Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Memory

1.6MiB live, 1.6MiB 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)

sample1.9s (20.7%)

Memory

40.9MiB live, 1 914.1MiB allocated

Samples

1.5s	8 075×	1	valid
13.0ms	181×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 329.0ms (28.1% of total)

ival-add: 286.0ms (24.5% of total)

const: 144.0ms (12.3% of total)

ival-sub: 130.0ms (11.1% of total)

adjust: 94.0ms (8% of total)

ival-<: 82.0ms (7% of total)

ival->: 69.0ms (5.9% of total)

ival-and: 19.0ms (1.6% of total)

exact: 11.0ms (0.9% of total)

ival-assert: 5.0ms (0.4% of total)

Bogosity

preprocess26.0ms (0.3%)

Memory

11.0MiB live, 50.3MiB 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)))

explain112.0ms (1.2%)

Memory

-17.5MiB live, 239.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
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	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

51.0ms	504×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sqrt: 15.0ms (44.9% of total)

ival-add: 7.0ms (21% of total)

adjust: 6.0ms (18% of total)

ival-sub: 4.0ms (12% of total)

exact: 1.0ms (3% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB 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)

localize35.0ms (0.4%)

Memory

2.5MiB live, 80.7MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

26.0ms	252×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sqrt: 7.0ms (41.3% of total)

ival-sub: 4.0ms (23.6% of total)

adjust: 3.0ms (17.7% of total)

ival-add: 3.0ms (17.7% of total)

exact: 0.0ms (0% of total)

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

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

series6.0ms (0.1%)

Memory

-28.1MiB live, 10.9MiB 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
2.0ms	x	@	0	(sqrt x)
1.0ms	x	@	-inf	(- (sqrt (+ x 1)) (sqrt x))
1.0ms	x	@	inf	(- (sqrt (+ x 1)) (sqrt x))
0.0ms	x	@	0	(- (sqrt (+ x 1)) (sqrt x))
0.0ms	x	@	-inf	(sqrt x)

rewrite373.0ms (4.1%)

Memory

20.0MiB live, 536.3MiB 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)))

simplify809.0ms (8.9%)

Memory

-28.0MiB live, 716.2MiB 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)

eval93.0ms (1%)

Memory: 4.7MiB live, 118.8MiB allocated
Compiler: Compiled 8 900 to 1 375 computations (84.6% saved)

prune55.0ms (0.6%)

Memory

-0.4MiB live, 159.0MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	398	7	405
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	398	8	406

Accuracy

99.9%

Counts

406 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	7.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	4.4%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
	5.7%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	3.8%	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	98.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 138 to 96 computations (30.4% saved)

simplify79.0ms (0.9%)

Memory

10.8MiB live, 89.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1472	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Rules

944×	`accelerator-lowering-fma.f32`
944×	`accelerator-lowering-fma.f64`
780×	`times-frac`
560×	`-lowering-.f32`
560×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	87
1	30	87
2	40	87
3	57	87
4	89	87
5	141	87
6	244	87
7	314	87
8	464	87
9	536	87
10	616	87
11	698	87
12	1159	87
13	2043	87
14	2558	87
15	2633	87
16	2646	87
17	2652	87
18	2654	87
0	2654	83

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize126.0ms (1.4%)

Memory

10.9MiB live, 209.6MiB allocated

Localize:

Found 14 expressions of interest:

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

Samples

96.0ms

256×

valid

Compiler

Compiled 89 to 19 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

adjust: 13.0ms (19.9% of total)

ival-add: 13.0ms (19.9% of total)

ival-mult: 11.0ms (16.9% of total)

ival-div: 9.0ms (13.8% of total)

ival-sqrt: 9.0ms (13.8% of total)

ival-sub: 9.0ms (13.8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

10 → 120

Calls

Call 1

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

Outputs
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* 1/2 (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)))>

Calls

30 calls:

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

rewrite74.0ms (0.8%)

Memory

-1.3MiB live, 112.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

484×	`accelerator-lowering-fma.f32`
484×	`accelerator-lowering-fma.f64`
404×	`-lowering-.f32`
404×	`-lowering-.f64`
322×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	99	50
0	792	46

Stop Event

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

Counts

10 → 136

Calls

Call 1

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

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

simplify868.0ms (9.6%)

