Metrics for Octave 3.8, oct_fill

analyze16.0ms (0.2%)

Memory

-12.9MiB live, 25.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
66.7%	25%	12.5%	0.1%	0%	62.4%	0%	6
66.7%	25%	12.5%	0.1%	0%	62.4%	0%	7
80%	25%	6.2%	0.1%	0%	68.7%	0%	8
80%	25%	6.2%	0.1%	0%	68.7%	0%	9
88.9%	25%	3.1%	0.1%	0%	71.8%	0%	10
88.9%	25%	3.1%	0.1%	0%	71.8%	0%	11
94.1%	25%	1.6%	0.1%	0%	73.4%	0%	12

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.1s (12%)

Memory

41.9MiB live, 1 787.4MiB allocated

Samples

758.0ms	8 256×	0	valid
42.0ms	514×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 576.0ms

ival-div: 206.0ms (35.7% of total)

ival-mult: 175.0ms (30.4% of total)

ival-sqrt: 81.0ms (14.1% of total)

ival-sub: 51.0ms (8.9% of total)

ival-add: 43.0ms (7.5% of total)

exact: 11.0ms (1.9% of total)

ival-true: 6.0ms (1% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess319.0ms (3.4%)

Memory

-9.0MiB live, 223.8MiB allocated

Algorithm

2×	egg-herbie

Rules

2 560×	`accelerator-lowering-fma.f32`
2 560×	`accelerator-lowering-fma.f64`
1 346×	`unsub-neg`
1 036×	`div-sub`
864×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	104
1	104	90
2	368	84
3	1299	84
4	3619	84
5	5957	84
6	7166	84
7	7734	84
0	14	16
1	31	14
2	78	14
3	176	14
4	373	14
5	597	14
6	833	14
7	1410	14
8	2465	14
9	2911	14
10	3068	14
11	3220	14
12	3305	14
13	3311	14
0	3311	13

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))

Outputs

(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))

(fma.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))) #s(literal 0 binary64))

Call 2

Inputs
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))
(* (- (neg a) (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- (neg a) (/ 1 3))))) rand)))
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) (neg rand))))
(neg (* (- (neg a) (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- (neg a) (/ 1 3))))) rand))))
(neg (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) (neg rand)))))
(* (- rand (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- rand (/ 1 3))))) a)))

Outputs
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))
(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ -3 (* a 9))))))
(* (- (neg a) (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- (neg a) (/ 1 3))))) rand)))
(* (- -1/3 a) (+ 1 (/ rand (sqrt (+ -3 (* a -9))))))
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) (neg rand))))
(* (+ a -1/3) (- 1 (/ rand (sqrt (+ -3 (* a 9))))))
(neg (* (- (neg a) (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- (neg a) (/ 1 3))))) rand))))
(* (- -1/3 a) (- -1 (/ rand (sqrt (+ -3 (* a -9))))))
(neg (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) (neg rand)))))
(* (+ a -1/3) (+ (/ rand (sqrt (+ -3 (* a 9)))) -1))
(* (- rand (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- rand (/ 1 3))))) a)))
(* (+ rand -1/3) (+ 1 (/ a (sqrt (* 9 (+ rand -1/3))))))

explain226.0ms (2.4%)

Memory

-10.5MiB live, 349.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand))`
-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))`
-	-	`a`
-	-	`rand`
-	-	`#s(literal 3 binary64)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 9 binary64)`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))`
-	-	`(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))`
-	-	`(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))`
-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)`
-	-	`(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`
-	-	`(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

51.0ms	490×	0	valid
3.0ms	6×	2	valid
2.0ms	12×	1	valid
2.0ms	4×	5	exit

Compiler

Compiled 216 to 56 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-div: 12.0ms (32.1% of total)

ival-mult: 12.0ms (32.1% of total)

ival-sqrt: 4.0ms (10.7% of total)

ival-sub: 3.0ms (8% of total)

ival-add: 3.0ms (8% of total)

adjust: 2.0ms (5.4% of total)

exact: 1.0ms (2.7% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Status

Accuracy

Program

▶

99.8%

(*.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Compiler

Compiled 22 to 13 computations (40.9% saved)

simplify156.0ms (1.7%)

Memory

-0.5MiB live, 193.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
✓	cost-diff	128	(*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))
✓	cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))

Rules

2 560×	`accelerator-lowering-fma.f32`
2 560×	`accelerator-lowering-fma.f64`
768×	`-lowering-.f32`
768×	`-lowering-.f64`
610×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	31	60
2	78	60
3	176	60
4	373	60
5	597	60
6	833	60
7	1410	60
8	2465	60
9	2911	60
10	3068	60
11	3220	60
12	3305	60
13	3311	60
0	3311	54

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))
(- a (/ 1 3))
a
(/ 1 3)
1
3
(+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))
(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
(/ 1 (sqrt (* 9 (- a (/ 1 3)))))
(sqrt (* 9 (- a (/ 1 3))))
(* 9 (- a (/ 1 3)))
9
rand

Outputs
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))
(fma.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))) #s(literal 0 binary64))
(- a (/ 1 3))
(+.f64 a #s(literal -1/3 binary64))
a
(/ 1 3)
#s(literal 1/3 binary64)
1
#s(literal 1 binary64)
3
#s(literal 3 binary64)
(+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))
(+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
(/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))
(/ 1 (sqrt (* 9 (- a (/ 1 3)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))
(sqrt (* 9 (- a (/ 1 3))))
(sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))
(* 9 (- a (/ 1 3)))
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
9
#s(literal 9 binary64)
rand

localize43.0ms (0.5%)

Memory

21.6MiB live, 97.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))
✓	accuracy	99.8%	(sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))))))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)

Samples

23.0ms	245×	0	valid
1.0ms	6×	1	valid
1.0ms	2×	5	exit
1.0ms	3×	2	valid

Compiler

Compiled 86 to 15 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 5.0ms (35.5% of total)

ival-div: 4.0ms (28.4% of total)

ival-sqrt: 2.0ms (14.2% of total)

ival-sub: 1.0ms (7.1% of total)

ival-add: 1.0ms (7.1% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

series31.0ms (0.3%)

Memory

-13.5MiB live, 35.4MiB allocated

Counts

7 → 96

Calls

Call 1

Inputs
#<alt (/ 1 3)>
#<alt (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)>
#<alt (* 9 (- a (/ 1 3)))>
#<alt (- a (/ 1 3))>
#<alt (/ 1 (sqrt (* 9 (- a (/ 1 3)))))>
#<alt (sqrt (* 9 (- a (/ 1 3))))>
#<alt (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))>

Outputs
#<alt (* 1/3 (* rand (sqrt -3)))>
#<alt (+ (* -3/2 (/ (* a rand) (sqrt -3))) (* 1/3 (* rand (sqrt -3))))>
#<alt (+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* -1/6 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))))>
#<alt (+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* a (+ (* -1/6 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))>
#<alt (+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* rand (* (sqrt -1) (+ 1/27 (* -1/36 a)))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))>
#<alt -3>
#<alt (- (* 9 a) 3)>
#<alt (- (* 9 a) 3)>
#<alt (- (* 9 a) 3)>
#<alt (* 9 a)>
#<alt (* a (- 9 (* 3 (/ 1 a))))>
#<alt (* a (- 9 (* 3 (/ 1 a))))>
#<alt (* a (- 9 (* 3 (/ 1 a))))>
#<alt (* 9 a)>
#<alt (* -1 (* a (- (* 3 (/ 1 a)) 9)))>
#<alt (* -1 (* a (- (* 3 (/ 1 a)) 9)))>
#<alt (* -1 (* a (- (* 3 (/ 1 a)) 9)))>
#<alt -1/3>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt a>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt a>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* 1/3 (sqrt -3))>
#<alt (+ (* -3/2 (/ a (sqrt -3))) (* 1/3 (sqrt -3)))>
#<alt (+ (* 1/3 (sqrt -3)) (* a (- (* -1/6 (/ (* a (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 3/2 (/ 1 (sqrt -3))))))>
#<alt (+ (* 1/3 (sqrt -3)) (* a (- (* a (+ (* -1/6 (/ (* a (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3))) (* -1/6 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (sqrt -3))))) (* 3/2 (/ 1 (sqrt -3))))))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a))))>
#<alt (+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a)))))>
#<alt (+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (- 1/27 (* 1/36 a)))) (* 1/3 (sqrt (/ 1 a))))))>
#<alt (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9))))>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))>
#<alt (+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (sqrt -1) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* (sqrt -1) (+ 1/27 (* -1/36 a))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))>
#<alt (* 3 (sqrt -1/3))>
#<alt (+ (* 3/2 (/ a (sqrt -1/3))) (* 3 (sqrt -1/3)))>
#<alt (+ (* 3 (sqrt -1/3)) (* a (+ (* -3/8 (/ a (pow (sqrt -1/3) 3))) (* 3/2 (/ 1 (sqrt -1/3))))))>
#<alt (+ (* 3 (sqrt -1/3)) (* a (+ (* a (- (* 3/16 (/ a (pow (sqrt -1/3) 5))) (* 3/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 3/2 (/ 1 (sqrt -1/3))))))>
#<alt (* 3 (sqrt a))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))>
#<alt (* -1 (* (sqrt a) (* (sqrt -9) (sqrt -1))))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1)))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))))>
#<alt (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3)))))>
#<alt (+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (* 1/2 (/ rand (sqrt -3)))))))>
#<alt (+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))))>
#<alt (+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (+ (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* a (+ (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 1/18 (/ (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3)))))))))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))>
#<alt (* a (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* 1/3 (/ (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) a)))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1/6 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) a)))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* 1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/6 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)) (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)))))>
#<alt (- a 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>

Calls

24 calls:

Time	Variable		Point	Expression
17.0ms	a	@	inf	(/ 1 (sqrt (* 9 (- a (/ 1 3)))))
2.0ms	a	@	-inf	(sqrt (* 9 (- a (/ 1 3))))
2.0ms	rand	@	0	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
1.0ms	a	@	-inf	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
1.0ms	a	@	inf	(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)

rewrite421.0ms (4.6%)

Memory

2.1MiB live, 696.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 424×	`accelerator-lowering-fma.f32`
4 424×	`accelerator-lowering-fma.f64`
3 964×	`-lowering-.f32`
3 964×	`-lowering-.f64`
2 572×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	70	43
2	537	43
3	6480	43
0	8160	39

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 505

Calls

Call 1

Inputs
(/ 1 3)
(* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)
(* 9 (- a (/ 1 3)))
(- a (/ 1 3))
(/ 1 (sqrt (* 9 (- a (/ 1 3)))))
(sqrt (* 9 (- a (/ 1 3))))
(* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand)))

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

simplify505.0ms (5.5%)

Memory

-24.6MiB live, 930.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 592×	`accelerator-lowering-fma.f32`
12 592×	`accelerator-lowering-fma.f64`
5 434×	`+-lowering-+.f64`
5 434×	`+-lowering-+.f32`
5 342×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	339	1835
1	1032	1615
2	3428	1545
0	8039	1436

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 1/3 (* rand (sqrt -3)))
(+ (* -3/2 (/ (* a rand) (sqrt -3))) (* 1/3 (* rand (sqrt -3))))
(+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* -1/6 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))))
(+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* a (+ (* -1/6 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* rand (* (sqrt -1) (+ 1/27 (* -1/36 a)))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
-3
(- (* 9 a) 3)
(- (* 9 a) 3)
(- (* 9 a) 3)
(* 9 a)
(* a (- 9 (* 3 (/ 1 a))))
(* a (- 9 (* 3 (/ 1 a))))
(* a (- 9 (* 3 (/ 1 a))))
(* 9 a)
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
-1/3
(- a 1/3)
(- a 1/3)
(- a 1/3)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* 1/3 (sqrt -3))
(+ (* -3/2 (/ a (sqrt -3))) (* 1/3 (sqrt -3)))
(+ (* 1/3 (sqrt -3)) (* a (- (* -1/6 (/ (* a (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 3/2 (/ 1 (sqrt -3))))))
(+ (* 1/3 (sqrt -3)) (* a (- (* a (+ (* -1/6 (/ (* a (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3))) (* -1/6 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (sqrt -3))))) (* 3/2 (/ 1 (sqrt -3))))))
(* 1/3 (sqrt (/ 1 a)))
(+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a))))
(+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a)))))
(+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (- 1/27 (* 1/36 a)))) (* 1/3 (sqrt (/ 1 a))))))
(* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9))))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (sqrt -1) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* (sqrt -1) (+ 1/27 (* -1/36 a))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))
(* 3 (sqrt -1/3))
(+ (* 3/2 (/ a (sqrt -1/3))) (* 3 (sqrt -1/3)))
(+ (* 3 (sqrt -1/3)) (* a (+ (* -3/8 (/ a (pow (sqrt -1/3) 3))) (* 3/2 (/ 1 (sqrt -1/3))))))
(+ (* 3 (sqrt -1/3)) (* a (+ (* a (- (* 3/16 (/ a (pow (sqrt -1/3) 5))) (* 3/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 3/2 (/ 1 (sqrt -1/3))))))
(* 3 (sqrt a))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))
(* -1 (* (sqrt a) (* (sqrt -9) (sqrt -1))))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1)))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))))
(* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3)))))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (* 1/2 (/ rand (sqrt -3)))))))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (+ (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* a (+ (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 1/18 (/ (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3)))))))))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))
(* a (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* 1/3 (/ (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) a)))))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1/6 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) a)))))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* 1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/6 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)) (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)))))
(- a 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(* 1/3 (* rand (sqrt (- a 1/3))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))

