Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.3s (15%)

Memory

65.7MiB live, 2 092.9MiB allocated

Samples

1.0s	8 073×	1	valid
11.0ms	183×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 780.0ms

ival-sqrt: 266.0ms (34.1% of total)

const: 139.0ms (17.8% of total)

adjust: 100.0ms (12.8% of total)

ival-add: 98.0ms (12.6% of total)

ival-sub: 74.0ms (9.5% of total)

ival->: 49.0ms (6.3% of total)

ival-<: 20.0ms (2.6% of total)

ival-and: 18.0ms (2.3% of total)

exact: 10.0ms (1.3% of total)

ival-assert: 5.0ms (0.6% of total)

Bogosity

preprocess27.0ms (0.3%)

Memory

-12.6MiB live, 24.5MiB 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)))

explain102.0ms (1.2%)

Memory

16.0MiB live, 171.9MiB 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

48.0ms	498×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

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

ival-sqrt: 15.0ms (48% of total)

adjust: 5.0ms (16% of total)

ival-add: 5.0ms (16% of total)

ival-sub: 4.0ms (12.8% of total)

exact: 0.0ms (0% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify12.0ms (0.1%)

Memory

-26.7MiB live, 16.2MiB 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)

localize34.0ms (0.4%)

Memory

22.0MiB live, 59.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	6.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

24.0ms	249×	1	valid
0.0ms	7×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sqrt: 7.0ms (43.8% of total)

adjust: 3.0ms (18.8% of total)

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

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

exact: 0.0ms (0% of total)

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

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

series5.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite342.0ms (3.9%)

Memory

21.8MiB live, 485.2MiB 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)))

simplify475.0ms (5.4%)

Memory

-3.8MiB live, 660.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval50.0ms (0.6%)

Memory: 20.2MiB live, 95.0MiB allocated
Compiler: Compiled 8 900 to 1 375 computations (84.6% saved)

prune59.0ms (0.7%)

Memory

-22.1MiB live, 137.9MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

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

Accuracy

99.9%

Counts

406 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	99.3%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
▶	98.7%	(/.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)
	9.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	9.1%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
▶	6.9%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.9%	(-.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))
	7.0%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
	97.8%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 298 to 182 computations (38.9% saved)

simplify196.0ms (2.2%)

Memory

35.6MiB live, 149.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(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)
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1472	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
✓	cost-diff	0	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)

Rules

2 336×	`accelerator-lowering-fma.f32`
2 336×	`accelerator-lowering-fma.f64`
1 040×	`-lowering-.f32`
1 040×	`-lowering-.f64`
828×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	173
1	45	173
2	59	173
3	68	173
4	80	173
5	105	173
6	154	173
7	221	173
8	405	173
9	847	173
10	1458	173
11	1786	173
12	2457	173
13	4064	173
14	4632	173
15	4708	173
16	4726	173
17	4744	173
18	4796	173
19	5175	173
20	5279	173
21	5279	173
22	5279	173
0	5279	166

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize435.0ms (4.9%)

Memory

-93.9MiB live, 338.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.5%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(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	6.9%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	69.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

380.0ms

256×

valid

Compiler

Compiled 184 to 28 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

ival-div: 22.0ms (22.9% of total)

ival-mult: 20.0ms (20.8% of total)

ival-sqrt: 16.0ms (16.6% of total)

adjust: 15.0ms (15.6% of total)

ival-sub: 12.0ms (12.5% of total)

ival-add: 11.0ms (11.4% of total)

exact: 1.0ms (1% of total)

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

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

series9.0ms (0.1%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

15 → 180

Calls

Call 1

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

Outputs
#<alt (* 1/16 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))>
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))>
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* 1/16 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))>
#<alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1/8 (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 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ 1 (* x (* x x)))
1.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
1.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)
0.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
0.0ms	x	@	inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (* x (* x x))))) (* (sqrt x) 1/2))) x)

rewrite106.0ms (1.2%)

Memory

4.9MiB live, 154.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

862×	`accelerator-lowering-fma.f32`
862×	`accelerator-lowering-fma.f64`
696×	`-lowering-.f32`
696×	`-lowering-.f64`
630×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	117
1	155	98
0	1320	94