Memory

8.5MiB live, 1 149.7MiB allocated

Algorithm

1×	egg-herbie

Rules

34 032×	`accelerator-lowering-fma.f32`
34 032×	`accelerator-lowering-fma.f64`
3 784×	`-lowering-.f32`
3 784×	`-lowering-.f64`
3 728×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	855
1	155	738
2	354	738
3	824	732
4	1596	732
5	2564	732
6	3558	732
7	4235	732
8	5005	732
9	5394	732
10	5559	732
11	5654	732
12	5849	732
13	5909	732
14	5909	732
15	5909	732
16	5909	732
17	5909	732
18	7549	732
0	8405	696

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
0
0
0
0
0
0
0
0
0
0
0
0
(* 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)))

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

eval40.0ms (0.4%)

Memory: -5.9MiB live, 69.2MiB allocated
Compiler: Compiled 4 348 to 462 computations (89.4% saved)

prune27.0ms (0.3%)

Memory

16.4MiB live, 54.3MiB allocated

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	369	5	374
Fresh	0	2	2
Picked	4	1	5
Done	0	1	1
Total	373	9	382

Accuracy

100.0%

Counts

382 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
▶	98.1%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) x)
	7.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	98.1%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	4.4%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))
	5.7%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	98.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 135 to 94 computations (30.4% saved)

simplify331.0ms (3.7%)

Memory

-387.7MiB live, 58.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

768×	`accelerator-lowering-fma.f32`
768×	`accelerator-lowering-fma.f64`
528×	`-lowering-.f32`
528×	`-lowering-.f64`
488×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	27	67
2	43	67
3	51	67
4	68	67
5	90	67
6	137	67
7	184	67
8	271	67
9	396	67
10	662	67
11	984	67
12	1439	67
13	1552	67
14	1692	67
15	1868	67
16	2309	67
17	2657	67
18	2659	67
19	2673	67
20	2685	67
21	2685	67
0	2685	65

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize48.0ms (0.5%)

Memory

26.5MiB live, 64.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64))
✓	accuracy	100.0%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)

Samples

28.0ms

256×

valid

Compiler

Compiled 71 to 17 computations (76.1% saved)

Precisions

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

ival-div: 6.0ms (37.6% of total)

ival-add: 3.0ms (18.8% of total)

ival-mult: 3.0ms (18.8% of total)

ival-sqrt: 2.0ms (12.5% of total)

ival-sub: 1.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

9 → 108

Calls

Call 1

Inputs
#<alt (/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x)>
#<alt (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x)))>
#<alt (sqrt x)>
#<alt (/ -1/8 (sqrt x))>
#<alt (- (+ (* x 1/2) 0) (sqrt x))>
#<alt (+ (* x 1/2) 0)>
#<alt (/ 1/2 (sqrt x))>
#<alt (/ (+ (* (sqrt x) 1/2) 0) x)>
#<alt (+ (* (sqrt x) 1/2) 0)>

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

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x)
0.0ms	x	@	-inf	(/ -1/8 (sqrt x))
0.0ms	x	@	-inf	(/ (+ (* (sqrt x) 1/2) 0) x)
0.0ms	x	@	-inf	(/ 1/2 (sqrt x))
0.0ms	x	@	inf	(- (+ (* x 1/2) 0) (sqrt x))

rewrite422.0ms (4.7%)

Memory

19.5MiB live, 562.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 464×	`accelerator-lowering-fma.f32`
6 464×	`accelerator-lowering-fma.f64`
5 132×	`/-lowering-/.f32`
5 132×	`/-lowering-/.f64`
4 638×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	105	47
2	1089	47
0	8262	45

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 995

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) (/.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 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 0 binary64) x)))
(-.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(neg.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (.f64 x (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))) (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))) x) (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.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 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))) (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (/.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (*.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))) x))
(/.f64 (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) (neg.f64 (.f64 x (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x))) (neg.f64 (*.f64 x (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))))
(/.f64 (*.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))) x)))
(/.f64 (neg.f64 (.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(pow.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64))
(*.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) x))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) (/.f64 (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))))
(*.f64 (pow.f64 (/.f64 x (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))) (sqrt.f64 x)))
(*.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (sqrt.f64 x)))
(.f64 (/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64))) x) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal -1/16 binary64)))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(+.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 0 binary64))
(+.f64 #s(literal 0 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) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(+.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(-.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(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 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (sqrt.f64 x)) x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x (sqrt.f64 x)) x) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
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(.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) #s(literal 0 binary64))) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(*.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) x) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) x))
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)) (sqrt.f64 x)))
(.f64 (/.f64 (.f64 x (sqrt.f64 x)) x) #s(literal 1/2 binary64))
(*.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) x) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (/.f64 x #s(literal 1/2 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal 1 binary64))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (/.f64 (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64))) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 (.f64 x (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 x (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))))
(.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))) (/.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))) (/.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (/.f64 (.f64 x (sqrt.f64 x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))) #s(literal 1/4 binary64))
(.f64 (/.f64 (.f64 x (sqrt.f64 x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) x))
(*.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))))
(.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x))) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64))) (/.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 3/2 binary64)) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) #s(literal 0 binary64))) (/.f64 (*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x)) (fma.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) #s(literal 0 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 0 binary64)))))

