt (+ x (+ x 1))>
#<alt (sqrt (/ 1 (* x (* x x))))>
#<alt (/ 1 (* x (* x x)))>
#<alt (* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1)))>

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

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
1.0ms	x	@	inf	(- 1 x)
1.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
1.0ms	x	@	0	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite371.0ms (4.2%)

Memory

-23.0MiB live, 610.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 356×	`/-lowering-/.f32`
4 356×	`/-lowering-/.f64`
4 216×	`-lowering-.f32`
4 216×	`-lowering-.f64`
2 834×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	149
1	207	114
2	2144	113
0	8189	104

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 887

Calls

Call 1

Inputs
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
(+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2)))
(sqrt (/ 1 x))
(/ 1 x)
(- 1 (sqrt x))
(sqrt x)
(- (sqrt x) (sqrt x))
(+ x (- 1 x))
(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
(- 1 x)
(+ (sqrt (+ x 1)) (sqrt x))
(/ (* (+ x (+ x 1)) (+ x (- 1 x))) (* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1))))
(* (+ x (+ x 1)) (+ x (- 1 x)))
(+ x (+ x 1))
(sqrt (/ 1 (* x (* x x))))
(/ 1 (* x (* x x)))
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ x (+ x 1)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (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)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))) x) (/.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) 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)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))))) (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))) (.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))))))
(neg.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))))))
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x)))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (.f64 x (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))) (.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))))
(/.f64 (.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)) (.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64))) x))
(/.f64 (.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x))))) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal -1 binary64)) (.f64 (fma.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))) #s(literal 1 binary64)) (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))) x))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x (sqrt.f64 x)))))) #s(literal -1 binary64)) (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x (sqrt.f64 x))))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
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(/.f64 (neg.f64 (fma.f64 (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))))) (neg.f64 (fma.f64 (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))) (neg.f64 (/.f64 (-.f64 x (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))) (neg.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 2 binary64) x #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)))))) (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x)))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))) (neg.f64 (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 x x (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)))) (neg.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x)))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (neg.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 x x (*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (*.f64 #s(literal -1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

simplify463.0ms (5.2%)

Memory

42.7MiB live, 621.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 546×	`accelerator-lowering-fma.f32`
14 546×	`accelerator-lowering-fma.f64`
4 286×	`-lowering-.f32`
4 286×	`-lowering-.f64`
3 420×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	277	2186
1	814	1935
2	2576	1910
3	6897	1899
0	8079	1791

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

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

eval198.0ms (2.2%)

Memory: 22.6MiB live, 289.6MiB allocated
Compiler: Compiled 51 291 to 4 030 computations (92.1% saved)

prune154.0ms (1.7%)

Memory

-3.3MiB live, 273.5MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1 434	9	1 443
Fresh	2	3	5
Picked	5	0	5
Done	0	1	1
Total	1 441	13	1 454

Accuracy

100.0%

Counts

1 454 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	67.8%	(/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
▶	98.3%	(/.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)
	8.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
	6.6%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
	8.7%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
▶	97.4%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	67.8%	(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	18.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.6%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 314 to 202 computations (35.7% saved)

simplify5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

16×	`+-lowering-+.f64`
16×	`-lowering-.f32`
16×	`-lowering-.f64`
16×	`+-lowering-+.f32`
14×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
1	28	97
2	31	97
3	32	97
0	32	95

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
1
(+ (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
x
(sqrt x)
0
(/ 1 (+ 1 (sqrt x)))
1
(+ 1 (sqrt x))
(sqrt x)
x
(/ (* (sqrt x) 1/2) x)
(* (sqrt x) 1/2)
(sqrt x)
x
1/2
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))
-1/8
(sqrt (/ 1 x))
(/ 1 x)
1
x
(* (sqrt x) 1/2)
(sqrt x)
1/2

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

localize70.0ms (0.8%)

Memory

-14.2MiB live, 62.4MiB allocated

Localize:

Found 14 expressions of interest:

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

Samples

43.0ms

256×

valid

Compiler

Compiled 97 to 21 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sqrt: 14.0ms (46.1% of total)

ival-div: 8.0ms (26.3% of total)

ival-add: 5.0ms (16.5% of total)

ival-mult: 3.0ms (9.9% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#<alt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))>
#<alt (+ (sqrt (+ x 1)) (sqrt x))>
#<alt (sqrt (+ x 1))>
#<alt (+ x 1)>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ (* (sqrt x) 1/2) x)>
#<alt (* (sqrt x) 1/2)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)>
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 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 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 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (- (sqrt x) 1) x)>
#<alt (/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)>
#<alt (/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 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 (* -1/8 (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)>

Calls

39 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ 1 (+ 1 (sqrt x)))
0.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
0.0ms	x	@	0	(/ 1 (+ 1 (sqrt x)))
0.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
0.0ms	x	@	inf	(/ 1 (+ 1 (sqrt x)))

rewrite417.0ms (4.7%)

Memory

-6.4MiB live, 551.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 326×	`accelerator-lowering-fma.f32`
7 326×	`accelerator-lowering-fma.f64`
5 618×	`-lowering-.f32`
5 618×	`-lowering-.f64`
4 290×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	76
1	108	71
2	806	70
0	8235	68

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 926

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.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 #s(literal 1 binary64) x)) (.f64 (/.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 (sqrt.f64 (fma.f64 x x x)))))
(+.f64 (.f64 (/.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 (sqrt.f64 (fma.f64 x x x)))) (.f64 (/.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 #s(literal 1 binary64) x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) 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 (-.f64 x (sqrt.f64 (fma.f64 x x 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 (.f64 (-.f64 x (sqrt.f64 (fma.f64 x x 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 (+.f64 #s(literal 1 binary64) 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 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x)))))
(exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(-.f64 (/.f64 (+.f64 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 (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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (-.f64 x x))))
(fma.f64 (+.f64 #s(literal 1 binary64) 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 (-.f64 x (sqrt.f64 (fma.f64 x x 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)))))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x)))))
(fma.f64 (-.f64 x (sqrt.f64 (fma.f64 x x 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 (+.f64 #s(literal 1 binary64) 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)))))))
(fma.f64 (/.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 #s(literal 1 binary64) x) (.f64 (/.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 (sqrt.f64 (fma.f64 x x x)))))
(fma.f64 (/.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 (sqrt.f64 (fma.f64 x x x))) (.f64 (/.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 #s(literal 1 binary64) x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (+.f64 x (+.f64 #s(literal 1 binary64) 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 #s(literal 1 binary64) (-.f64 x x)) (*.f64 (+.f64 #s(literal 1 binary64) (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) (-.f64 x x)))
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(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 x x) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal 1/4 binary64))))
(pow.f64 (/.f64 #s(literal -1 binary64) (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) (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))) #s(literal 1 binary64))
(.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(.f64 (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (*.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x)))))
(.f64 (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (/.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x)))))
(.f64 (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x)))) #s(literal 1 binary64)))
(.f64 (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))))
(.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (*.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (/.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 x #s(literal -1/4 binary64))))
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(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (*.f64 x #s(literal -1/4 binary64)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(.f64 (/.f64 (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))))) (fma.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1/64 binary64) x) (.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (-.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 #s(literal 1/64 binary64) x)))))
(.f64 (/.f64 (fma.f64 x (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))))) (+.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (+.f64 (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))) (.f64 #s(literal -1/8 binary64) (.f64 x (sqrt.f64 x))))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 x #s(literal 1/4 binary64) (/.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)) (sqrt.f64 x)))))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal -1 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) #s(literal 0 binary64))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt.f64 (/.f64 x (*.f64 x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(neg.f64 (*.f64 (sqrt.f64 x) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (sqrt.f64 x) x)
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)))
(exp.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x)) (sqrt.f64 x)))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x)) (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 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) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))

simplify448.0ms (5%)

Memory

4.8MiB live, 632.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 798×	`accelerator-lowering-fma.f32`
13 798×	`accelerator-lowering-fma.f64`
3 934×	`-lowering-.f32`
3 934×	`-lowering-.f64`
3 234×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	246	1655
1	738	1459
2	2341	1446
3	6861	1441
0	8328	1368