Stop Event

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

Counts

15 → 234

Calls

Call 1

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

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

simplify719.0ms (8.1%)

Memory

-19.4MiB live, 774.4MiB allocated

Algorithm

1×	egg-herbie

Rules

22 490×	`accelerator-lowering-fma.f32`
22 490×	`accelerator-lowering-fma.f64`
4 660×	`-lowering-.f32`
4 660×	`-lowering-.f64`
3 104×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	1921
1	452	1668
2	1362	1651
3	3778	1637
0	8164	1535

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 1/16 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* 1/16 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
0
0
0
0
0
0
0
0
0
0
0
0
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1/8 (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 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))

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

eval106.0ms (1.2%)

Memory: 22.8MiB live, 96.4MiB allocated
Compiler: Compiled 10 690 to 1 035 computations (90.3% saved)

prune83.0ms (0.9%)

Memory

4.8MiB live, 86.4MiB allocated

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	570	8	578
Fresh	0	5	5
Picked	4	1	5
Done	0	1	1
Total	574	15	589

Accuracy

100.0%

Counts

589 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	34.7%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
	34.6%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
▶	98.7%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	98.6%	(/.f64 (/.f64 (-.f64 (.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 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
▶	67.5%	(/.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)))))
	9.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	9.1%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
▶	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	98.5%	(/.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)))))
✓	6.9%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	7.0%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
	97.8%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 430 to 267 computations (37.9% saved)

simplify324.0ms (3.7%)

Memory

-8.3MiB live, 299.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	cost-diff	192	(-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64)))
✓	cost-diff	192	(/.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)))))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
✓	cost-diff	704	(/.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)))))
✓	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)
✓	cost-diff	0	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)

Rules

4 914×	`accelerator-lowering-fma.f32`
4 914×	`accelerator-lowering-fma.f64`
3 406×	`-lowering-.f32`
3 406×	`-lowering-.f64`
1 848×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	156
1	53	156
2	132	154
3	288	154
4	629	154
5	1534	154
6	2943	154
7	4617	154
8	7435	154
0	8120	145

Stop Event

1×	iter limit
1×	node limit

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
(/ (* (sqrt x) 1/2) x)
(* (sqrt x) 1/2)
(sqrt x)
x
1/2
(/ 1 (/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x)))))
1
(/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))))
x
(+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x)))
(sqrt x)
1/2
(/ -1/8 (sqrt x))
-1/8
(/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))
(- (* (/ 1 x) 1/64) (* x 1/4))
(* (/ 1 x) 1/64)
(/ 1 x)
1
x
1/64
(* x 1/4)
1/4
(* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x))))
(+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))
(/ -1/8 (sqrt x))
-1/8
(sqrt x)
(* -1/2 (sqrt x))
-1/2

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

localize76.0ms (0.9%)

Memory

25.9MiB live, 141.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	accuracy	99.7%	(.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	68.4%	(/.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)))))
✓	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 binary64) (/.f64 x (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	99.2%	(/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (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)
✓	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	99.5%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)

Samples

39.0ms

256×

valid

Compiler

Compiled 161 to 26 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-div: 10.0ms (40.7% of total)

ival-mult: 8.0ms (32.6% of total)

ival-add: 2.0ms (8.1% of total)

ival-sqrt: 2.0ms (8.1% of total)

ival-sub: 1.0ms (4.1% of total)

exact: 1.0ms (4.1% of total)

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

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

series18.0ms (0.2%)