simplify253.0ms (2.8%)

Memory

-8.0MiB live, 223.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4 048×	`accelerator-lowering-fma.f32`
4 048×	`accelerator-lowering-fma.f64`
2 960×	`-lowering-.f32`
2 960×	`-lowering-.f64`
1 582×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	719
1	110	719
2	249	719
3	532	719
4	1419	719
5	2465	719
6	3149	719
7	3920	719
8	5115	719
9	5576	719
10	5683	719
11	7147	719
12	7625	719
13	7976	719
0	8081	701

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

eval156.0ms (1.7%)

Memory: 1.7MiB live, 244.7MiB allocated
Compiler: Compiled 23 303 to 2 506 computations (89.2% saved)

prune125.0ms (1.4%)

Memory

-2.8MiB live, 234.1MiB allocated

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	1 210	5	1 215
Fresh	0	2	2
Picked	2	3	5
Done	0	2	2
Total	1 212	12	1 224

Accuracy

100.0%

Counts

1 224 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	7.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	65.7%	(/.f64 (.f64 (/.f64 (.f64 x (sqrt.f64 x)) x) #s(literal 1/2 binary64)) x)
▶	98.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	97.9%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	98.1%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	5.7%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
▶	4.4%	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	66.4%	(.f64 #s(literal 1/2 binary64) (/.f64 x (.f64 x (sqrt.f64 x))))
✓	98.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 167 to 113 computations (32.3% saved)

simplify154.0ms (1.7%)

Memory

28.4MiB live, 185.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 x (sqrt.f64 x))
✓	cost-diff	320	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	cost-diff	-64	(*.f64 x (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	320	(.f64 #s(literal 1/2 binary64) (/.f64 x (.f64 x (sqrt.f64 x))))
✓	cost-diff	384	(/.f64 x (*.f64 x (sqrt.f64 x)))
✓	cost-diff	-64	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	cost-diff	-64	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)

Rules

3 410×	`-lowering-.f32`
3 410×	`-lowering-.f64`
2 248×	`accelerator-lowering-fma.f32`
2 248×	`accelerator-lowering-fma.f64`
1 824×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	93
1	34	87
2	57	87
3	109	87
4	179	87
5	537	87
6	1829	87
7	2736	87
8	5745	87
0	8604	87

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize104.0ms (1.1%)

Memory

-8.7MiB live, 110.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.2%	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	6.2%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (/.f64 x (.f64 x (sqrt.f64 x))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 x))
✓	accuracy	68.0%	(/.f64 x (*.f64 x (sqrt.f64 x)))
✓	accuracy	100.0%	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 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)

Samples

75.0ms	251×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 95 to 19 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 16.0ms (31.8% of total)

ival-div: 15.0ms (29.8% of total)

ival-sqrt: 8.0ms (15.9% of total)

adjust: 4.0ms (7.9% of total)

ival-sub: 4.0ms (7.9% of total)

ival-add: 2.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

14 → 168

Calls

Call 1

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

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

Calls

42 calls:

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

rewrite425.0ms (4.7%)

Memory

18.6MiB live, 561.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 402×	`accelerator-lowering-fma.f32`
8 402×	`accelerator-lowering-fma.f64`
4 312×	`-lowering-.f32`
4 312×	`-lowering-.f64`
3 548×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	75
1	104	71
2	753	53
3	7854	53
0	8753	53