Outputs
(* 1/3 (* rand (sqrt -3)))
(.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))))
(+ (* -3/2 (/ (* a rand) (sqrt -3))) (* 1/3 (* rand (sqrt -3))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 #s(literal -3/2 binary64) (*.f64 rand a)) (sqrt.f64 #s(literal -3 binary64))))
(+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* -1/6 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))) (.f64 a (fma.f64 rand (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 (.f64 #s(literal -27/8 binary64) rand) a) (sqrt.f64 #s(literal -3 binary64))))))
(+ (* 1/3 (* rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* a (+ (* -1/6 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))
(fma.f64 a (fma.f64 rand (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (.f64 #s(literal -1/6 binary64) a) (fma.f64 rand (/.f64 #s(literal 81/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 rand (.f64 a #s(literal 405/8 binary64))) (sqrt.f64 #s(literal -3 binary64)))))) (.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64)))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 rand (fma.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (fma.f64 #s(literal 1/54 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(fma.f64 rand (fma.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (fma.f64 #s(literal 1/54 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 rand (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64))) #s(literal 1/6 binary64))))
(* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))
(/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -9 binary64)))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))
(.f64 (/.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(.f64 (/.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* rand (* (sqrt -1) (+ 1/27 (* -1/36 a)))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (* rand (sqrt -1)) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(-.f64 (.f64 (/.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -9 binary64))) (/.f64 (.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal 1/18 binary64) (sqrt.f64 a))) (sqrt.f64 #s(literal -9 binary64)))) (.f64 a (.f64 a a))))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (/ 1 (- a 1/3)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)))) (.f64 #s(literal 1/3 binary64) rand))
-3
#s(literal -3 binary64)
(- (* 9 a) 3)
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
(- (* 9 a) 3)
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
(- (* 9 a) 3)
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
(* 9 a)
(*.f64 a #s(literal 9 binary64))
(* a (- 9 (* 3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
(* a (- 9 (* 3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
(* a (- 9 (* 3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
(* 9 a)
(*.f64 a #s(literal 9 binary64))
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
(* -1 (* a (- (* 3 (/ 1 a)) 9)))
(*.f64 a (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -3 binary64) a)))
-1/3
#s(literal -1/3 binary64)
(- a 1/3)
(+.f64 a #s(literal -1/3 binary64))
(- a 1/3)
(+.f64 a #s(literal -1/3 binary64))
(- a 1/3)
(+.f64 a #s(literal -1/3 binary64))
a
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 a (/.f64 #s(literal -1/3 binary64) a) a)
(* 1/3 (sqrt -3))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal -3 binary64)))
(+ (* -3/2 (/ a (sqrt -3))) (* 1/3 (sqrt -3)))
(fma.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal -3 binary64)) (*.f64 #s(literal -3/2 binary64) (/.f64 a (sqrt.f64 #s(literal -3 binary64)))))
(+ (* 1/3 (sqrt -3)) (* a (- (* -1/6 (/ (* a (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 3/2 (/ 1 (sqrt -3))))))
(fma.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal -3 binary64)) (*.f64 a (fma.f64 a (/.f64 #s(literal -27/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(+ (* 1/3 (sqrt -3)) (* a (- (* a (+ (* -1/6 (/ (* a (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3))) (* -1/6 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (sqrt -3))))) (* 3/2 (/ 1 (sqrt -3))))))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal -135/16 binary64) (/.f64 a (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal -27/8 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal -3 binary64))))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a))))
(fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a))))))
(+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (* 1/3 (sqrt (/ 1 a)))))
(fma.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (fma.f64 #s(literal 1/54 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(+ (* 1/54 (sqrt (/ 1 (pow a 5)))) (+ (* 1/18 (sqrt (/ 1 (pow a 3)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 7))) (- 1/27 (* 1/36 a)))) (* 1/3 (sqrt (/ 1 a))))))
(fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64)) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/54 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))))))
(* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64)))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9))))
(.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))
(.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) (/ (sqrt -1) (sqrt -9)))) (* 1/2 (* (sqrt (/ 1 a)) (/ (* (sqrt -1) (+ 1/27 (* -1/36 a))) (sqrt -9))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) (/ (sqrt -1) (sqrt -9)))) (* (sqrt (/ 1 a)) (/ (sqrt -1) (sqrt -9)))))
(-.f64 (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -9 binary64))) (/.f64 (.f64 (.f64 #s(literal 1/18 binary64) (sqrt.f64 a)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64)))) (.f64 a (*.f64 a a))))
(* 3 (sqrt -1/3))
(*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (* 3/2 (/ a (sqrt -1/3))) (* 3 (sqrt -1/3)))
(fma.f64 a (/.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* 3 (sqrt -1/3)) (* a (+ (* -3/8 (/ a (pow (sqrt -1/3) 3))) (* 3/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (/.f64 #s(literal 9/8 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* 3 (sqrt -1/3)) (* a (+ (* a (- (* 3/16 (/ a (pow (sqrt -1/3) 5))) (* 3/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 3/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (fma.f64 a (/.f64 #s(literal 3/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 9/8 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (/.f64 #s(literal 3/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal -1/3 binary64))))
(* 3 (sqrt a))
(*.f64 #s(literal 3 binary64) (sqrt.f64 a))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 3 binary64))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/24 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 3 binary64)))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/24 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/144 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 3 binary64))))))
(* -1 (* (sqrt a) (* (sqrt -9) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -9 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 a))))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))
(.f64 a (.f64 (.f64 (sqrt.f64 #s(literal -9 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1)))))))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -9 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* (sqrt -9) (sqrt -1)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* (sqrt -9) (sqrt -1)))) (* (sqrt (/ 1 a)) (* (sqrt -9) (sqrt -1))))))))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -9 binary64))) (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 1/432 binary64))))) (-.f64 #s(literal 0 binary64) a))
(* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3)))))
(fma.f64 (*.f64 rand (sqrt.f64 #s(literal -3 binary64))) #s(literal -1/9 binary64) #s(literal -1/3 binary64))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (* 1/2 (/ rand (sqrt -3)))))))
(fma.f64 a (fma.f64 rand (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 rand (sqrt.f64 #s(literal -3 binary64))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))))))
(fma.f64 a (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))) (fma.f64 (/.f64 rand (sqrt.f64 #s(literal -3 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/2 binary64) a)) (fma.f64 (.f64 #s(literal 9/8 binary64) rand) (/.f64 a (sqrt.f64 #s(literal -3 binary64))) #s(literal 1 binary64)))) (fma.f64 (.f64 rand (sqrt.f64 #s(literal -3 binary64))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)))
(+ (* -1/3 (+ 1 (* 1/3 (* rand (sqrt -3))))) (* a (+ 1 (+ (* 1/3 (* rand (sqrt -3))) (+ (* 1/2 (/ rand (sqrt -3))) (* a (+ (* -3/2 (/ rand (sqrt -3))) (+ (* 1/18 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* a (+ (* -1/6 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))) (* 1/18 (/ (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2))))) (sqrt -3)))))))))))))
(fma.f64 a (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -3 binary64))) (fma.f64 (/.f64 rand (sqrt.f64 #s(literal -3 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/2 binary64) a)) (fma.f64 a (fma.f64 (/.f64 (.f64 rand #s(literal 81/4 binary64)) (sqrt.f64 #s(literal -3 binary64))) (+.f64 #s(literal 1/18 binary64) (.f64 #s(literal -1/6 binary64) a)) (/.f64 (.f64 a (.f64 #s(literal 45/16 binary64) rand)) (sqrt.f64 #s(literal -3 binary64)))) #s(literal 1 binary64)))) (fma.f64 (*.f64 rand (sqrt.f64 #s(literal -3 binary64))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(.f64 a (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)) (/.f64 #s(literal -1/3 binary64) a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)) (/.f64 #s(literal -1/3 binary64) a) #s(literal 1 binary64))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)) (/.f64 #s(literal -1/3 binary64) a) #s(literal 1 binary64))))
(* a (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))
(.f64 a (fma.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -9 binary64))) #s(literal 1 binary64)))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* 1/3 (/ (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) a)))))
(-.f64 #s(literal 0 binary64) (.f64 a (-.f64 (.f64 (fma.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1/3 binary64) a)) (fma.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -9 binary64))) #s(literal 1 binary64)))))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1/6 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) a)))))
(.f64 a (+.f64 (fma.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (fma.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -9 binary64))) #s(literal -1/2 binary64) #s(literal -1/3 binary64)) a)))
(* -1 (* a (+ (* -1 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9))))) (* -1 (/ (+ (* -1 (/ (+ (* -1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (+ (* 1/18 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))) (* 1/6 (* (sqrt a) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)) (* -1/3 (+ 1 (* (sqrt (/ 1 a)) (/ (* rand (sqrt -1)) (sqrt -9)))))) a)))))
(.f64 a (+.f64 (fma.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (sqrt.f64 #s(literal -9 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/3 binary64) (sqrt.f64 #s(literal -9 binary64))) #s(literal -1/3 binary64)) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 (/.f64 (.f64 rand (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -9 binary64))) (sqrt.f64 a)) #s(literal 0 binary64)) a)) a)))
(- a 1/3)
(+.f64 a #s(literal -1/3 binary64))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))

eval205.0ms (2.2%)

Memory: 40.8MiB live, 191.9MiB allocated
Compiler: Compiled 20 534 to 2 646 computations (87.1% saved)

prune157.0ms (1.7%)

Memory

-25.2MiB live, 184.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	682	9	691
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	683	9	692

Accuracy

100.0%

Counts

692 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(fma.f64 (/.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64)))) rand (+.f64 a #s(literal -1/3 binary64)))
	90.2%	(fma.f64 (/.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (*.f64 (+.f64 a #s(literal -1/3 binary64)) rand) (+.f64 a #s(literal -1/3 binary64)))
▶	99.8%	(fma.f64 (*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))
▶	99.8%	(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
▶	61.8%	(+.f64 a #s(literal -1/3 binary64))
▶	99.8%	(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
	39.0%	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
	78.6%	(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
▶	98.2%	(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))

Compiler

Compiled 242 to 156 computations (35.5% saved)

simplify65.0ms (0.7%)

Memory

22.4MiB live, 101.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))
✓	cost-diff	0	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	64	(fma.f64 (*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))
✓	cost-diff	128	(*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64))
✓	cost-diff	0	(/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64)))))
✓	cost-diff	0	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	0	(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) a)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
✓	cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) rand)
✓	cost-diff	0	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	cost-diff	0	(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))

Rules

1 372×	`accelerator-lowering-fma.f32`
1 372×	`accelerator-lowering-fma.f64`
732×	`-lowering-.f32`
732×	`-lowering-.f64`
436×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	157
1	67	157
2	158	155
3	401	155
4	831	155
5	1124	155
6	1275	155
7	1579	155
8	1579	155
9	1607	155
10	1649	155
11	1649	155
12	1651	155
0	1651	145

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (sqrt (+ a -1/3)) (* 1/3 rand)) (+ a -1/3))
(sqrt (+ a -1/3))
(+ a -1/3)
a
-1/3
(* 1/3 rand)
1/3
rand
(+ a -1/3)
a
-1/3
(* a (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1))
a
(+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1)
(sqrt (/ 1 a))
(/ 1 a)
1
(* 1/3 rand)
1/3
rand
(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
(+ a -1/3)
a
-1/3
(+ 1 (/ rand (sqrt (+ (* 9 a) -3))))
1
(/ rand (sqrt (+ (* 9 a) -3)))
rand
(sqrt (+ (* 9 a) -3))
(+ (* 9 a) -3)
9
-3
(+ (* (* (+ a -1/3) 1/3) (/ rand (sqrt (+ a -1/3)))) (+ a -1/3))
(* (+ a -1/3) 1/3)
(+ a -1/3)
a
-1/3
1/3
(/ rand (sqrt (+ a -1/3)))
rand
(sqrt (+ a -1/3))

Outputs
(+ (* (sqrt (+ a -1/3)) (* 1/3 rand)) (+ a -1/3))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(sqrt (+ a -1/3))
(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
1/3
#s(literal 1/3 binary64)
rand
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
(* a (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1))
(.f64 a (fma.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 1 binary64)))
a
(+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 1 binary64))
(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
1
#s(literal 1 binary64)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
1/3
#s(literal 1/3 binary64)
rand
(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
(+ 1 (/ rand (sqrt (+ (* 9 a) -3))))
(+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
1
#s(literal 1 binary64)
(/ rand (sqrt (+ (* 9 a) -3)))
(/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))
rand
(sqrt (+ (* 9 a) -3))
(sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))
(+ (* 9 a) -3)
(fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))
9
#s(literal 9 binary64)
-3
#s(literal -3 binary64)
(+ (* (* (+ a -1/3) 1/3) (/ rand (sqrt (+ a -1/3)))) (+ a -1/3))
(*.f64 (+.f64 a #s(literal -1/3 binary64)) (fma.f64 #s(literal 1/3 binary64) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) #s(literal 1 binary64)))
(* (+ a -1/3) 1/3)
(fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
1/3
#s(literal 1/3 binary64)
(/ rand (sqrt (+ a -1/3)))
(/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))
rand
(sqrt (+ a -1/3))
(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))

localize106.0ms (1.1%)

Memory

-28.0MiB live, 244.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.9%	(fma.f64 (*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.6%	(/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))
✓	accuracy	99.5%	(*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64)))))
✓	accuracy	99.9%	(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
✓	accuracy	99.8%	(sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64)))
✓	accuracy	99.6%	(/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))
✓	accuracy	99.9%	(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
✓	accuracy	99.8%	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) rand)
✓	accuracy	100.0%	(+.f64 a #s(literal -1/3 binary64))
✓	accuracy	100.0%	(+.f64 a #s(literal -1/3 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.9%	(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) rand)

Samples

52.0ms	247×	0	valid
7.0ms	6×	1	valid
1.0ms	3×	2	valid

Compiler

Compiled 150 to 29 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-div: 11.0ms (25.1% of total)

ival-mult: 11.0ms (25.1% of total)

ival-add: 8.0ms (18.3% of total)

const: 7.0ms (16% of total)

ival-sqrt: 5.0ms (11.4% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.3%)