Memory

-25.4MiB live, 17.5MiB allocated

Counts

13 → 156

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 (/ (* (sqrt x) 1/2) x)>
#<alt (* (sqrt x) 1/2)>
#<alt (/ 1 (/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x)))))>
#<alt (/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))))>
#<alt (* (/ 1 x) 1/64)>
#<alt (/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))>
#<alt (- (* (/ 1 x) 1/64) (* x 1/4))>
#<alt (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))>
#<alt (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt 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)))))>
#<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 (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<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 (* -8 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* -32 (sqrt x)) (* -8 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* -128 (sqrt x)) (* 32 (sqrt (/ 1 x)))))))>
#<alt (* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* x (- (* -512 (sqrt x)) (* 128 (sqrt (/ 1 x))))) (* 32 (sqrt (/ 1 x)))))))>
#<alt (* 2 (sqrt x))>
#<alt (+ (* 1/2 (sqrt (/ 1 x))) (* 2 (sqrt x)))>
#<alt (- (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt x))) (* -1/2 (sqrt (/ 1 x))))>
#<alt (- (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* -2 (sqrt x))>
#<alt (+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (+ (* -2 (sqrt x)) (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))>
#<alt (+ (* -2 (sqrt x)) (* -1 (/ (- (* -1 (/ (- (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 6)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (/ 1/64 x)>
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 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 (/ (- (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/32 (sqrt (/ 1 x)))) (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/32 (sqrt x)) (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))))) (* -1/4 (/ (- (* 1/32 (sqrt x)) (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) (* x (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) x))>
#<alt (/ 1/64 x)>
#<alt (/ (+ 1/64 (* -1/4 (pow x 2))) x)>
#<alt (/ (+ 1/64 (* -1/4 (pow x 2))) x)>
#<alt (/ (+ 1/64 (* -1/4 (pow x 2))) x)>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))>
#<alt (* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))>
#<alt (* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)>
#<alt (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)>
#<alt (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)>
#<alt (* -1/2 (sqrt x))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1/8 (sqrt x))>
#<alt (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))>
#<alt (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))>
#<alt (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))>
#<alt (* -1/2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>

Calls

39 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	(* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x))))
1.0ms	x	@	-inf	(/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))
1.0ms	x	@	-inf	(/ (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))) x)
1.0ms	x	@	0	(/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))
1.0ms	x	@	inf	(/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))

rewrite536.0ms (6%)

Memory

38.8MiB live, 999.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 912×	`accelerator-lowering-fma.f32`
7 912×	`accelerator-lowering-fma.f64`
4 218×	`-lowering-.f32`
4 218×	`-lowering-.f64`
3 838×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	99
1	129	99
2	1154	97
0	9082	89

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 1 779

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))
(/ (* (sqrt x) 1/2) x)
(* (sqrt x) 1/2)
(/ 1 (/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x)))))
(/ x (+ (* (sqrt x) 1/2) (/ -1/8 (sqrt x))))
(* (/ 1 x) 1/64)
(/ (- (* (/ 1 x) 1/64) (* x 1/4)) (* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))))
(- (* (/ 1 x) 1/64) (* x 1/4))
(+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x)))
(* x (+ (/ -1/8 (sqrt x)) (* -1/2 (sqrt x))))

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

simplify378.0ms (4.3%)

Memory

9.5MiB live, 557.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 766×	`accelerator-lowering-fma.f32`
8 766×	`accelerator-lowering-fma.f64`
5 214×	`-lowering-.f32`
5 214×	`-lowering-.f64`
1 934×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	172	1597
1	463	1529
2	1442	1522
3	4555	1504
0	8249	1428

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -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)))))
(* -8 (sqrt (pow x 3)))
(* (pow x 2) (+ (* -32 (sqrt x)) (* -8 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* -128 (sqrt x)) (* 32 (sqrt (/ 1 x)))))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* x (- (* -512 (sqrt x)) (* 128 (sqrt (/ 1 x))))) (* 32 (sqrt (/ 1 x)))))))
(* 2 (sqrt x))
(+ (* 1/2 (sqrt (/ 1 x))) (* 2 (sqrt x)))
(- (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt x))) (* -1/2 (sqrt (/ 1 x))))
(- (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* -2 (sqrt x))
(+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* -1 (/ (- (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 6)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(/ 1/64 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 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 (/ (- (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/32 (sqrt (/ 1 x)))) (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/32 (sqrt x)) (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))))) (* -1/4 (/ (- (* 1/32 (sqrt x)) (* 1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) (* x (pow (sqrt -1) 2))))) x)) (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) x))
(/ 1/64 x)
(/ (+ 1/64 (* -1/4 (pow x 2))) x)
(/ (+ 1/64 (* -1/4 (pow x 2))) x)
(/ (+ 1/64 (* -1/4 (pow x 2))) x)
(* -1/4 x)
(* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))
(* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))
(* x (- (* 1/64 (/ 1 (pow x 2))) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/4 (* 1/64 (/ 1 (pow x 2))))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(* -1/2 (sqrt x))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(* -1/8 (sqrt x))
(+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))
(+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))
(+ (* -1/2 (sqrt (pow x 3))) (* -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))))))
(* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 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) (.f64 x (.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 (.f64 x (.f64 x x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (sqrt (/ 1 x)))
(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 (.f64 x (.f64 x x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) 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)))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
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(*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))))
(* -1/8 (sqrt x))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))
(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))
(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x)))
(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(* -1/2 (sqrt (pow x 3)))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(* 1/2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal -1/2 binary64))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))
(* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))))