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 1 345

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(neg.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x (sqrt.f64 x))))
(/.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (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)) (-.f64 #s(literal 0 binary64) x))
(/.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))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) #s(literal -2 binary64)))
(/.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 x #s(literal -1/2 binary64))) (.f64 x (sqrt.f64 x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(/.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) x)
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) x)
(/.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(/.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (.f64 x (sqrt.f64 x)))
(pow.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(.f64 x (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(.f64 (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(.f64 (.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64))
(.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 x)))))
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(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 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 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 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 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.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) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (fma.f64 x (.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) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.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 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 x #s(literal -1 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal -1 binary64) x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(.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))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(.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 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.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 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.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 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (fma.f64 x (.f64 x 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 (pow.f64 (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x 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 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 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 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (+.f64 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)))

simplify467.0ms (5.1%)

Memory

5.7MiB live, 677.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 596×	`accelerator-lowering-fma.f32`
18 596×	`accelerator-lowering-fma.f64`
4 288×	`-lowering-.f32`
4 288×	`-lowering-.f64`
2 256×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	124	1218
1	328	1135
2	874	1128
3	2443	1120
4	5060	1120
0	8223	1066

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

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

eval309.0ms (3.4%)

Memory: 24.2MiB live, 410.9MiB allocated
Compiler: Compiled 35 087 to 3 995 computations (88.6% saved)

prune203.0ms (2.2%)

Memory

-50.2MiB live, 404.3MiB allocated

Pruning

14 alts after pruning (4 fresh and 10 done)

	Pruned	Kept	Total
New	2 039	3	2 042
Fresh	1	1	2
Picked	0	5	5
Done	0	5	5
Total	2 040	14	2 054

Accuracy

100.0%

Counts

2 054 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.0%	(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) x (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	98.9%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	7.7%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	65.7%	(/.f64 (.f64 (/.f64 (.f64 x (sqrt.f64 x)) x) #s(literal 1/2 binary64)) x)
✓	98.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	97.9%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	98.1%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	5.7%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	4.4%	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	6.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	67.7%	(.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
✓	66.4%	(.f64 #s(literal 1/2 binary64) (/.f64 x (.f64 x (sqrt.f64 x))))
✓	98.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 286 to 138 computations (51.7% saved)

regimes12.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated

Counts

21 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes13.0ms (0.1%)

Memory

-19.0MiB live, 19.9MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.3%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	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

7.8MiB live, 7.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

5.5MiB live, 5.5MiB 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:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	21	27
2	25	27
3	27	27
4	28	27

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (14.2%)

Memory

-6.4MiB live, 451.9MiB allocated

Rules

34 032×	`accelerator-lowering-fma.f32`
34 032×	`accelerator-lowering-fma.f64`
17 328×	`accelerator-lowering-fma.f32`
17 328×	`accelerator-lowering-fma.f64`
6 464×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	57
1	99	50
0	792	46
0	15	47
1	105	47
2	1089	47
0	8262	45
0	63	855
1	155	738
2	354	738
3	824	732
4	1596	732
5	2564	732
6	3558	732
7	4235	732
8	5005	732
9	5394	732
10	5559	732
11	5654	732
12	5849	732
13	5909	732
14	5909	732
15	5909	732
16	5909	732
17	5909	732
18	7549	732
0	8405	696
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398

Stop Event

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

Compiler

Compiled 102 to 70 computations (31.4% saved)

preprocess110.0ms (1.2%)

Memory: 23.6MiB live, 143.7MiB allocated
Compiler: Compiled 104 to 66 computations (36.5% 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%)

sample1.9s (20.7%)

preprocess26.0ms (0.3%)

explain112.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize35.0ms (0.4%)

series6.0ms (0.1%)

rewrite373.0ms (4.1%)

simplify809.0ms (8.9%)

eval93.0ms (1%)

prune55.0ms (0.6%)

simplify79.0ms (0.9%)

localize126.0ms (1.4%)

series6.0ms (0.1%)

rewrite74.0ms (0.8%)

simplify868.0ms (9.6%)

eval40.0ms (0.4%)

prune27.0ms (0.3%)

simplify331.0ms (3.7%)

localize48.0ms (0.5%)

series5.0ms (0.1%)

rewrite422.0ms (4.7%)

simplify253.0ms (2.8%)

eval156.0ms (1.7%)

prune125.0ms (1.4%)

simplify154.0ms (1.7%)

localize104.0ms (1.1%)

series5.0ms (0.1%)

rewrite425.0ms (4.7%)

simplify467.0ms (5.1%)

eval309.0ms (3.4%)

prune203.0ms (2.2%)

regimes12.0ms (0.1%)

regimes13.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

simplify7.0ms (0.1%)

soundness1.3s (14.2%)

preprocess110.0ms (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