Memory

22.3MiB live, 62.4MiB allocated

Counts

15 → 276

Calls

Call 1

Inputs
#<alt (+ (* (sqrt (+ a -1/3)) (* 1/3 rand)) (+ a -1/3))>
#<alt (sqrt (+ a -1/3))>
#<alt (+ a -1/3)>
#<alt (* 1/3 rand)>
#<alt (* a (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1))>
#<alt (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1)>
#<alt (sqrt (/ 1 a))>
#<alt (/ 1 a)>
#<alt (* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))>
#<alt (+ 1 (/ rand (sqrt (+ (* 9 a) -3))))>
#<alt (/ rand (sqrt (+ (* 9 a) -3)))>
#<alt (* (+ a -1/3) 1/3)>
#<alt (+ (* (* (+ a -1/3) 1/3) (/ rand (sqrt (+ a -1/3)))) (+ a -1/3))>
#<alt (/ rand (sqrt (+ a -1/3)))>
#<alt (sqrt (+ (* 9 a) -3))>

Outputs
#<alt (- (* 1/3 (* rand (sqrt -1/3))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))>
#<alt (- a 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (sqrt -1/3)>
#<alt (+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))>
#<alt (+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt -1/3>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt a>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt a>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt a>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))>
#<alt 1>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (sqrt (/ 1 a))>
#<alt (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (* -1/3 (+ 1 (* rand (sqrt -1/3))))>
#<alt (+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* rand (sqrt -1/3))))))>
#<alt (+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))))))>
#<alt (+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (+ (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* a (+ (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* 1/6 (/ (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2))))) (sqrt -1/3)))))))) (* rand (sqrt -1/3)))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))>
#<alt (* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1/18 (* (sqrt (/ 1 a)) rand))) a)))))>
#<alt (* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/54 (* (sqrt (/ 1 a)) rand)) (+ (* 1/54 (* (sqrt (/ 1 a)) rand)) (* 1/18 (* (sqrt a) rand)))) a)) (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))) a)))))>
#<alt (- a 1/3)>
#<alt (- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)>
#<alt (- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)>
#<alt (- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)>
#<alt (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))>
#<alt (* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))>
#<alt (* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))>
#<alt 1>
#<alt (+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))>
#<alt (+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))>
#<alt (+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))>
#<alt (* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))>
#<alt (* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))>
#<alt (+ 1 (* rand (sqrt -1/3)))>
#<alt (+ 1 (+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3))))>
#<alt (+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3))))>
#<alt (+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3))))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a)))))))))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (+ 1 (+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt (/ 1 (- (* 9 a) 3))))>
#<alt (* rand (sqrt -1/3))>
#<alt (+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3)))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a))))))))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt -1/9>
#<alt (- (* 1/3 a) 1/9)>
#<alt (- (* 1/3 a) 1/9)>
#<alt (- (* 1/3 a) 1/9)>
#<alt (* 1/3 a)>
#<alt (* a (- 1/3 (* 1/9 (/ 1 a))))>
#<alt (* a (- 1/3 (* 1/9 (/ 1 a))))>
#<alt (* a (- 1/3 (* 1/9 (/ 1 a))))>
#<alt (* 1/3 a)>
#<alt (* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))>
#<alt (* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))>
#<alt (* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))>
#<alt (- (* 1/3 (* rand (sqrt -1/3))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))>
#<alt (* -1 (* a (- (* -1/3 (* (sqrt (/ 1 a)) rand)) 1)))>
#<alt (* -1 (* a (- (+ (* -1/3 (* (sqrt (/ 1 a)) rand)) (* 1/3 (/ 1 a))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* 1/18 (* (sqrt (/ 1 a)) rand)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/18 (* (sqrt a) rand)) (* 1/216 (* (sqrt (/ 1 a)) rand))) a)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))>
#<alt (- a 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt (/ 1 (- a 1/3))))>
#<alt (* rand (sqrt -3))>
#<alt (+ (* -9/2 (/ (* a rand) (sqrt -3))) (* rand (sqrt -3)))>
#<alt (+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* -1/2 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))) (* rand (sqrt -3)))>
#<alt (+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/2 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))) (* rand (sqrt -3)))>
#<alt (* (sqrt (/ 1 a)) rand)>
#<alt (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))>
#<alt (+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))>
#<alt (+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* (sqrt (/ 1 a)) rand))))>
#<alt (* (sqrt (/ 1 a)) rand)>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))>
#<alt (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand)))>
#<alt (+ (* -1 (/ (+ (* 1/18 (* (sqrt a) rand)) (* 1/2 (* (sqrt (/ 1 a)) (* rand (+ 1/27 (* -1/36 a)))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))>
#<alt (sqrt -3)>
#<alt (+ (sqrt -3) (* 9/2 (/ a (sqrt -3))))>
#<alt (+ (sqrt -3) (* a (+ (* -81/8 (/ a (pow (sqrt -3) 3))) (* 9/2 (/ 1 (sqrt -3))))))>
#<alt (+ (sqrt -3) (* a (+ (* a (- (* 729/16 (/ a (pow (sqrt -3) 5))) (* 81/8 (/ 1 (pow (sqrt -3) 3))))) (* 9/2 (/ 1 (sqrt -3))))))>
#<alt (* 3 (sqrt a))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))>
#<alt (* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))>
#<alt (* -3 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/144 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))>

Calls

69 calls:

Time	Variable		Point	Expression
3.0ms	a	@	-inf	(* a (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1))
2.0ms	rand	@	inf	(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
2.0ms	a	@	0	(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
1.0ms	rand	@	0	(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
1.0ms	a	@	-inf	(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))

rewrite444.0ms (4.8%)

Memory

-17.6MiB live, 616.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 026×	`-lowering-.f32`
5 026×	`-lowering-.f64`
3 968×	`/-lowering-/.f32`
3 968×	`/-lowering-/.f64`
3 146×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	116
1	167	111
2	1462	109
0	8167	99

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 491

Calls

Call 1

Inputs
(+ (* (sqrt (+ a -1/3)) (* 1/3 rand)) (+ a -1/3))
(sqrt (+ a -1/3))
(+ a -1/3)
(* 1/3 rand)
(* a (+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1))
(+ (* (sqrt (/ 1 a)) (* 1/3 rand)) 1)
(sqrt (/ 1 a))
(/ 1 a)
(* (+ a -1/3) (+ 1 (/ rand (sqrt (+ (* 9 a) -3)))))
(+ 1 (/ rand (sqrt (+ (* 9 a) -3))))
(/ rand (sqrt (+ (* 9 a) -3)))
(* (+ a -1/3) 1/3)
(+ (* (* (+ a -1/3) 1/3) (/ rand (sqrt (+ a -1/3)))) (+ a -1/3))
(/ rand (sqrt (+ a -1/3)))
(sqrt (+ (* 9 a) -3))

Outputs
(+.f64 a (+.f64 #s(literal -1/3 binary64) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))))
(+.f64 #s(literal -1/3 binary64) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) a))
(+.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(+.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)) (+.f64 a #s(literal -1/3 binary64)))
(+.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) a) #s(literal -1/3 binary64))
(+.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)) a)
(-.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand))) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) (neg.f64 (+.f64 a #s(literal -1/3 binary64))))) (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (neg.f64 (+.f64 a #s(literal -1/3 binary64))))))
(-.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))) (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand))) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand)))))
(-.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) a) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) a)) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) a) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) a) #s(literal -1/3 binary64))))
(fma.f64 a #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))))
(fma.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) (*.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 rand (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) #s(literal 1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 #s(literal 1 binary64) a (+.f64 #s(literal -1/3 binary64) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))))
(fma.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(fma.f64 (fma.f64 a (.f64 a a) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 a a #s(literal 1/9 binary64)) (.f64 a #s(literal -1/3 binary64)))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(fma.f64 (fma.f64 a a #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal 1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) #s(literal 1/3 binary64)) rand (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))))) (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) (neg.f64 (+.f64 a #s(literal -1/3 binary64)))) (-.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))))) (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand) (neg.f64 (+.f64 a #s(literal -1/3 binary64)))) (-.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (.f64 #s(literal 1/3 binary64) rand) (.f64 #s(literal 1/3 binary64) rand))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))))))
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(fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))) #s(literal -1/3 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))))) a))
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(/.f64 (neg.f64 (fma.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (-.f64 (fma.f64 a a #s(literal 1/9 binary64)) (.f64 a #s(literal -1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (fma.f64 a (.f64 a a) #s(literal -1/27 binary64))))) (neg.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 a a #s(literal 1/9 binary64)) (.f64 a #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (+.f64 a #s(literal 1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (fma.f64 a a #s(literal -1/9 binary64))))) (neg.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (+.f64 a #s(literal 1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))))) (neg.f64 (neg.f64 (-.f64 (/.f64 (*.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (fma.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a)) #s(literal -1/27 binary64))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (-.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64))))) (neg.f64 (-.f64 (+.f64 a #s(literal -1/3 binary64)) (/.f64 (*.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a)) #s(literal 1/9 binary64))) (neg.f64 (-.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) #s(literal -1/3 binary64))))
(/.f64 (fma.f64 a (.f64 a a) (pow.f64 (+.f64 #s(literal -1/3 binary64) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) #s(literal 3 binary64))) (fma.f64 a a (-.f64 (.f64 (+.f64 #s(literal -1/3 binary64) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (+.f64 #s(literal -1/3 binary64) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))) (.f64 a (+.f64 #s(literal -1/3 binary64) (/.f64 (*.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))))))
(/.f64 (+.f64 #s(literal -1/27 binary64) (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a)))) (+.f64 #s(literal 1/9 binary64) (-.f64 (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a)) (.f64 #s(literal -1/3 binary64) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) a)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) #s(literal -1/3 binary64)) #s(literal 3 binary64)) (.f64 a (.f64 a a))) (fma.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) #s(literal -1/3 binary64)) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) #s(literal -1/3 binary64)) (-.f64 (.f64 a a) (.f64 (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) #s(literal -1/3 binary64)) a))))
(pow.f64 (/.f64 (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64)))) (fma.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64))) (*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (*.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64))))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (+.f64 a #s(literal -1/3 binary64))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))) (/.f64 rand (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))))
(neg.f64 (/.f64 rand (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) rand) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))
(/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) rand) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))
(/.f64 (*.f64 rand #s(literal 1 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) rand)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))))
(/.f64 (neg.f64 (*.f64 rand #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) rand))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 rand (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))))
(*.f64 (-.f64 #s(literal 0 binary64) rand) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) rand)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) rand) #s(literal -1 binary64)))
(*.f64 (/.f64 rand (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (.f64 a #s(literal -27 binary64)))) (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64)) (fma.f64 (*.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64))) (sqrt.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (.f64 a #s(literal -27 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64))) (sqrt.f64 (+.f64 #s(literal 9 binary64) (-.f64 (.f64 (.f64 a a) #s(literal 81 binary64)) (*.f64 a #s(literal -27 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (*.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64))) (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (.f64 a #s(literal -27 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 9 binary64) (.f64 (.f64 a a) #s(literal 81 binary64)))) (sqrt.f64 (-.f64 #s(literal -3 binary64) (*.f64 a #s(literal 9 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (.f64 a #s(literal -27 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64)))))
(pow.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (*.f64 a #s(literal -27 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 a (.f64 a a)) #s(literal 729 binary64) #s(literal -27 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 a a) #s(literal 81 binary64) (-.f64 #s(literal 9 binary64) (*.f64 a #s(literal -27 binary64)))))))
(.f64 (sqrt.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 a a) #s(literal 81 binary64) #s(literal -9 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)) #s(literal 1/4 binary64)))

simplify462.0ms (5%)

Memory

-10.6MiB live, 919.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 082×	`accelerator-lowering-fma.f32`
11 082×	`accelerator-lowering-fma.f64`
5 666×	`-lowering-.f32`
5 666×	`-lowering-.f64`
3 732×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	539	4095
1	1661	3661
2	5735	3579
0	8320	3271

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(- a 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(* 1/3 (* rand (sqrt (- a 1/3))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(sqrt -1/3)
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
-1/3
(- a 1/3)
(- a 1/3)
(- a 1/3)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 (* (sqrt a) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
a
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* 1/3 (* (sqrt a) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* 1/3 (* (sqrt a) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
1
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(sqrt (/ 1 a))
(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(* -1/3 (+ 1 (* rand (sqrt -1/3))))
(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* rand (sqrt -1/3))))))
(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))))))
(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (+ (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* a (+ (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* 1/6 (/ (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2))))) (sqrt -1/3)))))))) (* rand (sqrt -1/3)))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)))))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1/18 (* (sqrt (/ 1 a)) rand))) a)))))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/54 (* (sqrt (/ 1 a)) rand)) (+ (* 1/54 (* (sqrt (/ 1 a)) rand)) (* 1/18 (* (sqrt a) rand)))) a)) (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))) a)))))
(- a 1/3)
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
1
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(+ 1 (* rand (sqrt -1/3)))
(+ 1 (+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3))))
(+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3))))
(+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3))))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a)))))))))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(+ 1 (+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(* rand (sqrt -1/3))
(+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))
(+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a))))))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
-1/9
(- (* 1/3 a) 1/9)
(- (* 1/3 a) 1/9)
(- (* 1/3 a) 1/9)
(* 1/3 a)
(* a (- 1/3 (* 1/9 (/ 1 a))))
(* a (- 1/3 (* 1/9 (/ 1 a))))
(* a (- 1/3 (* 1/9 (/ 1 a))))
(* 1/3 a)
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(* -1 (* a (- (* -1/3 (* (sqrt (/ 1 a)) rand)) 1)))
(* -1 (* a (- (+ (* -1/3 (* (sqrt (/ 1 a)) rand)) (* 1/3 (/ 1 a))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* 1/18 (* (sqrt (/ 1 a)) rand)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/18 (* (sqrt a) rand)) (* 1/216 (* (sqrt (/ 1 a)) rand))) a)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))
(- a 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(* 1/3 (* rand (sqrt (- a 1/3))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt (/ 1 (- a 1/3))))
(* rand (sqrt -3))
(+ (* -9/2 (/ (* a rand) (sqrt -3))) (* rand (sqrt -3)))
(+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* -1/2 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))) (* rand (sqrt -3)))
(+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/2 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))) (* rand (sqrt -3)))
(* (sqrt (/ 1 a)) rand)
(+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* (sqrt (/ 1 a)) rand))))
(* (sqrt (/ 1 a)) rand)
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand)))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) rand)) (* 1/2 (* (sqrt (/ 1 a)) (* rand (+ 1/27 (* -1/36 a)))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(sqrt -3)
(+ (sqrt -3) (* 9/2 (/ a (sqrt -3))))
(+ (sqrt -3) (* a (+ (* -81/8 (/ a (pow (sqrt -3) 3))) (* 9/2 (/ 1 (sqrt -3))))))
(+ (sqrt -3) (* a (+ (* a (- (* 729/16 (/ a (pow (sqrt -3) 5))) (* 81/8 (/ 1 (pow (sqrt -3) 3))))) (* 9/2 (/ 1 (sqrt -3))))))
(* 3 (sqrt a))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))
(* -3 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/144 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))