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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))))))))
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 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(sqrt (/ 1 x))
(/ (- (sqrt x) 1) x)
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 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)))
(* -1/8 (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)

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

eval152.0ms (1.7%)

Memory: 6.9MiB live, 276.0MiB allocated
Compiler: Compiled 23 025 to 2 995 computations (87% saved)

prune148.0ms (1.7%)

Memory

32.5MiB live, 353.1MiB allocated

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	1 220	7	1 227
Fresh	3	4	7
Picked	1	4	5
Done	0	1	1
Total	1 224	16	1 240

Accuracy

100.0%

Counts

1 240 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	98.3%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	67.8%	(/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	18.8%	(/.f64 (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) x)
✓	97.4%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	67.8%	(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
▶	99.5%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	18.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	97.5%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
▶	18.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.3%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
▶	97.6%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	18.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 254 to 173 computations (31.9% saved)

simplify49.0ms (0.5%)

Memory

3.3MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	384	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x))))

Rules

576×	`accelerator-lowering-fma.f32`
576×	`accelerator-lowering-fma.f64`
324×	`-lowering-.f32`
324×	`-lowering-.f64`
192×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	91
1	32	89
2	44	89
3	69	89
4	104	89
5	180	89
6	286	89
7	428	89
8	535	89
9	748	89
10	933	89
11	994	89
12	1033	89
13	1049	89
14	1054	89
15	1055	89
0	1055	88

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize79.0ms (0.9%)

Memory

-7.9MiB live, 67.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	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 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x))))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))

Samples

44.0ms

256×

valid

Compiler

Compiled 92 to 21 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sqrt: 14.0ms (45% of total)

ival-div: 8.0ms (25.7% of total)

ival-add: 4.0ms (12.9% of total)

ival-mult: 4.0ms (12.9% of total)

ival-sub: 1.0ms (3.2% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

14 → 168

Calls

Call 1

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

Calls

42 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/ 1 (+ (sqrt (+ x 1)) (/ x (sqrt x))))
0.0ms	x	@	-inf	(/ 1 (sqrt x))
0.0ms	x	@	-inf	(/ x (sqrt x))
0.0ms	x	@	-inf	(/ 1 (* (sqrt x) 2))
0.0ms	x	@	inf	(/ 1 (+ (sqrt (+ x 1)) (/ x (sqrt x))))

rewrite373.0ms (4.2%)

Memory

-3.3MiB live, 531.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 922×	`accelerator-lowering-fma.f32`
7 922×	`accelerator-lowering-fma.f64`
3 498×	`-lowering-.f32`
3 498×	`-lowering-.f64`
3 328×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	70
1	112	64
2	853	60
0	8800	59

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 669

Calls

Call 1

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

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

simplify491.0ms (5.5%)

Memory

-14.1MiB live, 577.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 278×	`accelerator-lowering-fma.f32`
13 278×	`accelerator-lowering-fma.f64`
5 398×	`-lowering-.f32`
5 398×	`-lowering-.f64`
2 660×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	229	1780
1	667	1459
2	2136	1438
3	7942	1417
0	8557	1356

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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

eval142.0ms (1.6%)

Memory: -16.2MiB live, 212.3MiB allocated
Compiler: Compiled 14 671 to 2 180 computations (85.1% saved)

prune101.0ms (1.1%)

Memory

-0.3MiB live, 234.9MiB allocated

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	991	2	993
Fresh	2	4	6
Picked	3	2	5
Done	1	4	5
Total	997	12	1 009

Accuracy

100.0%

Counts

1 009 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
	98.3%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	67.8%	(/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	97.4%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	67.8%	(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal -1 binary64)) x)))
✓	99.5%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 x (sqrt.f64 x))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	97.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.3%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	97.6%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 442 to 161 computations (63.6% saved)

regimes17.0ms (0.2%)

Memory

-7.8MiB live, 30.8MiB allocated

Counts

29 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	x
6.0ms	(-.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)

regimes10.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes9.0ms (0.1%)

Memory

-22.1MiB live, 18.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	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