eval313.0ms (3.5%)

Memory: 11.4MiB live, 434.1MiB allocated
Compiler: Compiled 60 409 to 3 203 computations (94.7% saved)

prune202.0ms (2.3%)

Memory

15.7MiB live, 368.0MiB allocated

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	2 283	2	2 285
Fresh	1	7	8
Picked	2	3	5
Done	0	2	2
Total	2 286	14	2 300

Accuracy

100.0%

Counts

2 300 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	34.7%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
▶	34.6%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
✓	98.7%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	9.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	97.4%	(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
	9.1%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	97.6%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	6.9%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	7.0%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
▶	97.8%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 328 to 195 computations (40.5% saved)

simplify180.0ms (2%)

Memory

25.6MiB live, 216.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x x)))
✓	cost-diff	0	(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64))))
✓	cost-diff	0	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x x)))
✓	cost-diff	0	(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
✓	cost-diff	-64	(*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 x (sqrt.f64 x))
✓	cost-diff	1088	(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Rules

2 954×	`accelerator-lowering-fma.f32`
2 954×	`accelerator-lowering-fma.f64`
2 572×	`-lowering-.f32`
2 572×	`-lowering-.f64`
1 994×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	171
1	72	171
2	131	171
3	206	167
4	260	167
5	420	167
6	812	167
7	2480	167
8	5985	167
9	7737	167
0	8064	158

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 x)))
1/2
(sqrt (/ 1 x))
(/ 1 x)
1
x
(+ (* x 1/2) (- 1 (sqrt x)))
x
1/2
(- 1 (sqrt x))
1
(sqrt x)
(/ (* (/ x (sqrt x)) 1/2) x)
(* (/ x (sqrt x)) 1/2)
(/ x (sqrt x))
x
(sqrt x)
1/2
(/ (+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x))) (* x x))
(+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x)))
(sqrt (* x (* x x)))
(* x (* x x))
x
(* x x)
1/2
(* -1/8 (sqrt x))
-1/8
(sqrt x)
(/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))
(+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16)))
(sqrt (* x (* x x)))
(* x (* x x))
x
(* x x)
(+ (* x 1/2) 0)
1/2
0
(* (sqrt x) (+ (* x -1/8) 1/16))
(sqrt x)
(+ (* x -1/8) 1/16)
-1/8
1/16

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

localize113.0ms (1.3%)

Memory

-51.7MiB live, 172.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))
✓	accuracy	73.7%	(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64))))
✓	accuracy	70.5%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	36.7%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.7%	(fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
✓	accuracy	70.5%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	51.9%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
✓	accuracy	100.0%	(*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Samples

63.0ms

256×

valid

Compiler

Compiled 185 to 32 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-add: 16.0ms (34.3% of total)

ival-mult: 16.0ms (34.3% of total)

ival-div: 8.0ms (17.1% of total)

ival-sqrt: 5.0ms (10.7% of total)

ival-sub: 1.0ms (2.1% of total)

exact: 1.0ms (2.1% of total)

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

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

series10.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (+ (* x 1/2) (- 1 (sqrt x)))>
#<alt (- 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ (* (/ x (sqrt x)) 1/2) x)>
#<alt (/ x (sqrt x))>
#<alt (* (/ x (sqrt x)) 1/2)>
#<alt (/ (+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x))) (* x x))>
#<alt (+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x)))>
#<alt (sqrt (* x (* x x)))>
#<alt (/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))>
#<alt (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16)))>
#<alt (+ (* x 1/2) 0)>
#<alt (* x (* x x))>
#<alt (* (sqrt x) (+ (* x -1/8) 1/16))>