Outputs
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(fma.f64 a (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(fma.f64 a (fma.f64 a (/.f64 (.f64 #s(literal 1/8 binary64) rand) (sqrt.f64 #s(literal -1/3 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(fma.f64 a (fma.f64 a (fma.f64 a (.f64 (/.f64 rand (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) #s(literal 1/48 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) rand) (sqrt.f64 #s(literal -1/3 binary64)))) (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(*.f64 a (fma.f64 #s(literal 1/3 binary64) (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (/.f64 #s(literal -1 binary64) a)) #s(literal 1 binary64)))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(.f64 a (+.f64 #s(literal 1 binary64) (fma.f64 rand (fma.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))))) (/.f64 #s(literal -1/3 binary64) a))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))
(*.f64 a (fma.f64 #s(literal 1/3 binary64) (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (/.f64 #s(literal -1 binary64) a)) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal 1/18 binary64)) #s(literal -1/3 binary64)) a)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(.f64 a (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 1/216 binary64) (.f64 #s(literal -1/18 binary64) (sqrt.f64 a)))) a)) a))))
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
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(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
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(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
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(sqrt -1/3)
(sqrt.f64 #s(literal -1/3 binary64))
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1/3 binary64))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 (/.f64 a (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 3/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal 1/16 binary64) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(.f64 a (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64))) (fma.f64 #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) a) (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (fma.f64 #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))) (-.f64 #s(literal 0 binary64) a))
-1/3
#s(literal -1/3 binary64)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
(* a (- 1 (* 1/3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
(* a (- 1 (* 1/3 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a)))
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
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(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
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(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64)))
a
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a) a)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* 1/3 (* (sqrt (/ 1 a)) rand))
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(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
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(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
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(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
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(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
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(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
(sqrt.f64 (/.f64 #s(literal 1 binary64) a))
(sqrt (/ 1 a))
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(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
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(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
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(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* (sqrt (/ 1 a)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(/ 1 a)
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(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
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(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
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(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
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(/ 1 a)
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(/ 1 a)
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(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
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(* -1/3 (+ 1 (* rand (sqrt -1/3))))
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(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* rand (sqrt -1/3))))))
(fma.f64 a (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal -1/3 binary64)))
(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))))))
(fma.f64 #s(literal -1/3 binary64) (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 a (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) (fma.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) a)) (/.f64 (.f64 a (*.f64 #s(literal 3/8 binary64) rand)) (sqrt.f64 #s(literal -1/3 binary64))))) a))
(+ (* -1/3 (+ 1 (* rand (sqrt -1/3)))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (+ (* 1/6 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* a (+ (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))) (* 1/6 (/ (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2))))) (sqrt -1/3)))))))) (* rand (sqrt -1/3)))))))
(fma.f64 #s(literal -1/3 binary64) (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64)) (fma.f64 a (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) (fma.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) a)) (.f64 a (fma.f64 (/.f64 (.f64 rand #s(literal 9/4 binary64)) (sqrt.f64 #s(literal -1/3 binary64))) (+.f64 #s(literal 1/6 binary64) (.f64 #s(literal -1/2 binary64) a)) (/.f64 (.f64 a (.f64 #s(literal 15/16 binary64) rand)) (sqrt.f64 #s(literal -1/3 binary64))))))) a))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(fma.f64 a (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (/.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)) a)) a)
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(fma.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) (/.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)) a)) a)
(* a (+ 1 (+ (* -1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))))
(fma.f64 a (+.f64 (/.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/9 binary64) #s(literal -1/3 binary64)) a) (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) #s(literal 0 binary64))) a)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) a)))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 #s(literal 1/3 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)) a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal -1/3 binary64)) #s(literal -1 binary64)))))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1/18 (* (sqrt (/ 1 a)) rand))) a)))))
(.f64 a (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (/.f64 (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/6 binary64))) a))))
(* -1 (* a (+ (* -1 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/54 (* (sqrt (/ 1 a)) rand)) (+ (* 1/54 (* (sqrt (/ 1 a)) rand)) (* 1/18 (* (sqrt a) rand)))) a)) (* -1/3 (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))) a)))))
(.f64 a (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)) (/.f64 (+.f64 #s(literal -1/3 binary64) (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/9 binary64) (/.f64 (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal -1/18 binary64)) #s(literal 0 binary64)) a))) a)))
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(*.f64 (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(*.f64 (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))) 1/3)
(*.f64 (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal -1/3 binary64) a))
(* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))
(.f64 (.f64 rand (+.f64 #s(literal -1/3 binary64) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3)))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* (* rand (- a 1/3)) (sqrt (/ 1 (- (* 9 a) 3))))
(.f64 (.f64 rand (+.f64 #s(literal -1/3 binary64) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (* (- a 1/3) (sqrt (/ 1 (- (* 9 a) 3))))) (* -1 (/ (- a 1/3) rand)))))
(*.f64 rand (fma.f64 (+.f64 #s(literal -1/3 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
1
#s(literal 1 binary64)
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(+ 1 (* rand (sqrt (/ 1 (- (* 9 a) 3)))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* rand (+ (sqrt (/ 1 (- (* 9 a) 3))) (/ 1 rand)))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(* -1 (* rand (- (* -1 (sqrt (/ 1 (- (* 9 a) 3)))) (/ 1 rand))))
(fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))) #s(literal 1 binary64))
(+ 1 (* rand (sqrt -1/3)))
(fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64))
(+ 1 (+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3))))
(fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) (fma.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (*.f64 #s(literal -1/2 binary64) a) #s(literal 1 binary64)))
(+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3))))
(fma.f64 (.f64 #s(literal -1/2 binary64) a) (fma.f64 (.f64 rand a) (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))) (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(+ 1 (+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3))))
(fma.f64 a (.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 rand (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 (.f64 (*.f64 rand a) #s(literal 45/8 binary64)) (sqrt.f64 #s(literal -1/3 binary64)))) a (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))) (fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 1 binary64)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal 1/18 binary64))) #s(literal 1 binary64))
(+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(fma.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/54 binary64) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal 1/18 binary64)))) #s(literal 1 binary64))
(+ 1 (+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a)))))))))
(fma.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/54 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) (fma.f64 rand (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 3/2 binary64)) (fma.f64 a #s(literal -1/324 binary64) #s(literal 1/243 binary64)) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) #s(literal 1 binary64)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))))) #s(literal 1 binary64))
(+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(fma.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/54 binary64) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a))))))) #s(literal 1 binary64))
(+ 1 (+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(-.f64 (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) #s(literal 1 binary64)) (/.f64 (.f64 rand (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 3/2 binary64)) (fma.f64 a #s(literal -1/324 binary64) #s(literal 1/243 binary64)) (.f64 (sqrt.f64 a) #s(literal 1/54 binary64)))) (.f64 a (.f64 a a))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt (/ 1 (- (* 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a #s(literal 9 binary64) #s(literal -3 binary64)))))
(* rand (sqrt -1/3))
(*.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))
(+ (* -1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) (/.f64 (.f64 (.f64 rand a) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* -1/2 (/ (* a (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))))) (sqrt -1/3))))) (* rand (sqrt -1/3)))
(fma.f64 (.f64 #s(literal -1/2 binary64) a) (fma.f64 (.f64 rand a) (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))) (*.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* a (+ (* -1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 9 (* 1/2 (/ (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2)))) (pow (sqrt -1/3) 2)))))) (sqrt -1/3))) (* -1/2 (/ (* rand (+ 3 (* 1/4 (/ 1 (pow (sqrt -1/3) 2))))) (sqrt -1/3))))))) (* rand (sqrt -1/3)))
(fma.f64 a (.f64 #s(literal -1/2 binary64) (fma.f64 (fma.f64 rand (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 (.f64 (.f64 rand a) #s(literal 45/8 binary64)) (sqrt.f64 #s(literal -1/3 binary64)))) a (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/54 binary64) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64)))))
(+ (* 1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/3 (* (sqrt (/ 1 a)) rand)) (* 3/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/243 (* 1/324 a))))))))
(fma.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/54 binary64) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (.f64 rand (fma.f64 a #s(literal -1/324 binary64) #s(literal 1/243 binary64))) #s(literal 3/2 binary64))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))
(.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))))
(+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/54 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/54 binary64) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))))))
(+ (* -1 (/ (+ (* 1/54 (* (sqrt a) rand)) (* 3/2 (* (sqrt (/ 1 a)) (* rand (+ 1/243 (* -1/324 a)))))) (pow a 3))) (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(-.f64 (.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))))) (/.f64 (.f64 rand (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 3/2 binary64)) (fma.f64 a #s(literal -1/324 binary64) #s(literal 1/243 binary64)) (.f64 (sqrt.f64 a) #s(literal 1/54 binary64)))) (.f64 a (*.f64 a a))))
-1/9
#s(literal -1/9 binary64)
(- (* 1/3 a) 1/9)
(fma.f64 #s(literal 1/3 binary64) a #s(literal -1/9 binary64))
(- (* 1/3 a) 1/9)
(fma.f64 #s(literal 1/3 binary64) a #s(literal -1/9 binary64))
(- (* 1/3 a) 1/9)
(fma.f64 #s(literal 1/3 binary64) a #s(literal -1/9 binary64))
(* 1/3 a)
(*.f64 #s(literal 1/3 binary64) a)
(* a (- 1/3 (* 1/9 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(* a (- 1/3 (* 1/9 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(* a (- 1/3 (* 1/9 (/ 1 a))))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(* 1/3 a)
(*.f64 #s(literal 1/3 binary64) a)
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(* -1 (* a (- (* 1/9 (/ 1 a)) 1/3)))
(*.f64 a (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/9 binary64) a)))
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(fma.f64 a (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(fma.f64 a (fma.f64 a (/.f64 (.f64 #s(literal 1/8 binary64) rand) (sqrt.f64 #s(literal -1/3 binary64))) (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(fma.f64 a (fma.f64 a (fma.f64 a (.f64 (/.f64 rand (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) #s(literal 1/48 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) rand) (sqrt.f64 #s(literal -1/3 binary64)))) (fma.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1/3 binary64)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal -1/3 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(*.f64 a (fma.f64 #s(literal 1/3 binary64) (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (/.f64 #s(literal -1 binary64) a)) #s(literal 1 binary64)))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/3 binary64) a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(.f64 a (+.f64 #s(literal 1 binary64) (fma.f64 rand (fma.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a))))))) (/.f64 #s(literal -1/3 binary64) a))))
(* -1 (* a (- (* -1/3 (* (sqrt (/ 1 a)) rand)) 1)))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* -1/3 (* (sqrt (/ 1 a)) rand)) (* 1/3 (/ 1 a))) 1)))
(*.f64 a (fma.f64 #s(literal 1/3 binary64) (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (/.f64 #s(literal -1 binary64) a)) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* -1 (/ (- (* 1/18 (* (sqrt (/ 1 a)) rand)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))
(.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 rand #s(literal 1/18 binary64)) #s(literal -1/3 binary64)) a)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/18 (* (sqrt a) rand)) (* 1/216 (* (sqrt (/ 1 a)) rand))) a)) 1/3) a)) (* -1/3 (* (sqrt (/ 1 a)) rand))) 1)))
(.f64 a (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 rand #s(literal -1/3 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 1/216 binary64) (.f64 #s(literal -1/18 binary64) (sqrt.f64 a)))) a)) a))))
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt (/ 1 (- a 1/3))))
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) a))))
(* rand (sqrt -3))
(*.f64 rand (sqrt.f64 #s(literal -3 binary64)))
(+ (* -9/2 (/ (* a rand) (sqrt -3))) (* rand (sqrt -3)))
(fma.f64 rand (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (.f64 rand a) #s(literal -9/2 binary64)) (sqrt.f64 #s(literal -3 binary64))))
(+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* -1/2 (/ (* a (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))))) (sqrt -3))))) (* rand (sqrt -3)))
(fma.f64 rand (sqrt.f64 #s(literal -3 binary64)) (.f64 a (fma.f64 a (/.f64 (.f64 #s(literal -81/8 binary64) rand) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (*.f64 rand #s(literal -9/2 binary64)) (sqrt.f64 #s(literal -3 binary64))))))
(+ (* a (+ (* -9/2 (/ rand (sqrt -3))) (* a (+ (* -1/2 (/ (* a (* rand (+ 81 (* 9/2 (/ (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2)))) (pow (sqrt -3) 2)))))) (sqrt -3))) (* -1/2 (/ (* rand (+ 27 (* 81/4 (/ 1 (pow (sqrt -3) 2))))) (sqrt -3))))))) (* rand (sqrt -3)))
(fma.f64 a (fma.f64 (.f64 #s(literal -1/2 binary64) a) (fma.f64 rand (/.f64 #s(literal 81/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 (.f64 rand a) #s(literal 405/8 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 (.f64 rand #s(literal -9/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (*.f64 rand (sqrt.f64 #s(literal -3 binary64))))
(* (sqrt (/ 1 a)) rand)
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))
(.f64 rand (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/18 binary64) (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(+ (* 1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* 1/2 (* (sqrt (/ 1 (pow a 7))) (* rand (- 1/27 (* 1/36 a))))) (* (sqrt (/ 1 a)) rand))))
(fma.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/18 binary64) (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (.f64 (*.f64 rand (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64))) #s(literal 1/2 binary64))))
(* (sqrt (/ 1 a)) rand)
(*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand))
(.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/18 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand)))
(.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(+ (* -1 (/ (+ (* 1/18 (* (sqrt a) rand)) (* 1/2 (* (sqrt (/ 1 a)) (* rand (+ 1/27 (* -1/36 a)))))) (pow a 3))) (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(-.f64 (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (/.f64 (.f64 rand (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal 1/2 binary64)) (fma.f64 a #s(literal -1/36 binary64) #s(literal 1/27 binary64)) (.f64 #s(literal 1/18 binary64) (sqrt.f64 a)))) (.f64 a (.f64 a a))))
(sqrt -3)
(sqrt.f64 #s(literal -3 binary64))
(+ (sqrt -3) (* 9/2 (/ a (sqrt -3))))
(fma.f64 a (/.f64 #s(literal 9/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (sqrt.f64 #s(literal -3 binary64)))
(+ (sqrt -3) (* a (+ (* -81/8 (/ a (pow (sqrt -3) 3))) (* 9/2 (/ 1 (sqrt -3))))))
(fma.f64 a (fma.f64 a (/.f64 #s(literal 27/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 9/2 binary64) (sqrt.f64 #s(literal -3 binary64)))) (sqrt.f64 #s(literal -3 binary64)))
(+ (sqrt -3) (* a (+ (* a (- (* 729/16 (/ a (pow (sqrt -3) 5))) (* 81/8 (/ 1 (pow (sqrt -3) 3))))) (* 9/2 (/ 1 (sqrt -3))))))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal 729/16 binary64) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 27/8 binary64) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal 9/2 binary64) (sqrt.f64 #s(literal -3 binary64)))) (sqrt.f64 #s(literal -3 binary64)))
(* 3 (sqrt a))
(*.f64 #s(literal 3 binary64) (sqrt.f64 a))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (* 3 (sqrt (/ 1 a)))))
(.f64 a (fma.f64 #s(literal 3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (* 3 (sqrt (/ 1 a))))))
(.f64 a (fma.f64 #s(literal -1/24 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 #s(literal 3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64)))))
(* a (+ (* -1/2 (sqrt (/ 1 (pow a 3)))) (+ (* -1/24 (sqrt (/ 1 (pow a 5)))) (+ (* -1/144 (sqrt (/ 1 (pow a 7)))) (* 3 (sqrt (/ 1 a)))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/24 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/144 binary64) (.f64 #s(literal 3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -3 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 3 binary64) (sqrt.f64 a))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal -3 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64)))))
(* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/24 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal -3 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64))))))
(* -1 (* a (+ (* -1/24 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/144 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* 3 (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/24 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/144 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal -3 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) a))