15.0MiB live, 15.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) 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
18.7%	1	`x`
18.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 0 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
4.5%	1	`x`
4.5%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

-31.3MiB live, 7.8MiB allocated

Accuracy

Total -1.4b remaining (-2.3%)

Threshold costs -1.4b (-2.3%)

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:

2.0ms	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)

simplify7.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub0-neg_binary64`
2×	`sub-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (15.1%)

Memory

13.6MiB live, 724.6MiB allocated

Rules

17 328×	`accelerator-lowering-fma.f32`
17 328×	`accelerator-lowering-fma.f64`
14 546×	`accelerator-lowering-fma.f32`
14 546×	`accelerator-lowering-fma.f64`
13 798×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	246	1655
1	738	1459
2	2341	1446
3	6861	1441
0	8328	1368
0	6	16
1	39	16
2	286	16
3	3385	16
0	8673	16
0	277	2186
1	814	1935
2	2576	1910
3	6897	1899
0	8079	1791
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398
0	229	1780
1	667	1459
2	2136	1438
3	7942	1417
0	8557	1356
0	19	70
1	112	64
2	853	60
0	8800	59
0	30	149
1	207	114
2	2144	113
0	8189	104

Stop Event

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

Compiler

Compiled 125 to 82 computations (34.4% saved)

preprocess105.0ms (1.2%)

Memory: -23.8MiB live, 222.8MiB allocated
Compiler: Compiled 112 to 66 computations (41.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	26
1	25	24
2	51	23
3	90	23
4	145	23
5	214	23
6	268	23
7	299	23
8	342	23
9	357	23
10	365	23
0	6	7
1	11	7
2	15	7
3	21	7
4	29	7
5	44	7
6	76	7
7	101	7
8	143	7
9	158	7
10	166	7
0	166	7

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	21	18
4	29	18
5	44	18
6	76	18
7	101	18
8	143	18
9	158	18
10	166	18
0	166	18

Iter	Nodes	Cost
0	12	26
1	25	24
2	51	23
3	90	23
4	145	23
5	214	23
6	268	23
7	299	23
8	342	23
9	357	23
10	365	23
0	6	7
1	11	7
2	15	7
3	21	7
4	29	7
5	44	7
6	76	7
7	101	7
8	143	7
9	158	7
10	166	7
0	166	7

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	21	18
4	29	18
5	44	18
6	76	18
7	101	18
8	143	18
9	158	18
10	166	18
0	166	18

analyze2.0ms (0%)

sample1.4s (15.4%)

preprocess30.0ms (0.3%)

explain128.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify42.0ms (0.5%)

localize53.0ms (0.6%)

series5.0ms (0.1%)

rewrite534.0ms (6%)

simplify552.0ms (6.2%)

eval50.0ms (0.6%)

prune60.0ms (0.7%)

simplify616.0ms (6.9%)

localize273.0ms (3.1%)

series13.0ms (0.1%)

rewrite371.0ms (4.2%)

simplify463.0ms (5.2%)

eval198.0ms (2.2%)

prune154.0ms (1.7%)

simplify5.0ms (0.1%)

localize70.0ms (0.8%)

series6.0ms (0.1%)

rewrite417.0ms (4.7%)

simplify448.0ms (5%)

eval152.0ms (1.7%)

prune148.0ms (1.7%)

simplify49.0ms (0.5%)

localize79.0ms (0.9%)

series8.0ms (0.1%)

rewrite373.0ms (4.2%)

simplify491.0ms (5.5%)

eval142.0ms (1.6%)

prune101.0ms (1.1%)

regimes17.0ms (0.2%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify7.0ms (0.1%)

soundness1.3s (15.1%)

preprocess105.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	26
1	25	24
2	51	23
3	90	23
4	145	23
5	214	23
6	268	23
7	299	23
8	342	23
9	357	23
10	365	23
0	6	7
1	11	7
2	15	7
3	21	7
4	29	7
5	44	7
6	76	7
7	101	7
8	143	7
9	158	7
10	166	7
0	166	7

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	21	18
4	29	18
5	44	18
6	76	18
7	101	18
8	143	18
9	158	18
10	166	18
0	166	18