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

Calls

51 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/ x (sqrt x))
1.0ms	x	@	-inf	(/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))
0.0ms	x	@	-inf	(/ (+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x))) (* x x))
0.0ms	x	@	0	(/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))
0.0ms	x	@	inf	(/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))

rewrite492.0ms (5.5%)

Memory

-19.5MiB live, 694.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 936×	`accelerator-lowering-fma.f32`
5 936×	`accelerator-lowering-fma.f64`
5 048×	`-lowering-.f32`
5 048×	`-lowering-.f64`
4 716×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	123
1	184	113
2	1636	107
0	8783	99

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1 283

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
(+ (* x 1/2) (- 1 (sqrt x)))
(- 1 (sqrt x))
(sqrt x)
(/ (* (/ x (sqrt x)) 1/2) x)
(/ x (sqrt x))
(* (/ x (sqrt x)) 1/2)
(/ (+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x))) (* x x))
(+ (* (sqrt (* x (* x x))) 1/2) (* -1/8 (sqrt x)))
(sqrt (* x (* x x)))
(/ (+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16))) (* x (* x x)))
(+ (* (sqrt (* x (* x x))) (+ (* x 1/2) 0)) (* (sqrt x) (+ (* x -1/8) 1/16)))
(+ (* x 1/2) 0)
(* x (* x x))
(* (sqrt x) (+ (* x -1/8) 1/16))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64))) (*.f64 x (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(neg.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (*.f64 x (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) #s(literal 1 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 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x)))
(/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64))) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) x)
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) x)) (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 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) (neg.f64 (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 1 binary64))) (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal -1 binary64))) (neg.f64 (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (*.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(pow.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 x (/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (/.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 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (sqrt.f64 x) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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) x) (sqrt.f64 x))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) x))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64))) #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 x x) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (sqrt.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64) #s(literal 0 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal 0 binary64))) (sqrt.f64 x)))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal 0 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64))) (sqrt.f64 x)))
(*.f64 (/.f64 x (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal 1/4 binary64))))
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(fma.f64 #s(literal -1/8 binary64) (.f64 x (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))
(fma.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) x (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))
(fma.f64 (.f64 x #s(literal -1/8 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))
(fma.f64 #s(literal 1/16 binary64) (sqrt.f64 x) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4096 binary64))) (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) (.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))) (-.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64))))
(/.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/4096 binary64))) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/256 binary64)) (*.f64 x #s(literal -1/128 binary64))))
(/.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal -1/256 binary64))) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/16 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/4096 binary64)) (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/256 binary64)) (*.f64 x #s(literal -1/128 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal -1/256 binary64)) (sqrt.f64 x)) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/16 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4096 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (-.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) (.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64))))) (neg.f64 (-.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/4096 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/256 binary64)) (*.f64 x #s(literal -1/128 binary64)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 x) (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal -1/256 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/16 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64) #s(literal 1/4096 binary64)) (sqrt.f64 x))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/256 binary64)) (*.f64 x #s(literal -1/128 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal -1/256 binary64)) (sqrt.f64 x))) (neg.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/16 binary64))))
(/.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)))) (fma.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (-.f64 (.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (*.f64 x (sqrt.f64 x)) #s(literal -1/8 binary64))))))
(*.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))
(*.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)) (sqrt.f64 x))

simplify444.0ms (5%)

Memory

-24.0MiB live, 644.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 404×	`accelerator-lowering-fma.f32`
14 404×	`accelerator-lowering-fma.f64`
5 222×	`-lowering-.f32`
5 222×	`-lowering-.f64`
2 066×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	1768
1	280	1537
2	896	1527
3	2564	1521
4	4609	1521
0	8057	1455

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

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

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

eval213.0ms (2.4%)

Memory: 44.0MiB live, 376.0MiB allocated
Compiler: Compiled 46 345 to 4 052 computations (91.3% saved)

prune241.0ms (2.7%)