eval282.0ms (3%)

Memory: 42.2MiB live, 346.5MiB allocated
Compiler: Compiled 24 794 to 2 371 computations (90.4% saved)

prune201.0ms (2.2%)

Memory

-32.7MiB live, 181.8MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	1 128	10	1 138
Fresh	3	1	4
Picked	4	1	5
Done	0	0	0
Total	1 135	12	1 147

Accuracy

100.0%

Counts

1 147 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a a)
▶	99.5%	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))
▶	98.3%	(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
	98.2%	(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
▶	98.2%	(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
✓	61.8%	(+.f64 a #s(literal -1/3 binary64))
	98.2%	(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
	39.0%	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
▶	38.2%	(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
	98.2%	(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
	60.9%	a
▶	1.4%	#s(literal -1/3 binary64)

Compiler

Compiled 205 to 146 computations (28.8% saved)

simplify6.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 a)
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) rand)
✓	cost-diff	0	(.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a))
✓	cost-diff	128	(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
✓	cost-diff	0	(sqrt.f64 a)
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) rand)
✓	cost-diff	0	(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
✓	cost-diff	0	(sqrt.f64 a)
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
✓	cost-diff	0	(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
✓	cost-diff	0	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	cost-diff	0	(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
✓	cost-diff	0	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))

Rules

48×	`accelerator-lowering-fma.f32`
48×	`accelerator-lowering-fma.f64`
44×	`-lowering-.f32`
44×	`-lowering-.f64`
28×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	83
1	31	83
2	48	83
3	51	83
0	51	80

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) (+ a -1/3))
(* (sqrt (+ a -1/3)) rand)
(sqrt (+ a -1/3))
(+ a -1/3)
a
-1/3
rand
1/3
-1/3
(* rand (* 1/3 (sqrt a)))
rand
(* 1/3 (sqrt a))
1/3
(sqrt a)
a
(+ (* (* 1/3 rand) (sqrt a)) a)
(* 1/3 rand)
1/3
rand
(sqrt a)
a
(+ (* (* 1/3 rand) (sqrt a)) a)
(* (* 1/3 rand) (sqrt a))
(* 1/3 rand)
1/3
rand
(sqrt a)
a

Outputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) (+ a -1/3))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))
(* (sqrt (+ a -1/3)) rand)
(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
(sqrt (+ a -1/3))
(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
rand
1/3
#s(literal 1/3 binary64)
-1/3
#s(literal -1/3 binary64)
(* rand (* 1/3 (sqrt a)))
(.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)))
rand
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
1/3
#s(literal 1/3 binary64)
(sqrt a)
(sqrt.f64 a)
a
(+ (* (* 1/3 rand) (sqrt a)) a)
(fma.f64 (sqrt.f64 a) (*.f64 rand #s(literal 1/3 binary64)) a)
(* 1/3 rand)
(*.f64 rand #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
rand
(sqrt a)
(sqrt.f64 a)
a
(+ (* (* 1/3 rand) (sqrt a)) a)
(fma.f64 (sqrt.f64 a) (*.f64 rand #s(literal 1/3 binary64)) a)
(* (* 1/3 rand) (sqrt a))
(.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)))
(* 1/3 rand)
(*.f64 rand #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
rand
(sqrt a)
(sqrt.f64 a)
a

localize104.0ms (1.1%)

Memory

4.0MiB live, 78.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 a)
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) rand)
✓	accuracy	100.0%	(sqrt.f64 a)
✓	accuracy	99.9%	(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) rand)
✓	accuracy	100.0%	(sqrt.f64 a)
✓	accuracy	99.6%	(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
✓	accuracy	100.0%	(+.f64 a #s(literal -1/3 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.7%	(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
✓	accuracy	99.5%	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 83 to 17 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 9.0ms (38.3% of total)

const: 7.0ms (29.8% of total)

ival-add: 4.0ms (17% of total)

ival-sqrt: 4.0ms (17% of total)

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

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

series8.0ms (0.1%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

11 → 204

Calls

Call 1

Inputs
#<alt (+ (* (* (sqrt (+ a -1/3)) rand) 1/3) (+ a -1/3))>
#<alt (* (sqrt (+ a -1/3)) rand)>
#<alt (sqrt (+ a -1/3))>
#<alt (+ a -1/3)>
#<alt (* rand (* 1/3 (sqrt a)))>
#<alt (* 1/3 (sqrt a))>
#<alt (sqrt a)>
#<alt (+ (* (* 1/3 rand) (sqrt a)) a)>
#<alt (* 1/3 rand)>
#<alt (+ (* (* 1/3 rand) (sqrt a)) a)>
#<alt (* (* 1/3 rand) (sqrt a))>

Outputs
#<alt (- (* 1/3 (* rand (sqrt -1/3))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)>
#<alt (- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))>
#<alt (* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))>
#<alt (* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))>
#<alt (- a 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* rand (sqrt -1/3))>
#<alt (+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))>
#<alt (* (sqrt a) rand)>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (sqrt -1/3)>
#<alt (+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))>
#<alt (+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt -1/3>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt a>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt a>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* 1/3 (sqrt a))>
#<alt (* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt a>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt a>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	rand	@	0	(* rand (* 1/3 (sqrt a)))
0.0ms	a	@	-inf	(* (sqrt (+ a -1/3)) rand)
0.0ms	rand	@	inf	(* rand (* 1/3 (sqrt a)))
0.0ms	a	@	-inf	(* 1/3 (sqrt a))
0.0ms	a	@	-inf	(* rand (* 1/3 (sqrt a)))

rewrite695.0ms (7.5%)

Memory

-11.6MiB live, 704.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 054×	`accelerator-lowering-fma.f32`
10 054×	`accelerator-lowering-fma.f64`
5 676×	`-lowering-.f32`
5 676×	`-lowering-.f64`
3 102×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	71	62
2	551	62
3	7702	62
0	8240	59

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 418

Calls

Call 1

Inputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) (+ a -1/3))
(* (sqrt (+ a -1/3)) rand)
(sqrt (+ a -1/3))
(+ a -1/3)
(* rand (* 1/3 (sqrt a)))
(* 1/3 (sqrt a))
(sqrt a)
(+ (* (* 1/3 rand) (sqrt a)) a)
(* 1/3 rand)
(+ (* (* 1/3 rand) (sqrt a)) a)
(* (* 1/3 rand) (sqrt a))

Outputs
(+.f64 a (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal -1/3 binary64)))
(+.f64 #s(literal -1/3 binary64) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) a))
(+.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(+.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))) (+.f64 a #s(literal -1/3 binary64)))
(+.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) a) #s(literal -1/3 binary64))
(+.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 rand rand))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(+.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal -1/3 binary64)) a)
(-.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 rand rand))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)))
(-.f64 (/.f64 (.f64 a a) (+.f64 a #s(literal 1/3 binary64))) (-.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 a #s(literal 1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))) (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 rand rand))) (-.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))))
(-.f64 (/.f64 (.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) a) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) a)) (+.f64 a (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 a (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)))))
(-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) (/.f64 (.f64 a a) (+.f64 a #s(literal 1/3 binary64)))) (/.f64 #s(literal 1/9 binary64) (+.f64 a #s(literal 1/3 binary64))))
(fma.f64 (+.f64 a #s(literal -1/3 binary64)) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (.f64 rand (.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/9 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 rand (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) #s(literal 1/3 binary64)) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 #s(literal 1/3 binary64) (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (.f64 rand (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))) (/.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (sqrt.f64 a) (sqrt.f64 a) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (*.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 rand rand))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/3 binary64) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) (+.f64 a #s(literal -1/3 binary64)))) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (fma.f64 a (.f64 a a) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a (+.f64 a #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1/9 binary64) (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 rand rand)) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (fma.f64 a a #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal 1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 a (.f64 a a) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 a (+.f64 a #s(literal 1/3 binary64)) #s(literal 1/9 binary64)))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 a a #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) a) #s(literal -1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 #s(literal 1/27 binary64) (.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 rand rand))) (.f64 a (.f64 a a))) (/.f64 #s(literal 1 binary64) (fma.f64 a (-.f64 a (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)))) (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (*.f64 rand rand))))) #s(literal -1/3 binary64))
(fma.f64 #s(literal 1 binary64) (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a (+.f64 a #s(literal 1/3 binary64)) #s(literal 1/9 binary64))) (fma.f64 a (.f64 a a) #s(literal -1/27 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 a #s(literal 1/3 binary64))) (fma.f64 a a #s(literal -1/9 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))) a)) #s(literal -1/3 binary64))
(fma.f64 (-.f64 #s(literal 1/9 binary64) (.f64 a a)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/3 binary64) a)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (.f64 rand #s(literal 1/3 binary64))) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 a #s(literal 1/4 binary64)) (.f64 (pow.f64 a #s(literal 1/4 binary64)) (sqrt.f64 a)) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (.f64 rand rand)) (/.f64 #s(literal 1/9 binary64) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) #s(literal 1/3 binary64)) rand (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64))) (/.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/9 binary64)) (/.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (.f64 rand (.f64 rand (fma.f64 a #s(literal 1/3 binary64) #s(literal -1/9 binary64)))) (/.f64 #s(literal 1/3 binary64) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a)) (neg.f64 (/.f64 (.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 a #s(literal -1/3 binary64))) (-.f64 (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) #s(literal 1/3 binary64)) a))))
(fma.f64 (.f64 (.f64 rand #s(literal 1/3 binary64)) (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (.f64 (sqrt.f64 a) (pow.f64 a #s(literal 1/4 binary64))) (pow.f64 a #s(literal 1/4 binary64)) (fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 (fma.f64 a a #s(literal -1/9 binary64)) (fma.f64 a a #s(literal -1/9 binary64))) (+.f64 a #s(literal -1/3 binary64)) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 (fma.f64 a (.f64 a a) #s(literal -1/27 binary64)) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (fma.f64 a #s(literal 1/3 binary64) #s(literal 1/9 binary64))) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) (fma.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 a #s(literal 1/3 binary64) #s(literal 1/9 binary64)) (.f64 a a)) (.f64 a (.f64 a (.f64 a a)))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 (fma.f64 a (.f64 a a) #s(literal -1/27 binary64)) (.f64 (fma.f64 a (+.f64 a #s(literal 1/3 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 a a #s(literal -1/9 binary64)) (.f64 a #s(literal -1/3 binary64))))) (+.f64 (fma.f64 a a #s(literal -1/9 binary64)) (.f64 a #s(literal -1/3 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64))))
(fma.f64 (/.f64 (fma.f64 a a #s(literal -1/9 binary64)) (fma.f64 a (.f64 a a) #s(literal 1/27 binary64))) (fma.f64 a a (fma.f64 a #s(literal -1/3 binary64) #s(literal 1/9 binary64))) (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64))))
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(sqrt.f64 a)
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(-.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
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(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
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(fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a))))
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(fma.f64 (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) rand a)
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(fma.f64 (*.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a) a)
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(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (.f64 (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)) (.f64 a a))) (.f64 (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a)))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 a (.f64 a a)) (-.f64 (.f64 a (.f64 a a)) (.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))))) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (*.f64 a (sqrt.f64 a)))))))
(/.f64 (.f64 (fma.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))) (neg.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (neg.f64 (.f64 a (.f64 a a)))) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (*.f64 a (sqrt.f64 a)))))))
(/.f64 (.f64 (fma.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))) (neg.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand))) (.f64 (.f64 a a) (fma.f64 a (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (.f64 a a)))) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
(/.f64 (.f64 (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand))) (neg.f64 (.f64 a (.f64 a (.f64 a a))))) #s(literal 1 binary64)) (.f64 (fma.f64 a (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (.f64 a a)) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (*.f64 a (sqrt.f64 a))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))))
(/.f64 (neg.f64 (fma.f64 a a (.f64 #s(literal -1/9 binary64) (.f64 a (.f64 rand rand))))) (neg.f64 (+.f64 a (.f64 #s(literal -1/3 binary64) (*.f64 rand (sqrt.f64 a))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (fma.f64 (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 a a) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))) (.f64 (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 a a) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))) (fma.f64 (.f64 a #s(literal 1/9 binary64)) (/.f64 (.f64 rand rand) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (/.f64 (.f64 a a) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))))
(/.f64 (.f64 (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))) #s(literal 1 binary64)) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))) #s(literal 1 binary64)) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a)))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))))) (fma.f64 (.f64 a (.f64 a a)) (-.f64 (.f64 a (.f64 a a)) (.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))) (neg.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))))) (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (neg.f64 (.f64 a (.f64 a a)))))
(/.f64 (.f64 (fma.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64))) (neg.f64 (.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a))))) (/.f64 #s(literal 1 binary64) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))) (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand))) (.f64 (.f64 a a) (fma.f64 a (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (.f64 a a)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand))) (neg.f64 (.f64 a (.f64 a (.f64 a a))))) (/.f64 #s(literal 1 binary64) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))) (fma.f64 a (.f64 #s(literal 1/9 binary64) (.f64 rand rand)) (*.f64 a a)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 a) (*.f64 rand #s(literal 1/3 binary64)) a)) #s(literal -1 binary64))
(.f64 (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a) (.f64 (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)) (/.f64 #s(literal 1 binary64) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))))
(.f64 (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a) (/.f64 (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
(.f64 (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a)))))))
(.f64 (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))) (.f64 (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (*.f64 a (sqrt.f64 a))))))))
(.f64 (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))) (/.f64 (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a)))))))
(.f64 (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))) (/.f64 #s(literal 1 binary64) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a))))))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a)))))
(.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 rand #s(literal 1/3 binary64)) (-.f64 (.f64 a (.f64 rand #s(literal 1/3 binary64))) (.f64 a (sqrt.f64 a)))))) (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) (-.f64 #s(literal 0 binary64) a))) (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (*.f64 a a))))
(.f64 (fma.f64 a a (.f64 #s(literal -1/9 binary64) (.f64 a (.f64 rand rand)))) (/.f64 #s(literal 1 binary64) (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))) (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a)))) (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a))
(.f64 (/.f64 (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))) (fma.f64 (.f64 a (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a))))) (.f64 (.f64 a a) (.f64 (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a)))) (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a)))))) (.f64 (.f64 a (.f64 a a)) (.f64 (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)) (.f64 (.f64 rand (.f64 rand rand)) #s(literal 1/27 binary64)))))) (fma.f64 (.f64 a (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a))))) (-.f64 (.f64 a (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a))))) (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)))) (.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand))))))
(.f64 (/.f64 (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (.f64 a (.f64 a a))) (-.f64 (.f64 #s(literal 1/81 binary64) (.f64 (.f64 a (.f64 rand rand)) (.f64 a (.f64 rand rand)))) (.f64 (.f64 a a) (.f64 (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a)))) (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a)))))))) (-.f64 (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand))) (.f64 a (+.f64 a (.f64 #s(literal -1/3 binary64) (.f64 rand (sqrt.f64 a)))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)) (-.f64 #s(literal 0 binary64) (.f64 a a))) (fma.f64 (.f64 rand (.f64 rand rand)) (.f64 #s(literal 1/27 binary64) (.f64 a (sqrt.f64 a))) (neg.f64 (.f64 a (.f64 a a))))) (fma.f64 a (fma.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)) a) (.f64 #s(literal 1/9 binary64) (.f64 a (.f64 rand rand)))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 a)))
(.f64 (sqrt.f64 a) (.f64 rand #s(literal 1/3 binary64)))
(.f64 (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) rand)
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
(.f64 (pow.f64 a #s(literal 1/4 binary64)) (.f64 (pow.f64 a #s(literal 1/4 binary64)) (*.f64 rand #s(literal 1/3 binary64))))
(.f64 (.f64 (*.f64 rand #s(literal 1/3 binary64)) (pow.f64 a #s(literal 1/4 binary64))) (pow.f64 a #s(literal 1/4 binary64)))

simplify583.0ms (6.3%)

Memory

-0.4MiB live, 1 203.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 456×	`accelerator-lowering-fma.f32`
16 456×	`accelerator-lowering-fma.f64`
5 302×	`-lowering-.f32`
5 302×	`-lowering-.f64`
4 068×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	253	2039
1	771	1849
2	2704	1831
3	6041	1816
0	8163	1710

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(- a 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(* 1/3 (* rand (sqrt (- a 1/3))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(* rand (sqrt -1/3))
(+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))
(+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))
(* (sqrt a) rand)
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(sqrt -1/3)
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
-1/3
(- a 1/3)
(- a 1/3)
(- a 1/3)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* 1/3 (sqrt a))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
a
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* 1/3 (* (sqrt a) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* 1/3 (* (sqrt a) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* 1/3 (* (sqrt a) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
a
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* 1/3 (* (sqrt a) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* 1/3 (* (sqrt a) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* 1/3 (* (sqrt a) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))

Outputs
(- (* 1/3 (* rand (sqrt -1/3))) 1/3)
(fma.f64 #s(literal 1/3 binary64) (*.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal -1/3 binary64))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3)))))) 1/3)
(fma.f64 a (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal 1/3 binary64) (*.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))) 1/3)
(fma.f64 a (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (fma.f64 a (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal -1/3 binary64)))
(- (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))) 1/3)
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (fma.f64 a (fma.f64 a (fma.f64 a (.f64 (/.f64 rand (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) #s(literal 1/48 binary64)) (*.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64))) (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))) #s(literal -1/3 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (- (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))) (* 1/3 (/ 1 a))))
(*.f64 a (fma.f64 #s(literal 1/3 binary64) (fma.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (/.f64 #s(literal -1 binary64) a)) #s(literal 1 binary64)))
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))) (* 1/3 (/ 1 a))))
(fma.f64 a (fma.f64 rand (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (/.f64 #s(literal -1/3 binary64) a)) a)
(* a (- (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))) (* 1/3 (/ 1 a))))
(fma.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))) (/.f64 #s(literal -1/3 binary64) a)) a)
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (+ (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/3 (/ 1 a))) 1)))
(.f64 a (-.f64 (/.f64 #s(literal -1/3 binary64) a) (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64))))
(* -1 (* a (- (+ (* -1 (/ (- (* -1/18 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(.f64 a (-.f64 #s(literal 1 binary64) (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) (/.f64 (fma.f64 (*.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal 1/18 binary64) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) a)))))
(* -1 (* a (- (+ (* -1 (/ (- (* -1 (/ (+ (* -1/216 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) (* 1/18 (* (sqrt a) (* rand (pow (sqrt -1) 2))))) a)) 1/3) a)) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(.f64 a (-.f64 #s(literal 1 binary64) (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) #s(literal -1/216 binary64) (.f64 #s(literal 1/18 binary64) (sqrt.f64 a)))) a)) a))))
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(- (+ a (* 1/3 (* rand (sqrt (- a 1/3))))) 1/3)
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 #s(literal -1/3 binary64) a))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (- (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)) (* 1/3 (/ 1 rand))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* -1 (* rand (+ (* -1 (/ (- a 1/3) rand)) (* -1/3 (sqrt (- a 1/3))))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (/.f64 (+.f64 #s(literal -1/3 binary64) a) rand)))
(* rand (sqrt -1/3))
(*.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))
(+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(fma.f64 a (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/2 binary64)) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))
(fma.f64 a (fma.f64 a (.f64 rand (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/2 binary64))) (*.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))
(fma.f64 a (fma.f64 rand (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 rand (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 (.f64 (.f64 rand a) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64)))))) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(.f64 (.f64 rand a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))
(.f64 a (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))
(.f64 a (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (.f64 rand (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) rand) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) rand) (+.f64 (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 1/432 binary64))))) (-.f64 #s(literal 0 binary64) a))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(sqrt -1/3)
(sqrt.f64 #s(literal -1/3 binary64))
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(fma.f64 a (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (fma.f64 #s(literal 1/16 binary64) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (fma.f64 #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))))
-1/3
#s(literal -1/3 binary64)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* 1/3 (sqrt a))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(* -1/3 (* (sqrt a) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
a
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
a
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 a) (/.f64 a rand)))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 (fma.f64 (.f64 rand (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1/3 binary64) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* (sqrt a) rand))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand))

eval135.0ms (1.5%)

Memory: 28.7MiB live, 259.7MiB allocated
Compiler: Compiled 19 141 to 1 374 computations (92.8% saved)

prune70.0ms (0.8%)

Memory

-22.6MiB live, 176.2MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	752	5	757
Fresh	1	5	6
Picked	2	3	5
Done	0	1	1
Total	755	14	769

Accuracy

100.0%

Counts

769 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a a)
▶	98.7%	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)
	97.9%	(fma.f64 (*.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64) a)
✓	98.3%	(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
	97.9%	(+.f64 (.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64)) a)
✓	61.8%	(+.f64 a #s(literal -1/3 binary64))
▶	98.2%	(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
▶	37.9%	(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
	38.2%	(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
▶	39.0%	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
✓	38.2%	(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
	98.2%	(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
▶	60.9%	a
✓	1.4%	#s(literal -1/3 binary64)

Compiler

Compiled 213 to 155 computations (27.2% saved)

simplify16.0ms (0.2%)

Memory

29.0MiB live, 29.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 a)
✓	cost-diff	(/.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
✓	cost-diff	(fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64))
✓	cost-diff	(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
✓	cost-diff	(*.f64 #s(literal 1/3 binary64) rand)
✓	cost-diff	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	cost-diff	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
✓	cost-diff	(sqrt.f64 a)
✓	cost-diff	(*.f64 rand (sqrt.f64 a))
✓	cost-diff	(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
✓	cost-diff	(+.f64 a #s(literal -1/3 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	cost-diff	(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
✓	cost-diff	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)

Rules

244×	`-lowering-.f32`
244×	`-lowering-.f64`
136×	`associate-l`
98×	`associate-r`
76×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	93
1	39	93
2	58	93
3	79	93
4	139	93
5	159	93
6	216	93
7	254	93
8	307	93
9	307	93
10	312	93
11	324	93
12	324	93
0	324	90

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)
(* (sqrt (+ a -1/3)) rand)
(sqrt (+ a -1/3))
(+ a -1/3)
a
-1/3
rand
1/3
a
(* (* rand (sqrt a)) 1/3)
(* rand (sqrt a))
rand
(sqrt a)
a
1/3
(* (sqrt (+ a -1/3)) (* 1/3 rand))
(sqrt (+ a -1/3))
(+ a -1/3)
a
-1/3
(* 1/3 rand)
1/3
rand
(* (+ (* rand (/ 1/3 (sqrt a))) 1) a)
(+ (* rand (/ 1/3 (sqrt a))) 1)
rand
(/ 1/3 (sqrt a))
1/3
(sqrt a)
a
1

Outputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 rand #s(literal 1/3 binary64)) a)
(* (sqrt (+ a -1/3)) rand)
(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
(sqrt (+ a -1/3))
(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
rand
1/3
#s(literal 1/3 binary64)
a
(* (* rand (sqrt a)) 1/3)
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* rand (sqrt a))
(*.f64 rand (sqrt.f64 a))
rand
(sqrt a)
(sqrt.f64 a)
a
1/3
#s(literal 1/3 binary64)
(* (sqrt (+ a -1/3)) (* 1/3 rand))
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 rand #s(literal 1/3 binary64)))
(sqrt (+ a -1/3))
(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
(+ a -1/3)
(+.f64 a #s(literal -1/3 binary64))
a
-1/3
#s(literal -1/3 binary64)
(* 1/3 rand)
(*.f64 rand #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
rand
(* (+ (* rand (/ 1/3 (sqrt a))) 1) a)
(*.f64 a (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)))
(+ (* rand (/ 1/3 (sqrt a))) 1)
(fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64))
rand
(/ 1/3 (sqrt a))
(/.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
1/3
#s(literal 1/3 binary64)
(sqrt a)
(sqrt.f64 a)
a
1
#s(literal 1 binary64)

localize80.0ms (0.9%)

Memory

-28.9MiB live, 135.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 a)
✓	accuracy	99.9%	(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
✓	accuracy	99.8%	(fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64))
✓	accuracy	99.4%	(/.f64 #s(literal 1/3 binary64) (sqrt.f64 a))
✓	accuracy	100.0%	(+.f64 a #s(literal -1/3 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
✓	accuracy	99.4%	(*.f64 #s(literal 1/3 binary64) rand)
✓	accuracy	100.0%	(sqrt.f64 a)
✓	accuracy	99.7%	(*.f64 rand (sqrt.f64 a))
✓	accuracy	99.2%	(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
✓	accuracy	100.0%	(+.f64 a #s(literal -1/3 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))
✓	accuracy	99.7%	(*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand)
✓	accuracy	99.5%	(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)

Samples

44.0ms

256×

valid

Compiler

Compiled 92 to 21 computations (77.2% saved)