Memory

-0.3MiB live, 370.3MiB allocated

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	1 752	5	1 757
Fresh	1	3	4
Picked	2	3	5
Done	0	5	5
Total	1 755	16	1 771

Accuracy

100.0%

Counts

1 771 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.5%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
	34.9%	(/.f64 (fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
	34.7%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (.f64 x x)))
✓	34.6%	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
✓	98.7%	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
	9.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	97.4%	(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
	9.1%	(/.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	49.7%	(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 x x) x)) #s(literal 1/2 binary64)) x)
✓	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	97.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	6.9%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	6.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	7.0%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
✓	97.8%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 547 to 218 computations (60.1% saved)

regimes40.0ms (0.5%)

Memory

-17.7MiB live, 21.0MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 x 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 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.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 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (.f64 x x)))
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
(/.f64 (/.f64 (-.f64 (.f64 (/.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 #s(literal -1/2 binary64) (sqrt.f64 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)

Outputs

(/.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)

Calls

2 calls:

32.0ms	x
6.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes15.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.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 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (.f64 (sqrt.f64 (/.f64 (.f64 x 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 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.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 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (.f64 x x)))
(/.f64 (fma.f64 (sqrt.f64 (.f64 x (.f64 x x))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 0 binary64)) (.f64 (sqrt.f64 x) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/16 binary64)))) (.f64 x (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x))))
(/.f64 (/.f64 (-.f64 (.f64 (/.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 #s(literal -1/2 binary64) (sqrt.f64 x)))) 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:

7.0ms	x
6.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes19.0ms (0.2%)

Memory

-25.5MiB live, 13.0MiB allocated

Counts

14 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.8%	2	`x`
99.8%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes9.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	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

6.2MiB live, 6.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
4.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Memory

3.7MiB live, 3.7MiB 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

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
3.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	3.725290298461914e-8

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify11.0ms (0.1%)

Memory

-19.1MiB live, 17.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`
2×	`sub0-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	78
1	47	78
2	54	78
3	57	78
4	58	78

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (12.2%)

Memory

6.5MiB live, 683.9MiB allocated

Rules

17 328×	`accelerator-lowering-fma.f32`
17 328×	`accelerator-lowering-fma.f64`
14 404×	`accelerator-lowering-fma.f32`
14 404×	`accelerator-lowering-fma.f64`
5 936×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	1768
1	280	1537
2	896	1527
3	2564	1521
4	4609	1521
0	8057	1455
0	26	117
1	155	98
0	1320	94
0	30	123
1	184	113
2	1636	107
0	8783	99
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398
0	6	16
1	39	16
2	286	16
3	3385	16
0	8673	16

Stop Event

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

Compiler

Compiled 191 to 114 computations (40.3% saved)

preprocess62.0ms (0.7%)

Memory: 29.0MiB live, 143.9MiB allocated
Compiler: Compiled 208 to 102 computations (51% 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%)

sample1.3s (15%)

preprocess27.0ms (0.3%)

explain102.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.1%)

localize34.0ms (0.4%)

series5.0ms (0.1%)

rewrite342.0ms (3.9%)

simplify475.0ms (5.4%)

eval50.0ms (0.6%)

prune59.0ms (0.7%)

simplify196.0ms (2.2%)

localize435.0ms (4.9%)

series9.0ms (0.1%)

rewrite106.0ms (1.2%)

simplify719.0ms (8.1%)

eval106.0ms (1.2%)

prune83.0ms (0.9%)

simplify324.0ms (3.7%)

localize76.0ms (0.9%)

series18.0ms (0.2%)

rewrite536.0ms (6%)

simplify378.0ms (4.3%)

eval313.0ms (3.5%)

prune202.0ms (2.3%)

simplify180.0ms (2%)

localize113.0ms (1.3%)

series10.0ms (0.1%)

rewrite492.0ms (5.5%)

simplify444.0ms (5%)

eval213.0ms (2.4%)

prune241.0ms (2.7%)

regimes40.0ms (0.5%)

regimes15.0ms (0.2%)

regimes19.0ms (0.2%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

soundness1.1s (12.2%)

preprocess62.0ms (0.7%)

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