Precisions

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

ival-mult: 12.0ms (40.3% of total)

const: 7.0ms (23.5% of total)

ival-add: 4.0ms (13.4% of total)

ival-sqrt: 4.0ms (13.4% of total)

ival-div: 3.0ms (10.1% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated

Counts

12 → 228

Calls

Call 1

Inputs
#<alt (+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)>
#<alt (* (sqrt (+ a -1/3)) rand)>
#<alt (sqrt (+ a -1/3))>
#<alt (+ a -1/3)>
#<alt (* (* rand (sqrt a)) 1/3)>
#<alt (* rand (sqrt a))>
#<alt (sqrt a)>
#<alt (* (sqrt (+ a -1/3)) (* 1/3 rand))>
#<alt (* 1/3 rand)>
#<alt (* (+ (* rand (/ 1/3 (sqrt a))) 1) a)>
#<alt (+ (* rand (/ 1/3 (sqrt a))) 1)>
#<alt (/ 1/3 (sqrt a))>

Outputs
#<alt (* 1/3 (* rand (sqrt -1/3)))>
#<alt (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3))))))>
#<alt (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3)))))))>
#<alt (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5)))))))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))>
#<alt (* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))))>
#<alt (* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))>
#<alt (* -1 (* a (- (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))>
#<alt (* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))) 1)))>
#<alt (* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))) 1)))>
#<alt a>
#<alt (+ a (* 1/3 (* rand (sqrt (- a 1/3)))))>
#<alt (+ a (* 1/3 (* rand (sqrt (- a 1/3)))))>
#<alt (+ a (* 1/3 (* rand (sqrt (- a 1/3)))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))>
#<alt (* rand (sqrt -1/3))>
#<alt (+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))>
#<alt (+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))>
#<alt (* (sqrt a) rand)>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (* rand (sqrt (- a 1/3)))>
#<alt (sqrt -1/3)>
#<alt (+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))>
#<alt (+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))>
#<alt (sqrt a)>
#<alt (* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))>
#<alt (* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))>
#<alt -1/3>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt (- a 1/3)>
#<alt a>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt (* a (- 1 (* 1/3 (/ 1 a))))>
#<alt a>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* -1 (* a (- (* 1/3 (/ 1 a)) 1)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* (sqrt a) rand)>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (sqrt a)>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt a) (pow (sqrt -1) 2)))>
#<alt (* 1/3 (* rand (sqrt -1/3)))>
#<alt (+ (* 1/6 (/ (* a rand) (sqrt -1/3))) (* 1/3 (* rand (sqrt -1/3))))>
#<alt (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))>
#<alt (+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))>
#<alt (* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))>
#<alt (* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))>
#<alt (* -1 (* a (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))>
#<alt (* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 (* rand (sqrt (- a 1/3))))>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt (* 1/3 rand)>
#<alt a>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* rand (+ (* 1/3 (sqrt a)) (/ a rand)))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))>
#<alt (* 1/3 (* (sqrt a) rand))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (+ a (* 1/3 (* (sqrt a) rand)))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt (* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))>
#<alt 1>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))>
#<alt (* 1/3 (* (sqrt (/ 1 a)) rand))>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (/ (+ a (* 1/3 (* (sqrt a) rand))) a)>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>
#<alt (* 1/3 (sqrt (/ 1 a)))>

Calls

57 calls:

Time	Variable		Point	Expression
5.0ms	a	@	-inf	(/ 1/3 (sqrt a))
1.0ms	a	@	-inf	(* (+ (* rand (/ 1/3 (sqrt a))) 1) a)
0.0ms	a	@	-inf	(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)
0.0ms	a	@	inf	(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)
0.0ms	rand	@	-inf	(* rand (sqrt a))

rewrite382.0ms (4.1%)

Memory

-18.2MiB live, 612.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 074×	`accelerator-lowering-fma.f32`
7 074×	`accelerator-lowering-fma.f64`
4 528×	`-lowering-.f32`
4 528×	`-lowering-.f64`
2 430×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	68
1	86	68
2	542	68
3	6143	68
0	8086	65

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 418

Calls

Call 1

Inputs
(+ (* (* (sqrt (+ a -1/3)) rand) 1/3) a)
(* (sqrt (+ a -1/3)) rand)
(sqrt (+ a -1/3))
(+ a -1/3)
(* (* rand (sqrt a)) 1/3)
(* rand (sqrt a))
(sqrt a)
(* (sqrt (+ a -1/3)) (* 1/3 rand))
(* 1/3 rand)
(* (+ (* rand (/ 1/3 (sqrt a))) 1) a)
(+ (* rand (/ 1/3 (sqrt a))) 1)
(/ 1/3 (sqrt a))

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

simplify773.0ms (8.3%)

Memory

13.3MiB live, 1 159.2MiB allocated

Algorithm

1×	egg-herbie

Rules

25 790×	`accelerator-lowering-fma.f32`
25 790×	`accelerator-lowering-fma.f64`
5 102×	`-lowering-.f32`
5 102×	`-lowering-.f64`
4 546×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	262	2412
1	816	2186
2	2931	2144
3	6578	2136
0	8348	2011

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* 1/3 (* rand (sqrt -1/3)))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3))))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3)))))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5)))))))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(* -1 (* a (- (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))) 1)))
(* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))) 1)))
a
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(* rand (sqrt -1/3))
(+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))
(+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))
(* (sqrt a) rand)
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(* rand (sqrt (- a 1/3)))
(sqrt -1/3)
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
-1/3
(- a 1/3)
(- a 1/3)
(- a 1/3)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
(* a (- 1 (* 1/3 (/ 1 a))))
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* 1/3 (* (sqrt a) rand))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* (sqrt a) rand)
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(sqrt a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* 1/3 (* rand (sqrt -1/3)))
(+ (* 1/6 (/ (* a rand) (sqrt -1/3))) (* 1/3 (* rand (sqrt -1/3))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))
(* 1/3 (* (sqrt a) rand))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(* -1 (* a (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
(* 1/3 rand)
a
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* 1/3 (* (sqrt a) rand))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(* 1/3 (* (sqrt a) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(* 1/3 (* (sqrt a) rand))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(+ a (* 1/3 (* (sqrt a) rand)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
1
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))
(* 1/3 (sqrt (/ 1 a)))

Outputs
(* 1/3 (* rand (sqrt -1/3)))
(.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (* 1/6 (/ rand (sqrt -1/3))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3)))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 a (*.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64)) (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64)))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ 1 (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5)))))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 a (fma.f64 a (.f64 (/.f64 rand (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) #s(literal 1/48 binary64)) (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64))) (fma.f64 rand (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1 binary64)))))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))))) #s(literal 1 binary64)))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))) #s(literal 1 binary64)))
(* a (+ 1 (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))))
(.f64 a (fma.f64 rand (+.f64 (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/1296 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))))) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))) #s(literal 1 binary64)))
(* -1 (* a (- (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))) 1)))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))) 1)))
(.f64 a (fma.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) #s(literal 1 binary64)))
(* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))) 1)))
(.f64 a (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 0 binary64) rand) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))))))
(* -1 (* a (- (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))) 1)))
(.f64 (fma.f64 (-.f64 #s(literal 0 binary64) rand) (+.f64 (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 1/1296 binary64) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) a))
a
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* rand (sqrt (- a 1/3)))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* rand (+ (* 1/3 (sqrt (- a 1/3))) (/ a rand)))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt (- a 1/3))))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) a)
(* rand (sqrt -1/3))
(*.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))
(+ (* 1/2 (/ (* a rand) (sqrt -1/3))) (* rand (sqrt -1/3)))
(fma.f64 rand (sqrt.f64 #s(literal -1/3 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 rand (/.f64 a (sqrt.f64 #s(literal -1/3 binary64))))))
(+ (* a (+ (* -1/8 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/2 (/ rand (sqrt -1/3))))) (* rand (sqrt -1/3)))
(fma.f64 a (fma.f64 rand (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (.f64 (.f64 rand (/.f64 a (sqrt.f64 #s(literal -1/3 binary64)))) #s(literal 3/8 binary64))) (*.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* a (+ (* 1/2 (/ rand (sqrt -1/3))) (* a (+ (* -1/8 (/ rand (pow (sqrt -1/3) 3))) (* 1/16 (/ (* a rand) (pow (sqrt -1/3) 5))))))) (* rand (sqrt -1/3)))
(fma.f64 a (fma.f64 a (fma.f64 rand (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (.f64 (.f64 rand (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64)))) #s(literal 1/16 binary64))) (.f64 rand (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))))) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (* (sqrt (/ 1 a)) rand)))
(.f64 (.f64 rand a) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (* (sqrt (/ 1 a)) rand))))
(.f64 a (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* a (+ (* -1/6 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/432 (* (sqrt (/ 1 (pow a 7))) rand)) (* (sqrt (/ 1 a)) rand)))))
(.f64 a (.f64 rand (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))
(.f64 a (.f64 rand (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) rand) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(.f64 a (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) rand) (+.f64 (fma.f64 #s(literal 1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 1/432 binary64)))))))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(* rand (sqrt (- a 1/3)))
(*.f64 rand (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)))
(sqrt -1/3)
(sqrt.f64 #s(literal -1/3 binary64))
(+ (sqrt -1/3) (* 1/2 (/ a (sqrt -1/3))))
(fma.f64 a (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* -1/8 (/ a (pow (sqrt -1/3) 3))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(+ (sqrt -1/3) (* a (+ (* a (- (* 1/16 (/ a (pow (sqrt -1/3) 5))) (* 1/8 (/ 1 (pow (sqrt -1/3) 3))))) (* 1/2 (/ 1 (sqrt -1/3))))))
(fma.f64 a (fma.f64 a (fma.f64 a (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 3/8 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/3 binary64)))) (sqrt.f64 #s(literal -1/3 binary64)))
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/6 (sqrt (/ 1 (pow a 3))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (* -1/72 (sqrt (/ 1 (pow a 5)))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/6 (sqrt (/ 1 (pow a 3)))) (+ (* -1/72 (sqrt (/ 1 (pow a 5)))) (* -1/432 (sqrt (/ 1 (pow a 7))))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal -1/6 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/72 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/432 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* a (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) (-.f64 #s(literal 0 binary64) a))
(* -1 (* a (+ (* -1/72 (* (sqrt (/ 1 (pow a 5))) (pow (sqrt -1) 2))) (+ (* 1/432 (* (sqrt (/ 1 (pow a 7))) (pow (sqrt -1) 2))) (+ (* 1/6 (* (sqrt (/ 1 (pow a 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal -1/6 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) #s(literal 1/72 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal -1/432 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (-.f64 #s(literal 0 binary64) a))
-1/3
#s(literal -1/3 binary64)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
(- a 1/3)
(+.f64 #s(literal -1/3 binary64) a)
a
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* a (- 1 (* 1/3 (/ 1 a))))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
a
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* -1 (* a (- (* 1/3 (/ 1 a)) 1)))
(fma.f64 #s(literal -1/3 binary64) (/.f64 a a) a)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* (sqrt a) rand)
(*.f64 rand (sqrt.f64 a))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(* -1 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(*.f64 rand (sqrt.f64 a))
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(sqrt a)
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(sqrt.f64 a)
(* 1/3 (* rand (sqrt -1/3)))
(.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))))
(+ (* 1/6 (/ (* a rand) (sqrt -1/3))) (* 1/3 (* rand (sqrt -1/3))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 #s(literal 1/6 binary64) (*.f64 rand (/.f64 a (sqrt.f64 #s(literal -1/3 binary64))))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* -1/24 (/ (* a rand) (pow (sqrt -1/3) 3))) (* 1/6 (/ rand (sqrt -1/3))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 a (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64)) (.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))))))
(+ (* 1/3 (* rand (sqrt -1/3))) (* a (+ (* 1/6 (/ rand (sqrt -1/3))) (* a (+ (* -1/24 (/ rand (pow (sqrt -1/3) 3))) (* 1/48 (/ (* a rand) (pow (sqrt -1/3) 5))))))))
(fma.f64 #s(literal 1/3 binary64) (.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) (.f64 a (fma.f64 a (fma.f64 a (.f64 (/.f64 rand (pow.f64 (sqrt.f64 #s(literal -1/3 binary64)) #s(literal 5 binary64))) #s(literal 1/48 binary64)) (.f64 (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64))) #s(literal 1/8 binary64))) (*.f64 #s(literal 1/6 binary64) (/.f64 rand (sqrt.f64 #s(literal -1/3 binary64)))))))
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a))))))))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand)))))
(.f64 a (.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))))))))
(* a (+ (* -1/18 (* (sqrt (/ 1 (pow a 3))) rand)) (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) rand)) (+ (* -1/1296 (* (sqrt (/ 1 (pow a 7))) rand)) (* 1/3 (* (sqrt (/ 1 a)) rand))))))
(.f64 a (.f64 rand (+.f64 (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal -1/1296 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))))) (fma.f64 #s(literal -1/18 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) (.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))))))))
(* -1/3 (* (sqrt a) (* rand (pow (sqrt -1) 2))))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1 (* a (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))
(.f64 a (.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (*.f64 a a)))) #s(literal 1/18 binary64)))))
(* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2))))))))
(.f64 a (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) rand) (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64) (*.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))))))
(* -1 (* a (+ (* -1/216 (* (sqrt (/ 1 (pow a 5))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/1296 (* (sqrt (/ 1 (pow a 7))) (* rand (pow (sqrt -1) 2)))) (+ (* 1/18 (* (sqrt (/ 1 (pow a 3))) (* rand (pow (sqrt -1) 2)))) (* 1/3 (* (sqrt (/ 1 a)) (* rand (pow (sqrt -1) 2)))))))))
(-.f64 #s(literal 0 binary64) (.f64 a (.f64 (-.f64 #s(literal 0 binary64) rand) (+.f64 (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 a (.f64 a a)))) #s(literal 1/18 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))) #s(literal 1/1296 binary64) (.f64 #s(literal -1/216 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64))))))))))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 (* rand (sqrt (- a 1/3))))
(.f64 (sqrt.f64 (+.f64 #s(literal -1/3 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
(* 1/3 rand)
(*.f64 #s(literal 1/3 binary64) rand)
a
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* rand (+ (* 1/3 (sqrt a)) (/ a rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* -1 (* rand (+ (* -1 (/ a rand)) (* -1/3 (sqrt a)))))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* 1/3 (* (sqrt a) rand))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(+ a (* 1/3 (* (sqrt a) rand)))
(fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a)
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(* a (+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* rand (+ (* 1/3 (sqrt (/ 1 a))) (/ 1 rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(-.f64 #s(literal 0 binary64) (fma.f64 rand (*.f64 #s(literal -1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1 binary64)))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(-.f64 #s(literal 0 binary64) (fma.f64 rand (*.f64 #s(literal -1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1 binary64)))
(* -1 (* rand (- (* -1/3 (sqrt (/ 1 a))) (/ 1 rand))))
(-.f64 #s(literal 0 binary64) (fma.f64 rand (*.f64 #s(literal -1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) #s(literal -1 binary64)))
(* 1/3 (* (sqrt (/ 1 a)) rand))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand))
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a) a)
(/ (+ a (* 1/3 (* (sqrt a) rand))) a)
(/.f64 (fma.f64 (sqrt.f64 a) (*.f64 #s(literal 1/3 binary64) rand) a) a)
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(+ 1 (* 1/3 (* (sqrt (/ 1 a)) rand)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (*.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))
(* 1/3 (sqrt (/ 1 a)))
(*.f64 #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))

eval98.0ms (1.1%)

Memory: 22.2MiB live, 223.9MiB allocated
Compiler: Compiled 16 237 to 1 800 computations (88.9% saved)

prune93.0ms (1%)

Memory

-8.9MiB live, 225.4MiB allocated

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	810	3	813
Fresh	3	2	5
Picked	1	4	5
Done	0	4	4
Total	814	13	827

Accuracy

100.0%

Counts

827 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(fma.f64 (*.f64 (sqrt.f64 a) rand) #s(literal 1/3 binary64) a)
	98.2%	(fma.f64 (*.f64 a #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 a)) a)
✓	98.3%	(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
	97.9%	(+.f64 (.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64)) a)
✓	61.8%	(+.f64 a #s(literal -1/3 binary64))
✓	98.2%	(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
	38.7%	(.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64))
✓	37.9%	(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
	38.2%	(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
✓	39.0%	(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
✓	38.2%	(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
✓	60.9%	a
✓	1.4%	#s(literal -1/3 binary64)

Compiler

Compiled 360 to 146 computations (59.4% saved)

regimes52.0ms (0.6%)

Memory

14.5MiB live, 87.2MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
(fma.f64 (*.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64) a)
(fma.f64 (*.f64 (sqrt.f64 a) rand) #s(literal 1/3 binary64) a)
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
(.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64))
(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
(+.f64 (.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64)) a)
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) (+.f64 a #s(literal -1/3 binary64)))
(*.f64 (fma.f64 rand (/.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) #s(literal 1 binary64)) a)
(fma.f64 (*.f64 a #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 a)) a)
(fma.f64 (/.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a a)
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
(.f64 a (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) a)) (.f64 #s(literal 1/3 binary64) rand) #s(literal 1 binary64)))
(*.f64 rand (fma.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (/.f64 (+.f64 a #s(literal -1/3 binary64)) rand)))
(*.f64 (+.f64 a #s(literal -1/3 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 rand (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64))))))
(fma.f64 (/.f64 (+.f64 a #s(literal -1/3 binary64)) (sqrt.f64 (fma.f64 #s(literal 9 binary64) a #s(literal -3 binary64)))) rand (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (+.f64 a #s(literal -1/3 binary64)) #s(literal 1/3 binary64)) (/.f64 rand (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (/.f64 #s(literal 1/3 binary64) (sqrt.f64 (+.f64 a #s(literal -1/3 binary64)))) (*.f64 (+.f64 a #s(literal -1/3 binary64)) rand) (+.f64 a #s(literal -1/3 binary64)))
(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))

Outputs
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))

Calls

4 calls:

25.0ms	a
10.0ms	(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))
8.0ms	(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))
8.0ms	rand

Results

Accuracy	Segments	Branch
99.8%	1	`a`
99.8%	1	`rand`
99.8%	1	`(.f64 (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 9 binary64) (-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))))) rand)))`
99.8%	1	`(-.f64 a (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)))`

Compiler

Compiled 35 to 23 computations (34.3% saved)

regimes40.0ms (0.4%)

Memory

-17.1MiB live, 26.7MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
(fma.f64 (*.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64) a)
(fma.f64 (*.f64 (sqrt.f64 a) rand) #s(literal 1/3 binary64) a)
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
(.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64))
(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
(+.f64 (.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64)) a)
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)

Outputs
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)

Calls

2 calls:

34.0ms	a
5.0ms	rand

Results

Accuracy	Segments	Branch
98.7%	1	`a`
98.7%	1	`rand`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

27.4MiB live, 27.4MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
(fma.f64 (*.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64) a)
(fma.f64 (*.f64 (sqrt.f64 a) rand) #s(literal 1/3 binary64) a)
(.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (.f64 #s(literal 1/3 binary64) rand))
(.f64 (.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64))
(+.f64 (.f64 (.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a)) a)
(+.f64 (.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64)) a)

Outputs
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)

Calls

2 calls:

5.0ms	a
5.0ms	rand

Results

Accuracy	Segments	Branch
98.3%	1	`a`
98.3%	1	`rand`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

-17.7MiB live, 21.4MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)

Outputs
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)

Calls

2 calls:

4.0ms	rand
3.0ms	a

Results

Accuracy	Segments	Branch
98.2%	1	`a`
98.2%	1	`rand`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

19.1MiB live, 19.2MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(.f64 (.f64 rand (sqrt.f64 a)) #s(literal 1/3 binary64))

Outputs
(.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a))
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))

Calls

2 calls:

3.0ms	rand
3.0ms	a

Results

Accuracy	Segments	Branch
66.0%	2	`a`
93.3%	3	`rand`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Memory

-30.0MiB live, 9.0MiB allocated

Counts

4 → 3

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))

Outputs
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))
(+.f64 a #s(literal -1/3 binary64))
(.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))

Calls

1 calls:

2.0ms

rand

Results

Accuracy	Segments	Branch
93.3%	3	`rand`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a
(+.f64 a #s(literal -1/3 binary64))

Outputs
(+.f64 a #s(literal -1/3 binary64))

Calls

2 calls:

2.0ms	rand
2.0ms	a

Results

Accuracy	Segments	Branch
61.8%	1	`a`
61.8%	1	`rand`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)
a

Outputs
a

Calls

2 calls:

2.0ms	a
2.0ms	rand

Results

Accuracy	Segments	Branch
60.9%	1	`rand`
60.9%	1	`a`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/3 binary64)

Outputs
#s(literal -1/3 binary64)

Calls

2 calls:

1.0ms	rand
1.0ms	a

Results

Accuracy	Segments	Branch
1.4%	1	`rand`
1.4%	1	`a`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch34.0ms (0.4%)

Memory

-25.5MiB live, 70.4MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
17.0ms	3.4965679313679154e+108	9.69353656684943e+109
13.0ms	-1.731456835243491e+99	-2.8411036027203842e+97

Samples

23.0ms

224×

valid

Compiler

Compiled 235 to 186 computations (20.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 4.0ms (33.2% of total)

ival-mult: 4.0ms (33.2% of total)

ival-sqrt: 2.0ms (16.6% of total)

ival-sub: 1.0ms (8.3% of total)

ival-add: 1.0ms (8.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch31.0ms (0.3%)

Memory

-7.7MiB live, 69.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	3.4965679313679154e+108	9.69353656684943e+109
13.0ms	-1.731456835243491e+99	-2.8411036027203842e+97

Samples

20.0ms

224×

valid

Compiler

Compiled 235 to 186 computations (20.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 7.0ms (48.7% of total)

ival-div: 3.0ms (20.9% of total)

ival-sqrt: 2.0ms (13.9% of total)

ival-sub: 1.0ms (7% of total)

ival-add: 1.0ms (7% of total)

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

exact: 0.0ms (0% of total)

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

simplify11.0ms (0.1%)

Memory

-13.3MiB live, 23.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	36	80

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(if (<=.f64 rand #s(literal -84999999999999992973986146606136415640887399617109606917761790828504944165007222017889764932321280 binary64)) (.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a)) (if (<=.f64 rand #s(literal 3500000000000000249366773480916995603484435577195345474290984696552483491744191675204998842186116256462012416 binary64)) (+.f64 a #s(literal -1/3 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))))
(if (<=.f64 rand #s(literal -29500000000000000463064447449712179035041066804815083516597394923318188373990710348965660567011328 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a))) (if (<=.f64 rand #s(literal 3500000000000000249366773480916995603484435577195345474290984696552483491744191675204998842186116256462012416 binary64)) (+.f64 a #s(literal -1/3 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))))
(+.f64 a #s(literal -1/3 binary64))
a
#s(literal -1/3 binary64)

Outputs
(fma.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) (*.f64 #s(literal 1/3 binary64) rand) (+.f64 a #s(literal -1/3 binary64)))
(fma.f64 (*.f64 (sqrt.f64 (+.f64 a #s(literal -1/3 binary64))) rand) #s(literal 1/3 binary64) a)
(fma.f64 (*.f64 #s(literal 1/3 binary64) rand) (sqrt.f64 a) a)
(fma.f64 rand (*.f64 #s(literal 1/3 binary64) (sqrt.f64 a)) a)
(if (<=.f64 rand #s(literal -84999999999999992973986146606136415640887399617109606917761790828504944165007222017889764932321280 binary64)) (.f64 (.f64 rand #s(literal 1/3 binary64)) (sqrt.f64 a)) (if (<=.f64 rand #s(literal 3500000000000000249366773480916995603484435577195345474290984696552483491744191675204998842186116256462012416 binary64)) (+.f64 a #s(literal -1/3 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))))
(if (<=.f64 rand #s(literal -84999999999999992973986146606136415640887399617109606917761790828504944165007222017889764932321280 binary64)) (.f64 (sqrt.f64 a) (.f64 #s(literal 1/3 binary64) rand)) (if (<=.f64 rand #s(literal 3500000000000000249366773480916995603484435577195345474290984696552483491744191675204998842186116256462012416 binary64)) (+.f64 a #s(literal -1/3 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))))
(if (<=.f64 rand #s(literal -29500000000000000463064447449712179035041066804815083516597394923318188373990710348965660567011328 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a))) (if (<=.f64 rand #s(literal 3500000000000000249366773480916995603484435577195345474290984696552483491744191675204998842186116256462012416 binary64)) (+.f64 a #s(literal -1/3 binary64)) (.f64 rand (.f64 #s(literal 1/3 binary64) (sqrt.f64 a)))))
(+.f64 a #s(literal -1/3 binary64))
a
#s(literal -1/3 binary64)

soundness1.0s (10.9%)

Memory

37.3MiB live, 794.5MiB allocated

Rules

16 456×	`accelerator-lowering-fma.f32`
16 456×	`accelerator-lowering-fma.f64`
12 592×	`accelerator-lowering-fma.f32`
12 592×	`accelerator-lowering-fma.f64`
11 082×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
1	71	62
2	551	62
3	7702	62
0	8240	59
0	539	4095
1	1661	3661
2	5735	3579
0	8320	3271
0	253	2039
1	771	1849
2	2704	1831
3	6041	1816
0	8163	1710
0	27	116
1	167	111
2	1462	109
0	8167	99
0	339	1835
1	1032	1615
2	3428	1545
0	8039	1436

Stop Event

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

Compiler

Compiled 283 to 163 computations (42.4% saved)

preprocess207.0ms (2.2%)

Memory: -28.1MiB live, 89.3MiB allocated
Compiler: Compiled 218 to 76 computations (65.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	19	93
1	39	93
2	58	93
3	79	93
4	139	93
5	159	93
6	216	93
7	254	93
8	307	93
9	307	93
10	312	93
11	324	93
12	324	93
0	324	90

Iter	Nodes	Cost
0	19	93
1	39	93
2	58	93
3	79	93
4	139	93
5	159	93
6	216	93
7	254	93
8	307	93
9	307	93
10	312	93
11	324	93
12	324	93
0	324	90

analyze16.0ms (0.2%)

sample1.1s (12%)

preprocess319.0ms (3.4%)

explain226.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify156.0ms (1.7%)

localize43.0ms (0.5%)

series31.0ms (0.3%)

rewrite421.0ms (4.6%)

simplify505.0ms (5.5%)

eval205.0ms (2.2%)

prune157.0ms (1.7%)

simplify65.0ms (0.7%)

localize106.0ms (1.1%)

series28.0ms (0.3%)

rewrite444.0ms (4.8%)

simplify462.0ms (5%)

eval282.0ms (3%)

prune201.0ms (2.2%)

simplify6.0ms (0.1%)

localize104.0ms (1.1%)

series8.0ms (0.1%)

rewrite695.0ms (7.5%)

simplify583.0ms (6.3%)

eval135.0ms (1.5%)

prune70.0ms (0.8%)

simplify16.0ms (0.2%)

localize80.0ms (0.9%)

series13.0ms (0.1%)

rewrite382.0ms (4.1%)

simplify773.0ms (8.3%)

eval98.0ms (1.1%)

prune93.0ms (1%)

regimes52.0ms (0.6%)

regimes40.0ms (0.4%)

regimes11.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

bsearch34.0ms (0.4%)

bsearch31.0ms (0.3%)

simplify11.0ms (0.1%)

soundness1.0s (10.9%)

preprocess207.0ms (2.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	93
1	39	93
2	58	93
3	79	93
4	139	93
5	159	93
6	216	93
7	254	93
8	307	93
9	307	93
10	312	93
11	324	93
12	324	93
0	324	90